Final Project

  Group 6

John

Robert

Patrick

Evan

Matthew

Ali

(Excellent Project; Last Names held for Privacy)

 

 

 

 

Table of Contents

                                               

·        Problem Statement

·        Executive Summary and Recommendations

·        Statistical Restatement

·        Report Notation

·        Descriptive Statistics and Residual Testing

·        Hypothesis Testing of the Variances

·        Hypothesis Testing of the Means

·        Simple Linear Regression Analysis

·        Cubic and Quadratic Regression Analysis

·        Multiple Regression Analysis

·        ANOVA

·        Two sample T-test of the means (small sample)

·        Best and Worst Case scenarios

·        Final Conclusions

·        Management Decision

 

 

 

 

Problem Statement

 

     With the decrease in the recent economy many corporations are finding it difficult to maintain a positive profit margin. A poultry distribution company with two main distribution centers has been deeply impacted by these recent events.  This company has two different distribution centers in the United States. One plant is located in Oakland, California and the other is in Albany, New York. The corporation’s management has made a decision to close one of the distribution centers.  Management has hired us, group 6, to analyze which location should be kept open.   Our group will analyze the major influences of profit for each distribution center.  We were asked to look at data from the last nine years when performing our analysis.

 

 

 

 

 

 

 

 

Executive Summary and Recommendations

 

The recommended decision is to close the California plant. It was determined that the poultry prices were the best predictor of profits for New York and California. Even in the worst case scenario, the plant in Albany, New York made a significantly larger profit than in Oakland, California. The enclosed statistical analyses of all of the contributing variables support this decision.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Statistical Restatement

     Our team has found seven variables that are influential in determining the profits of each distribution center.  The six expense variables that we are assessing are employment costs of truckers on the west coast and east coast, the employment costs of poultry process employees on the west coast and east coast, the price of diesel fuel on the east coast and west coast.  The price of the poultry is a variable market price that is standard nationwide.

Through our preliminary assessment we have also determined which statistical analysis will be needed in order to help the managers make an informed decision on which distribution center to close.  The data that has been collected over the past nine years gives us monthly wages for truckers and poultry process employees and weekly prices for diesel.  With such a large amount of data the analyses that we perform will be geared towards large data sets.

The comparison of means and variances between distribution centers will provide insight into the influence on the profits. Regression will further provide insight as to the effect of the variables on the profits.

 

 

 

Methodology

It has been decided that profit for each distribution center can be represented by the following general formula:

 

NY Profits (NYM) = Poultry($)–Diesel($)–Labor($)– Drivers($)

CA Profits (CAM) = Poultry($)–Diesel($)–Labor($)– Drivers($)

 

This means that as the Diesel, Labor, and Driver prices increase, the profits will decrease and vice-versa.  The criteria for each location is described as shown:

                   Albany, NY    San Franscisco, CA

Diesel Fuel Use (gal)   1200          750

Process Employees       115           198

Weekly Shipments (lbs)  1.2M          800K

     The analysis is based on data collected from the past 9 years.  It is important to determine how each of the variables (predictors) are related to the profits (responses) for each distribution center.

 A summary of each analysis and its usefulness is outlined below:

 

 

1. Descriptive Statistics and Residual Testing:

The descriptive statistics give us a general impression of our data and the overall idea of what type of data sets we have to work with.  Most of our analyses have been developed using the information calculated here.

2.  Hypothesis Testing: Our hypothesis testing tests the means and variance of the distribution center profits and datasets.

3. Simple Regression:  For each set of data determine the relationship between the dependent and independent variables of the profit equation and forecast some future behavior

4.  Multiple Regression: For each set of data we perform multiple regression analyses between the independent and dependent variables to evaluate the relationship

5.  One Way ANOVA: Perform a one-way analysis of variance (ANOVA) between specific variables and the distribution center profit

 

 

 

 

Report Notation

 

WC GAS – West Coast Diesel Prices

    

EC GAS – East Coast Diesel Prices

 

PCA – California Poultry Process Workers Weekly Salary

 

PNY – New York Poultry Process Workers Weekly Salary     

 

TCA – California Truckers Weekly Salary   

 

TNY – New York Truckers Weekly Salary

 

PP – Poultry Prices    

 

NYM – New York Profits 

 

CAM – California Profits    

 

 

 

 

 

 

 

 

 

 

Descriptive Statistics and Residual Testing

The descriptive statistics of the data allows for easier understanding.  In addition, it is important to analyze the residual plots of the data to be sure it is random.

 

POULTRY PRICES PER POUND (1993-2002)

 


 


 

The residual plot shown above is a healthy set of data.  This data is homogenous and has a random scatter around zero.  We can conclude that this data is random.

 

The above graph shows a non homogeneous data set.

East Coast Diesel Prices (1993-2002)

 

This data is nearly non-homogeneous and is acceptable for this analysis.

 

West Coast Diesel Prices (1993-2002)

 

 

 

This data is nearly non-homogeneous and is acceptable for this analysis.

 

New York Labor Prices (1993-2002)

 

 

 

This data is non-homogeneous and acceptable for this analysis.

California Labor Prices (1993-2002)

 

 

 

 

 This data is non-homogeneous and acceptable for this analysis.

 

New York Truck Drivers Salary (1993-2002)

 

This data is non-homogeneous and acceptable for this analysis.

California Truck Drivers Salary (1993-2002)

 

 

This data is non-homogeneous and acceptable for this analysis.

Hypothesis Testing of the Variances

 

Test for Equal Variances between the New York and California Profits

 

H0: s1 = s2

Level1     NYM

Level2     CAM

ConfLvl    95.0000

 

Bonferroni confidence intervals for standard deviations

 

 

 

Lower     Sigma     Upper     N  Factor Levels

 

  107680    123378    144186    120  NYM

   71663     82110     95958    120  CAM

 

 

F-Test (normal distribution)

 

 

Test Statistic: 2.258

P-Value       : 0.000

 

 

Levene's Test (any continuous distribution)

 

 

Test Statistic: 15.736

P-Value       :  0.000

 

In both cases the p-value is zero.  With such a low p-value there is very little chance of having the null hypothesis be true.

 

Decision : We cannot accept the H0 hypothesis, therefore we cannot conclude that the profit variances are equal between the two states.

 

 

 

 

 

Test for Equal Variances between the New York and California diesel prices

 

H0: H0: s1 = s2

 

Level1     EC DIESEL

Level2     WC DIESEL

ConfLvl    95.0000

 

Bonferroni confidence intervals for standard deviations

 

 

 

Lower     Sigma     Upper     N  Factor Levels

 

0.135417  0.155158  0.181326    120  EC DIESEL

0.143413  0.164320  0.192033    120  WC DIESEL

 

 

F-Test (normal distribution)

 

 

Test Statistic: 0.892

P-Value       : 0.532

 

Levene's Test (any continuous distribution)

 

 

Test Statistic: 0.977

P-Value       : 0.324

 

 

n this case the p-values are large and we can say that there is a significant chance of the null hypothesis being correct.

 

Decision : We cannot reject the H0 hypothesis, therefore we can conclude that the diesel price variances are similar between the two states.

 

 

Test for Equal Variances between the New York and California Truck Driver’s salaries

 

H0: s1 = s2  

 

Level1     TNY

Level2     TCA

ConfLvl    95.0000

 

Bonferroni confidence intervals for standard deviations

 

 

Lower     Sigma     Upper     N  Factor Levels

 

 35.4808   40.6533   47.5097    120  TNY

 31.7237   36.3485   42.4788    120  TCA

 

 

F-Test (normal distribution)

 

 

Test Statistic: 1.251

P-Value       : 0.224

 

 

Levene's Test (any continuous distribution)

 

 

Test Statistic: 0.513

P-Value       : 0.475

 

In this case the p-values are large and we can say that there is a significant chance of the null hypothesis being correct.

 

Decision : We cannot reject the H0 hypothesis, therefore we can conclude that the salary variances are equal between the two states.

 

 

 

Test for Equal Variances between the New York and California poultry worker salaries

 

H0: s1 = s2  

 

 

Level1     PNY

Level2     PCA

ConfLvl    95.0000

 

Bonferroni confidence intervals for standard deviations

 

 

 

 

Lower     Sigma     Upper     N  Factor Levels

 

 38.8825   44.5510   52.0647    120  PNY

 52.9050   60.6177   70.8410    120  PCA

 

 

F-Test (normal distribution)

 

 

Test Statistic: 0.540

P-Value       : 0.001

 

 

Levene's Test (any continuous distribution)

 

 

Test Statistic: 13.630

P-Value       :  0.000

 

 

In both cases the p-value is practically zero.  With such a low p-value there is very little chance of having the null hypothesis be true.

 

Decision : We cannot accept the H0 hypothesis, therefore we cannot conclude that the poultry worker salary variances are equal between the two states.

 

 

Hypothesis Summary For Variance Testing:

 

Test for Equal Variances between the New York and California Profits: we cannot accept H0, therefore we can’t assume equal variances.

 

Test for Equal Variances between the New York and California diesel prices: we cannot reject H0, therefore we can assume equal variances in this case

 

Test for Equal Variances between the New York and California Truck Driver’s salaries: we cannot reject H0, therefore we can assume equal variances.

 

Test for Equal Variances between the New York and California poultry worker salaries: we cannot accept H0, therefore we can’t assume equal variances.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hypothesis Testing of the means 

 

 

Test of the means for the New York and California diesel prices

 

Two Tailed Test

 

 

One-Sample Z: East Coast Diesel

 

Test of mu = 1.3142 vs mu not = 1.3142

The assumed sigma = 0.1552 EC Diesel Sigma

 

Variable          N      Mean     StDev   SE Mean

EC DIESEL          120    1.1534    0.1552    0.0142

 

Variable             95.0% CI            Z      P

EC DIESEL        (  1.1257,  1.1812)   -11.35  0.000

 

Since the P-Value is zero for both of the two tailed tests the East Coast diesel versus the West Coast diesel prices we can conclude that the means are not equal.  Reject the null.

 

One Tailed Tests

 

One-Sample Z: East Coast Diesel

 

This test shows that the mean price of east coast diesel is less than west coast diesel with 100% probability.

 

Test of mu = 1.3142 vs mu > 1.3142

The assumed sigma = 0.1552

 

Variable          N      Mean     StDev   SE Mean

EC DIESEL          120    1.1534    0.1552    0.0142

 

Variable      95.0% Lower Bound        Z      P

EC DIESEL                   1.1301   -11.35  1.000

 

 

 

 

One-Sample Z: East Coast Diesel

 

This test displays that we can accept H1 that the east coast diesel price is not equal to the west coast diesel price because the p value small.

 

Test of mu = 1.3142 vs mu < 1.3142

The assumed sigma = 0.1552

 

Variable          N      Mean     StDev   SE Mean

EC DIESEL          120    1.1534    0.1552    0.0142

 

Variable      95.0% Upper Bound        Z      P

EC DIESEL                   1.1767   -11.35  0.000

 

 

Test of the means for the New York and California Truckers Salaries.

 

Two Tailed Tests

 

 

The following two 1 sample z tests comparing the means of the trucker weekly salaries result in p values that are less that alpha (alpha=0.05).

 

One-Sample Z: Truckers NY

 

Test of mu = 598.54 vs mu not = 598.54

The assumed sigma = 40.65 NY Sigma

 

Variable          N      Mean     StDev   SE Mean

TNY             120    590.40     40.65      3.71

 

Variable             95.0% CI            Z      P

TNY           (  583.13,  597.67)    -2.19  0.028

 

 

 

 

 

 

 

 

 

 

 

 

Test of the means for the New York and California Process Workers salaries

 

Two Tailed Test

 

One-Sample Z: Process Workers NY

 

A one sample z test was performed to check if the process worker means were equal. The p value suggests that the mean are in fact not equal.

 

Test of mu = 701.92 vs mu not = 701.92

The assumed sigma = 44.55 NY Sigma

 

Variable          N      Mean     StDev   SE Mean

PNY             120    573.81     44.55      4.07

 

Variable             95.0% CI            Z      P

PNY           (  565.84,  581.78)   -31.50  0.000

 

One Tailed Tests

 

One-Sample Z: Process Workers NY

 

These two one tailed z tests were performed to determine whether or not the mean weekly salaries of the New York process workers was higher than the California process workers.

 

Test of mu = 701.92 vs mu > 701.92

The assumed sigma = 44.55

 

Variable          N      Mean     StDev   SE Mean

PNY             120    573.81     44.55      4.07

 

Variable      95.0% Lower Bound        Z      P

PNY                      567.12   -31.50  1.000

 

 

 

 

 

 

 

 

 

One-Sample Z: Process Workers NY

 

Test of mu = 701.92 vs mu < 701.92

The assumed sigma = 44.55

 

Variable          N      Mean     StDev   SE Mean

PNY             120    573.81     44.55      4.07

 

Variable      95.0% Upper Bound        Z      P

PNY                      580.50   -31.50  0.000

 

The result of this series of hypothesis tests shows that the weekly mean salary of New York process workers was less than the process workers in California.

 

 

Test of the means for the New York and California profits

 

Two Tailed Test

 

One-Sample Z: New York Profits

 

This test below was performed to determine if the means of the New York and California profits were equal. From this test is displayed that the mean profits from New York and California are not equal.

 

Test of mu = 889739 vs mu not = 889739

The assumed sigma = 123378 NY Sigma

 

Variable          N      Mean     StDev   SE Mean

NYM             120   1475919    123378     11263

 

Variable             95.0% CI            Z      P

NYM           ( 1453844, 1497993)    52.05  0.000

 

 

One Tailed Tests

 

One-Sample Z: New York Profits

 

These two tests were performed to determine if the New York profits were greater or less than the California profits.

 

Test of mu = 889739 vs mu > 889739

The assumed sigma = 123378 NY Sigma

 

Variable          N      Mean     StDev   SE Mean

NYM             120   1475919    123378     11263

 

Variable      95.0% Lower Bound        Z      P

NYM                     1457393    52.05  0.000

 

One-Sample Z: New York Profits

 

Test of mu = 889739 vs mu < 889739

The assumed sigma = 123378 NY Sigma

 

Variable          N      Mean     StDev   SE Mean

NYM             120   1475919    123378     11263

 

 

Variable      95.0% Upper Bound        Z      P

NYM                     1494444    52.05  1.000

 

The results of this test display that the New York profits were higher than the California profits.

 

 

Summary of the Test of the Means

 

The mean price of east coast diesel is less than west coast diesel.

 

The trucker weekly salaries were equal.

 

Mean salary of New York process workers was less than the process workers in California.

 

New York profits were higher than the California profits.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Simple Linear Regression Analysis

 

 

Regression Analysis: CA Profit versus West Coast Diesel Price

 

 

The regression equation is

CAM = 919267 - 22468 WC GAS

 

Predictor        Coef     SE Coef          T        P

Constant       919267       60861      15.10    0.000

WC GAS         -22468       45954      -0.49    0.626

 

S = 82374       R-Sq = 0.2%      R-Sq(adj) = 0.0%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1  1621960521  1621960521      0.24    0.626

Residual Error   118 8.00679E+11  6785419288

Total            119 8.02301E+11

 

Unusual Observations

Obs     WC GAS        CAM         Fit      SE Fit    Residual    St Resid

 42       1.34    1090325      889104        7631      201221        2.45R

 48       1.39    1085479      887969        8345      197510        2.41R

 68       1.12    1133048      894081       11636      238967        2.93R

 69       1.16    1071235      893272       10429      177963        2.18R

 70       1.16    1119303      893148       10255      226155        2.77R

100       1.71     935687      880825       19722       54862        0.69 X

101       1.71     903329      880943       19500       22386        0.28 X

118       1.19     724052      892570        9490     -168518       -2.06R

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

 

Based on the R-Squared value and such a large p-value, diesel prices are not a good predictor of California profits.  We can not reject the null hypothesis.

 

 

Regression Analysis: CA Profit versus Process Workers CA

 

 

The regression equation is

CAM = 995012 - 150 PCA

 

Predictor        Coef     SE Coef          T        P

Constant       995012       87310      11.40    0.000

PCA            -150.0       123.9      -1.21    0.229

 

S = 81950       R-Sq = 1.2%      R-Sq(adj) = 0.4%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1  9835731715  9835731715      1.46    0.229

Residual Error   118 7.92466E+11  6715811057

Total            119 8.02301E+11

 

Unusual Observations

Obs        PCA        CAM         Fit      SE Fit    Residual    St Resid

  1        537     825999      914479       21769      -88480       -1.12 X

  2        564     837479      910435       18666      -72956       -0.91 X

 25        559     801538      911143       19204     -109605       -1.38 X

 42        683    1090325      892519        7826      197806        2.42R

 48        635    1085479      899848       11214      185631        2.29R

 68        728    1133048      885897        8127      247151        3.03R

 69        696    1071235      890616        7516      180619        2.21R

 70        744    1119303      883420        9123      235883        2.90R

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

 

Based on the R-Squared value and large p-value, process worker salaries are not a good predictor of California profits.  We can not reject the null hypothesis.

 

 

Regression Analysis: CA Profit versus Truckers CA

 

 

The regression equation is

CAM = 1028215 - 231 TCA

 

Predictor        Coef     SE Coef          T        P

Constant      1028215      124040       8.29    0.000

TCA            -231.4       206.9      -1.12    0.266

 

S = 82023       R-Sq = 1.0%      R-Sq(adj) = 0.2%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1  8415627595  8415627595      1.25    0.266

Residual Error   118 7.93886E+11  6727845838

Total            119 8.02301E+11

 

Unusual Observations

Obs        TCA        CAM         Fit      SE Fit    Residual    St Resid

 42        576    1090325      894946        8817      195379        2.40R

 48        599    1085479      889560        7489      195919        2.40R

 68        610    1133048      887124        7844      245924        3.01R

 69        604    1071235      888468        7573      182767        2.24R

 70        616    1119303      885724        8304      233579        2.86R

 

R denotes an observation with a large standardized residual

 

 

Based on the R-Squared value and such a large p-value, Truckers salaries are not a good predictor of California profits.  We can not reject the null hypothesis.

 

 

Regression Analysis: CA Profit versus Poultry Price

 

 

The regression equation is

CAM = - 131895 + 791402 PP

 

Predictor        Coef     SE Coef          T        P

Constant      -131895       14405      -9.16    0.000

PP             791402       11124      71.14    0.000

 

S = 12446       R-Sq = 97.7%     R-Sq(adj) = 97.7%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1 7.84023E+11 7.84023E+11   5061.55    0.000

Residual Error   118 18277960962   154897974

Total            119 8.02301E+11

 

Unusual Observations

Obs         PP        CAM         Fit      SE Fit    Residual    St Resid

  1       1.17     825999      794045        1761       31954        2.59R

  2       1.19     837479      809873        1597       27606        2.24R

 25       1.14     801538      770303        2027       31235        2.54R

 42       1.54    1090325     1086864        2995        3461        0.29 X

 48       1.52    1085479     1071036        2790       14443        1.19 X

 68       1.60    1133048     1134348        3621       -1300       -0.11 X

 69       1.52    1071235     1071036        2790         199        0.02 X

 70       1.59    1119303     1126434        3516       -7131       -0.60 X

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

 

Based on the high R-Squared value and such a small p-value, poultry prices could be considered good predictor of California profits.  We can reject the null hypothesis.

Regression Analysis: NY Profits versus Poultry Price

 

 

The regression equation is

NYM = - 74829 + 1201276 PP

 

Predictor        Coef     SE Coef          T        P

Constant       -74829        7536      -9.93    0.000

PP            1201276        5820     206.41    0.000

 

S = 6511        R-Sq = 99.7%     R-Sq(adj) = 99.7%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1 1.80643E+12 1.80643E+12  42606.45    0.000

Residual Error   118  5002959891    42397965

Total            119 1.81143E+12

 

Unusual Observations

Obs         PP        NYM         Fit      SE Fit    Residual    St Resid

 13       1.16    1336224     1318652         966       17572        2.73R

 14       1.29    1490566     1474817         594       15749        2.43R

 15       1.34    1548627     1534881         659       13746        2.12R

 42       1.54    1773017     1775136        1567       -2119       -0.34 X

 48       1.52    1739709     1751111        1460      -11402       -1.80 X

 68       1.60    1852431     1847213        1894        5218        0.84 X

 69       1.52    1750430     1751111        1460        -681       -0.11 X

 70       1.59    1837179     1835200        1839        1979        0.32 X

107       1.30    1471152     1486830         597      -15678       -2.42R

108       1.22    1368258     1390728         724      -22470       -3.47R

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

 

Based on the large R-Squared value and such a small p-value, poultry prices are a good predictor of New York profits.  We can reject the null hypothesis.

Regression Analysis: NY Profits versus East Coast Diesel Price

 

The regression equation is

NYM = 1506806 - 26778 EC GAS

 

Predictor        Coef     SE Coef          T        P

Constant      1506806       85140      17.70    0.000

EC GAS         -26778       73160      -0.37    0.715

 

S = 123829      R-Sq = 0.1%      R-Sq(adj) = 0.0%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1  2054267811  2054267811      0.13    0.715

Residual Error   118 1.80938E+12 15333688724

Total            119 1.81143E+12

 

Unusual Observations

Obs     EC GAS        NYM         Fit      SE Fit    Residual    St Resid

 42       1.08    1773017     1477905       12540      295112        2.40R

 48       1.16    1739709     1475643       11329      264066        2.14R

 68       1.00    1852431     1479987       15854      372444        3.03R

 69       0.99    1750430     1480188       16243      270242        2.20R

 70       1.01    1837179     1479853       15600      357326        2.91R

 98       1.54    1518981     1465520       30575       53461        0.45 X

 99       1.51    1554798     1466357       28463       88441        0.73 X

109       1.55    1464805     1465393       30898        -588       -0.00 X

110       1.56    1456754     1464958       32008       -8204       -0.07 X

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

 

Based on the R-Squared value and such a large p-value, diesel prices are not a good predictor of New York profits.  We can not reject the null hypothesis.

 

Regression Analysis: NY Profits versus Process Workers Weekly Salary NY

 

The regression equation is

NYM = 1775009 - 521 PNY

 

Predictor        Coef     SE Coef          T        P

Constant      1775009      144101      12.32    0.000

PNY            -521.2       250.4      -2.08    0.040

 

S = 121685      R-Sq = 3.5%      R-Sq(adj) = 2.7%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1 64170222237 64170222237      4.33    0.040

Residual Error   118 1.74726E+12 14807282331

Total            119 1.81143E+12

 

Unusual Observations

Obs        PNY        NYM         Fit      SE Fit    Residual    St Resid

 13        471    1336224     1529719       28130     -193495       -1.63 X

 42        562    1773017     1482287       11522      290730        2.40R

 48        660    1739709     1430851       24332      308858        2.59R

 60        697    1317869     1411565       32848      -93696       -0.80 X

 68        541    1852431     1492962       13799      359469        2.97R

 69        541    1750430     1492915       13786      257515        2.13R

 70        538    1837179     1494791       14338      342388        2.83R

 84        673    1504509     1424184       27221       80325        0.68 X

108        741    1368258     1388641       43372      -20383       -0.18 X

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

Based on the low R-Squared value and low p-value, process workers weekly salaries are not a good predictor of New York profits.  We can not reject the null hypothesis, though we have to keep in mind that the low P-value reduces the probability of this being the correct decision.

Regression Analysis: NY Profits versus Truckers Weekly Salary NY

 

 

The regression equation is

NYM = 1683352 - 351 TNY

 

Predictor        Coef     SE Coef          T        P

Constant      1683352      164223      10.25    0.000

TNY            -351.3       277.5      -1.27    0.208

 

S = 123066      R-Sq = 1.3%      R-Sq(adj) = 0.5%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1 24277605903 24277605903      1.60    0.208

Residual Error   118 1.78715E+12 15145355351

Total            119 1.81143E+12

 

Unusual Observations

Obs        TNY        NYM         Fit      SE Fit    Residual    St Resid

 29        558    1241833     1487214       14346     -245381       -2.01R

 42        572    1773017     1482541       12392      290476        2.37R

 48        590    1739709     1475954       11234      263755        2.15R

 68        579    1852431     1480005       11689      372426        3.04R

 69        584    1750430     1478027       11357      272403        2.22R

 70        591    1837179     1475581       11238      361598        2.95R

120        684    1318840     1442987       28333     -124147       -1.04 X

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

 

 

Based on the R-Squared value and a large p-value, Truckers weekly salaries are not a good predictor of New York profits.  We can not reject the null hypothesis.

 

Regression Analysis: NY Profits versus CA Profits

 

 

The regression equation is

NYM = 150048 + 1.49 CAM

 

Predictor        Coef     SE Coef          T        P

Constant       150048       15855       9.46    0.000

CAM           1.49018     0.01774      83.98    0.000

 

S = 15894       R-Sq = 98.4%     R-Sq(adj) = 98.3%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         1 1.78162E+12 1.78162E+12   7052.42    0.000

Residual Error   118 29809789938   252625338

Total            119 1.81143E+12

 

Unusual Observations

Obs        CAM        NYM         Fit      SE Fit    Residual    St Resid

  1     825999    1332549     1380935        1840      -48386       -3.06R

  2     837479    1356116     1398042        1722      -41926       -2.65R

 23     776172    1270369     1306684        2483      -36315       -2.31R

 25     801538    1304446     1344483        2134      -40037       -2.54R

 42    1090325    1773017     1774828        3844       -1811       -0.12 X

 48    1085479    1739709     1767607        3764      -27898       -1.81 X

 68    1133048    1852431     1838493        4555       13938        0.92 X

 70    1119303    1837179     1818010        4324       19169        1.25 X

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

 

Based on the large R-Squared value and such a small p-value, NY profits are a good predictor of California profits.  We can reject the null hypothesis.

 

Regression Summary

 

 

NY profits are a good predictor of California profits due to the large R-Squared value and such a small p-value.

 

 

California

 

Diesel prices are not a good predictor of California profits due to the R-Squared value and such a large p-value.

 

Process worker salaries are not a good predictor of California profits based on the R-Squared value and large p-value

 

Truckers salaries are not a good predictor of California profits due to the R-Squared value and such a large p-value.

 

Poultry prices could be considered good predictor of California profit due to the high R-Squared value and such a small p-value.

 

New York

 

Diesel prices are not a good predictor of New York profits due to the R-Squared value and such a large p-value.

 

Based on the low R-Squared value and low p-value, process workers weekly salaries are not a good predictor of New York profits.  We can not reject the null hypothesis, though we have to keep in mind that the low P-value reduces the probability of this being the correct decision.

 

Truckers weekly salaries are not a good predictor of New York profits due to the R-Squared value and a large p-value.

 

Poultry prices are a good predictor of New York profits due to the large R-Squared value and such a small p-value.

 

 

 

 

 

Quadratic and Cubic Regressions

 

 

            Previously, linear regressions were used for all of the data sets versus the New York Profits.  The following section uses Quadratic and Cubic regressions on the datasets which had an unfavorable P-value.  This occurred because the data did not have a linear behavior.

 

 

California Profits vs. West Coast Diesel Prices

 

 

Polynomial Regression Analysis: CAM versus WC GAS

 

 

The regression equation is                         

CAM = 1251908 - 516464 WC GAS                      

 + 180495 WC GAS**2                                

                                                   

S = 82565.8      R-Sq = 0.6 %      R-Sq(adj) = 0.0 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         2  4.699E+09  2.349E+09  0.344622  0.709

Error            117  7.976E+11  6.817E+09                

Total            119  8.023E+11                           

 

 

Source      DF     Seq SS          F      P

Linear       1  1.622E+09   0.239036  0.626

Quadratic    1  3.077E+09   0.451320  0.503

 

 

Polynomial Regression Analysis: CAM versus WC GAS

 

 

The regression equation is                         

CAM = 5349413 - 9677988 WC GAS                     

 + 6938727 WC GAS**2 - 1644348 WC GAS**3           

                                                   

S = 82551.4      R-Sq = 1.5 %      R-Sq(adj) = 0.0 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         3  1.179E+10  3.931E+09  0.576789  0.631

Error            116  7.905E+11  6.815E+09                

Total            119  8.023E+11                           

 

 

Source      DF     Seq SS          F      P

Linear       1  1.622E+09    0.23904  0.626

Quadratic    1  3.077E+09    0.45132  0.503

Cubic        1  7.093E+09    1.04088  0.310

 

 

 

The above regressions show that by using a cubic regression a better fit is achieved for the regression of West Coast Diesel Prices vs. California profits.

 

 

 

 

 

 

 

 

 

 

 

California Profits vs. Process Workers Weekly Salary

 

 

Polynomial Regression Analysis: CAM versus PCA

 

 

The regression equation is                           

CAM = -3221303 + 12054.8 PCA                         

 - 8.76512 PCA**2                                    

                                                     

S = 72268.9      R-Sq = 23.8 %      R-Sq(adj) = 22.5 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         2  1.912E+11  9.562E+10   18.3076  0.000

Error            117  6.111E+11  5.223E+09                

Total            119  8.023E+11                           

 

 

Source      DF     Seq SS          F      P

Linear       1  9.836E+09     1.4646  0.229

Quadratic    1  1.814E+11    34.7321  0.000

 

 

 

 

 

Polynomial Regression Analysis: CAM versus PCA

 

 

The regression equation is                           

CAM = 7368846 - 34812.4 PCA                          

 + 59.9047 PCA**2 - 0.0333174 PCA**3                 

                                                     

S = 71518.4      R-Sq = 26.0 %      R-Sq(adj) = 24.1 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         3  2.090E+11  6.966E+10   13.6187  0.000

Error            116  5.933E+11  5.115E+09                

Total            119  8.023E+11                           

 

 

Source      DF     Seq SS          F      P

Linear       1  9.836E+09     1.4646  0.229

Quadratic    1  1.814E+11    34.7321  0.000

Cubic        1  1.774E+10     3.4684  0.065

 

 

The conclusion of this series of regressions is that the quadratic regression represents the behavior of the Process Workers weekly salary vs. California Profits.  This is shown by the P-value of zero.

 

 

 

 

 

 

 

 

 

California Profits vs. Truckers Weekly Salary

 

 

Polynomial Regression Analysis: CAM versus TCA

 

 

The regression equation is                           

CAM = -14149060 + 50852.8 TCA                        

 - 42.8262 TCA**2                                    

                                                      

S = 69126.0      R-Sq = 30.3 %      R-Sq(adj) = 29.1 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         2  2.432E+11  1.216E+11   25.4507  0.000

Error            117  5.591E+11  4.778E+09                

Total            119  8.023E+11                           

 

 

Source      DF     Seq SS          F      P

Linear       1  8.416E+09     1.2509  0.266

Quadratic    1  2.348E+11    49.1403  0.000

 

 

 

Polynomial Regression Analysis: CAM versus TCA

 

 

The regression equation is                           

CAM = -46612100 + 214266 TCA                         

 - 316.469 TCA**2 + 0.152438 TCA**3                  

                                                      

S = 69211.5      R-Sq = 30.7 %      R-Sq(adj) = 28.9 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         3  2.466E+11  8.221E+10   17.1623  0.000

Error            116  5.557E+11  4.790E+09                 

Total            119  8.023E+11                           

 

 

Source      DF     Seq SS          F      P

Linear       1  8.416E+09     1.2509  0.266

Quadratic    1  2.348E+11    49.1403  0.000

Cubic        1  3.406E+09     0.7111  0.401

 

 

The conclusion of this series of regressions is that the best description of the behavior of the Truckers Weekly salary vs. California Profits is as a quadratic.

 

 

 

 

 

 

 

 

 

 

 

Regression of New York Profits vs. East Coast Diesel Prices

 

 

Polynomial Regression Analysis: NYM versus EC GAS

 

 

The regression equation is                        

NYM = 2127301 - 1059063 EC GAS                    

 + 421017 EC GAS**2                               

                                                   

S = 123847      R-Sq = 0.9 %      R-Sq(adj) = 0.0 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         2  1.688E+10  8.438E+09  0.550117  0.578

Error            117  1.795E+12  1.534E+10                 

Total            119  1.811E+12                           

 

 

Source      DF     Seq SS          F      P

Linear       1  2.054E+09   0.133971  0.715

Quadratic    1  1.482E+10   0.966301  0.328

 

 

 

Polynomial Regression Analysis: NYM versus EC GAS

 

 

The regression equation is                        

NYM = 3989944 - 5763650 EC GAS                    

 + 4333049 EC GAS**2 - 1070097 EC GAS**3          

                                                  

S = 124277      R-Sq = 1.1 %      R-Sq(adj) = 0.0 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         3  1.983E+10  6.609E+09  0.427916  0.733

Error            116  1.792E+12  1.544E+10                

Total            119  1.811E+12                           

 

 

Source      DF     Seq SS          F      P

Linear       1  2.054E+09   0.133971  0.715

Quadratic    1  1.482E+10   0.966301  0.328

Cubic        1  2.952E+09   0.191123  0.663

 

 

The conclusion of this series of regressions is that the best description of the behavior of the East Coast Diesel Prices vs. New York Profits is as a quadratic.

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression of New York Profits vs. Process Worker Weekly Salary

 

 

 

Polynomial Regression Analysis: NYM versus PNY

 

 

The regression equation is                        

NYM = 859054 + 2624.91 PNY                        

 - 2.68499 PNY**2                                 

                                                   

S = 121878      R-Sq = 4.1 %      R-Sq(adj) = 2.4 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         2  7.348E+10  3.674E+10   2.47350  0.089

Error            117  1.738E+12  1.485E+10                 

Total            119  1.811E+12                           

 

 

Source      DF     Seq SS          F      P

Linear       1  6.417E+10    4.33369  0.040

Quadratic    1  9.314E+09    0.62701  0.430

 

 

 

 

Polynomial Regression Analysis: NYM versus PNY

 

 

The regression equation is                        

NYM = -9654218 + 56071.6 PNY                      

 - 92.5947 PNY**2 + 0.0500370 PNY**3              

                                                  

S = 121632      R-Sq = 5.3 %      R-Sq(adj) = 2.8 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         3  9.527E+10  3.176E+10   2.14661  0.098

Error            116  1.716E+12  1.479E+10                

Total            119  1.811E+12                           

 

 

Source      DF     Seq SS          F      P

Linear       1  6.417E+10    4.33369  0.040

Quadratic    1  9.314E+09    0.62701  0.430

Cubic        1  2.179E+10    1.47282  0.227

 

 

The conclusion of this series of regressions is that the best description of the behavior of the Process Workers Weekly Salary vs. New York Profits is as a quadratic.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regression of New York Profits vs. Truckers Weekly Salary

 

 

Polynomial Regression Analysis: NYM versus TNY

 

 

The regression equation is                          

NYM = -10013629 + 39291.2 TNY                       

 - 33.4312 TNY**2                                   

                                                    

S = 106805      R-Sq = 26.3 %      R-Sq(adj) = 25.1 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         2  4.768E+11  2.384E+11   20.8974  0.000

Error            117  1.335E+12  1.141E+10                

Total            119  1.811E+12                           

 

 

Source      DF     Seq SS          F      P

Linear       1  2.428E+10     1.6030  0.208

Quadratic    1  4.525E+11    39.6667  0.000

 

 

 

 

 

 

Polynomial Regression Analysis: NYM versus TNY

 

 

The regression equation is                          

NYM = -41244665 + 197822 TNY                        

 - 300.724 TNY**2 + 0.149698 TNY**3                 

                                                    

S = 106480      R-Sq = 27.4 %      R-Sq(adj) = 25.5 %

 

Analysis of Variance

 

Source            DF         SS         MS         F      P

Regression         3  4.962E+11  1.654E+11   14.5886  0.000

Error            116  1.315E+12  1.134E+10                

Total            119  1.811E+12                           

 

 

Source      DF     Seq SS          F      P

Linear       1  2.428E+10     1.6030  0.208

Quadratic    1  4.525E+11    39.6667  0.000

Cubic        1  1.945E+10     1.7153  0.193

 

 

 

The conclusion of this series of regressions is that the best description of the behavior of the Truckers Weekly Salary vs. New York Profits is as a quadratic.

 

 

 

 

 

 

 

 

 

 

 

Summary of Cubic and Quadratic Regression Analysis

 

A better fit is achieved for the regression of West Coast Diesel Prices vs. California profits when a cubic regression was used.

 

A quadratic regression represents the behavior of the Process Workers weekly salary vs. California Profits. 

 

The best description of the behavior of the Truckers Weekly salary vs. California Profits is as a quadratic.

 

The best description of the behavior of the East Coast Diesel Prices vs. New York Profits is as a quadratic.

 

The best description of the behavior of the Process Workers Weekly Salary vs. New York Profits is as a quadratic.

 

The best description of the behavior of the Truckers Weekly Salary vs. New York Profits is as a quadratic.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Multiple Regression

 

Regression Analysis: CAM versus PP, WC GAS, Process workers CA, TCA

 

The regression equation is

CAM = 3567 + 795954 PP - 2749 WC GAS - 199 PCA + 2.9 TCA

 

Predictor        Coef     SE Coef          T        P

Constant         3567        4785       0.75    0.458

PP             795954        2119     375.55    0.000

WC GAS          -2749        1599      -1.72    0.088

PCA          -198.702       8.403     -23.65    0.000

TCA              2.92       14.65       0.20    0.842

 

S = 2369        R-Sq = 99.9%     R-Sq(adj) = 99.9%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         4 8.01656E+11 2.00414E+11  35705.94    0.000

Residual Error   115   645483854     5612903

Total            119 8.02301E+11

 

Source       DF      Seq SS

PP            1 7.84023E+11

WC GAS        1  4913782411

PCA           1 12718471709

TCA           1      222988

 

The multiple regression equation reaffirms that Poultry Price is the most predictable factor for profits.  We see that the P-value is very significant for this variable.  The WC GAS and the Process Workers are the next predictors of profit. Finally the Truckers salary shows no evidence it adds to the predictability of profits with such a high p- value.

 

 

 

Regression Analysis: NYM versus PP, EC GAS, PNY, TNY

 

The regression equation is

NYM = 5455 + 1194226 PP - 6731 EC GAS - 111 PNY + 0.7 TNY

 

Predictor        Coef     SE Coef          T        P

Constant         5455        6876       0.79    0.429

PP            1194226        3206     372.45    0.000

EC GAS          -6731        2499      -2.69    0.008

PNY          -111.251       9.886     -11.25    0.000

TNY              0.71       10.85       0.07    0.948

 

S = 3539        R-Sq = 99.9%     R-Sq(adj) = 99.9%

 

Analysis of Variance

 

Source            DF          SS          MS         F        P

Regression         4 1.80999E+12 4.52497E+11  36121.31    0.000

Residual Error   115  1440622644    12527153

Total            119 1.81143E+12

 

Source       DF      Seq SS

PP            1 1.80643E+12

EC GAS        1  1397294839

PNY           1  2164989141

TNY           1       53267

 

Unusual Observations

Obs         PP        NYM         Fit      SE Fit    Residual    St Resid

101       1.32    1512449     1505428         760        7021        2.03R

108       1.22    1368258     1371169        1318       -2911       -0.89 X

 

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

 

The multiple regression equation reaffirms that Poultry Price is the most predictable factor for profits.  We see that the P-value is very significant for this variable.  The EC GAS and the Process Workers are the next predictors of  profit. Finally the Truckers salary shows no evidence it adds to the predictability of profits with such a high p- value.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summary of Multiple Regression Analysis

 

 

The multiple regression equation reaffirms that Poultry Price is the most predictable factor for profits.  The P-value is very significant for this variable.  The WC GAS and the Process Workers are the next predictors of profit. Finally the Truckers salary shows no evidence it adds to the predictability of profits with such a high p- value.

 

The multiple regression equation reaffirms that Poultry Price is the most predictable factor for profits.  The P-value is very significant for this variable.  The EC GAS and the Process Workers are the next predictors of  profit. Finally the Truckers salary shows no evidence it adds to the predictability of profits with such a high p- value.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

California ANOVAs

    

One-way ANOVA: CAM versus PP

Ho: The variances of the Poultry prices are equal

H1: The variances are not equal

 

Analysis of Variance for CAM    

Source     DF        SS        MS        F        P

PP         37 7.910E+11 2.138E+10   155.64    0.000

Error      82 1.126E+10 137364841

Total     119 8.023E+11

 

The variances are not equal.

 

One-way ANOVA: CAM versus PCA

 

Ho: The variances of the Process workers salaries are equal

H1: The variances are not equal

 

Analysis of Variance for CAM    

Source     DF        SS        MS        F        P

PCA       113 7.798E+11 6.901E+09     1.84    0.225

Error       6 2.246E+10 3.743E+09

Total     119 8.023E+11

 

The variances are equal.

 

One-way ANOVA: CAM versus WC GAS

 

Ho: The variances of the WC Gas prices are equal

H1: The variances are not equal

 

Analysis of Variance for CAM    

Source     DF        SS        MS        F        P

WC GAS    118 7.974E+11 6.757E+09     1.37    0.606

Error       1 4.949E+09 4.949E+09

Total     119 8.023E+11

Analysis of Variance for CAM    

Source     DF        SS        MS        F        P

WC GAS    118 7.974E+11 6.757E+09     1.37    0.606

Error       1 4.949E+09 4.949E+09

Total     119 8.023E+11

                                  

The variances are equal.

 

Below is the printout of the ANOVA between the California Profits and West Coast Diesel Prices.

 

Individual 95% CI’s For Mean Based on Pooled StDev (See Table Below)

 

Level       N      Mean     StDev  ---+---------+---------+---------+---

1.03675     1    884923         0     (--------------*--------------)

1.06725     1    920597         0     (--------------*--------------)

1.07950     1    824779         0    (--------------*--------------)

1.08775     1    952282         0      (--------------*--------------)

1.10625     1    944466         0      (--------------*--------------)

1.10950     1    911293         0     (--------------*--------------)

1.10975     1    863378         0    (--------------*--------------)

1.11100     1    944624         0      (--------------*--------------)

1.11850     1    944733         0      (--------------*--------------)

1.12000     1    917475         0     (--------------*--------------)

1.12100     1   1133048         0         (--------------*--------------)

1.12625     1   1019580         0       (--------------*--------------)

1.12775     1    959569         0      (--------------*--------------)

1.13075     1    803858         0   (--------------*--------------)

1.13700     1    944570         0      (--------------*--------------)

1.14025     1    946585         0      (--------------*--------------)

1.14550     1    958574         0      (--------------*--------------)

1.15325     1    856571         0    (--------------*--------------)

1.15450     1    875455         0     (--------------*-------------)

1.15625     1   1014554         0       (--------------*--------------)

1.15700     1   1071235         0        (--------------*--------------)

1.15775     1    862812         0    (--------------*--------------)

1.16250     1   1119303         0         (--------------*--------------)

1.16425     1    826425         0    (--------------*--------------)

1.16550     1    829097         0    (--------------*--------------)

1.16650     1    890019         0     (--------------*--------------)

1.17200     1    866804         0     (-------------*--------------)

1.17775     1    865813         0     (-------------*--------------)

1.18150     1    814100         0    (--------------*-------------)

1.18200     1    766514         0   (--------------*--------------)

1.18500     1    822676         0    (--------------*--------------)

1.18825     1    724052         0  (--------------*--------------)

1.19025     1    763086         0   (--------------*--------------)

1.19475     1    837479         0    (--------------*--------------)

1.20175     1    965858         0      (--------------*--------------)

1.20525     1    807753         0    (-------------*--------------)

1.20600     1    884349         0     (--------------*--------------)

1.20975     1    825999         0    (--------------*--------------)

1.21050     1    816757         0    (--------------*--------------)

1.21150     1    826824         0    (--------------*--------------)

1.22125     1    741004         0  (--------------*--------------)

1.22450     1    729828         0  (--------------*--------------)

1.22575     1    893279         0     (--------------*--------------)

1.22600     1    776172         0   (--------------*--------------)

1.22650     1    848657         0    (--------------*--------------)

1.22775     1    820962         0    (--------------*--------------)

1.22875     1    821720         0    (--------------*--------------)

1.22925     1    786182         0   (--------------*--------------)

1.23100     1    801538         0   (--------------*--------------)

1.23700     1    880611         0     (--------------*--------------)

1.24500     1    946625         0      (--------------*--------------)

1.25300     1   1005833         0       (--------------*--------------)

1.25325     1    993720         0       (--------------*-------------)

1.26075     1    831341         0    (--------------*--------------)

1.26100     1    967362         0      (--------------*--------------)

1.26825     1    918509         0     (--------------*--------------)

1.26900     1   1025322         0       (--------------*--------------)

1.27475     1    928116         0      (-------------*--------------)

1.27700     1    947466         0      (--------------*--------------)

1.27775     1    844446         0    (--------------*--------------)

 

1.28025     1    903828         0     (--------------*--------------)

1.28125     1    856788         0    (--------------*--------------)

1.28425     1    792120         0   (--------------*--------------)

1.29100     1    800508         0   (--------------*--------------)

1.29625     1    951052         0      (--------------*--------------)

1.30650     1    908793         0     (--------------*--------------)

1.30725     1    959355         0      (--------------*--------------)

1.31850     1    880936         0     (--------------*--------------)

1.32200     1   1001176         0       (--------------*--------------)

1.32600     1    917105         0     (--------------*--------------)

1.33225     1    904465         0     (--------------*--------------)

1.33350     1    912564         0     (--------------*--------------)

1.34250     2   1040580     70350            (---------*----------)

1.34625     1    834574         0    (--------------*--------------)

1.34800     1    961802         0      (--------------*--------------)

1.35025     1    930313         0      (--------------*-------------)

1.35250     1    802940         0   (--------------*--------------)

1.35450     1    840965         0    (--------------*--------------)

1.35500     1    792711         0   (--------------*--------------)

1.35675     1    817369         0    (--------------*--------------)

1.36100     1    870275         0     (--------------*-------------)

1.36775     1    806333         0    (-------------*--------------)

1.37175     1   1025152         0       (--------------*--------------)

1.37925     1    873550         0     (--------------*-------------)

1.38525     1    844337         0    (--------------*--------------)

1.38875     1    777387         0   (--------------*--------------)

1.38925     1    844731         0    (--------------*--------------)

1.39175     1    773789         0   (--------------*--------------)

1.39300     1   1085479         0        (--------------*--------------)

1.39475     1    801560         0   (--------------*--------------)

1.39725     1    871834         0     (--------------*-------------)

1.41075     1   1022339         0       (--------------*--------------)

1.41750     1    833385         0    (--------------*--------------)

1.43300     1    989538         0       (-------------*--------------)

1.44725     1    944021         0      (--------------*--------------)

1.46650     1    999264         0       (--------------*--------------)

1.47300     1    991471         0       (--------------*-------------)

1.50175     1    843922         0    (--------------*--------------)

1.50975     1    800790         0   (--------------*--------------)

1.51775     1    894032         0     (--------------*--------------)

1.53000     1    837929         0    (--------------*--------------)

1.53750     1    887699         0     (--------------*--------------)

1.54650     1    888880         0     (--------------*--------------)

1.54950     1    922948         0     (--------------*--------------)

1.56125     1    885759         0     (--------------*--------------)

1.56250     1    839317         0    (--------------*--------------)

1.57400     1    819198         0    (--------------*--------------)

1.59300     1    870309         0     (--------------*-------------)

1.59425     1    897253         0     (--------------*--------------)

1.59775     1    875113         0     (--------------*-------------)

1.61625     1    869396         0     (-------------*--------------)

1.61775     1    874251         0     (--------------*-------------)

1.62675     1    921422         0     (--------------*--------------)

1.63650     1    808090         0    (-------------*--------------)

1.64625     1    930315         0      (--------------*-------------)

1.65825     1    869783         0     (-------------*--------------)

1.67425     1    871713         0     (--------------*-------------)

1.70575     1    903329         0     (--------------*--------------)

1.71100     1    935687         0      (--------------*-------------)

                                   ---+---------+---------+---------+---

Pooled StDev =    70350               0    600000   1200000   1800000

 

 

 

 

 

One-way ANOVA: CAM versus TCA

 

Ho: The variances of the Truckers Wages are equal

H1: The variances are not equal

 

 

Analysis of Variance for CAM    

Source     DF        SS        MS        F        P

TCA       116 7.716E+11 6.652E+09     0.65    0.792

Error       3 3.073E+10 1.024E+10

Total     119 8.023E+11

 

The Variances are equal

 

New York ANOVAs

 

One-way ANOVA: NYM versus PP

 

Ho: The variances of the Poultry prices are equal

H1: The variances are not equal

 

 

Analysis of Variance for NYM    

Source     DF        SS        MS        F        P

PP         37 1.808E+12 4.886E+10  1113.99    0.000

Error      82 3.597E+09  43860497

Total     119 1.811E+12

 

 

The variances are not equal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

      Below is the printout of the ANOVA between New York Profits and Poultry Prices.

 

Individual 95% CIs For Mean Based on Pooled StDev

                                  

Level       N      Mean     StDev  ---------+---------+---------+-------

1.09        1   1241833         0  (*)

1.11        2   1254631      2064   (*

1.12        1   1270369         0    (*

1.13        1   1283305         0     *)

1.14        1   1304446         0      *)

1.16        3   1322036     12630       *

1.17        5   1327393      9575       *)

1.18        2   1343455      8784        *)

1.19        7   1355575      4134         *

1.20        6   1365406      4989         *)

1.21        2   1376892      6568         (*

1.22        3   1382181     13137          *

1.23        6   1404137      3059           *

1.24        4   1418956      6543            *

1.25        6   1427164      6129            *)

1.26        3   1445106      1245             *)

1.27        2   1452971      5145             (*

1.28        4   1460118      6920              *

1.29        9   1473707      8711              (*

1.30        3   1482511     10493               *)

1.31        2   1489536      2951               *)

1.32        4   1509259      3664                *)

1.33        5   1521710      3657                 *

1.34        3   1539267      8826                  *

1.35        5   1549734      4494                  *)

1.36        5   1559067      6481                   *

1.37        3   1572564      7686                   (*

1.38        4   1583473      2925                    *)

1.39        1   1596430         0                    (*

1.41        2   1625594      3405                      *)

1.42        3   1632712      5929                      (*

1.43        2   1646320      6397                       *)

1.45        3   1665205      2997                        *)

1.46        2   1674091      1205                        (*

1.52        2   1745070      7581                            *)

1.54        1   1773017         0                             (*

1.59        1   1837179         0                                (*)

1.60        1   1852431         0                                 (*

                                   ---------+---------+---------+-------

Pooled StDev =     6623               1400000   1600000   1800000

 

 

One-way ANOVA: NYM versus TNY

 

Ho: The variances of the Truckers Wages are equal

H1: The variances are not equal

 

Analysis of Variance for NYM    

Source     DF        SS        MS        F        P

TNY       116 1.804E+12 1.555E+10     6.16    0.078

Error       3 7.573E+09 2.524E+09

Total     119 1.811E+12

 

The variances are equal.

 

One-way ANOVA: NYM versus EC GAS

 

Ho: The variances of the EC Gas Prices are equal

H1: The variances are not equal

 

 

Analysis of Variance for NYM    

Source     DF        SS        MS        F        P

EC GAS    114 1.728E+12 1.516E+10     0.91    0.636

Error       5 8.345E+10 1.669E+10

Total     119 1.811E+12

 

The variances are equal

 

Summary of ANOVA Analysis

 

California

    

The variance of the California profits was not equal to the variance of the poultry prices. However, the variance of the California profits was equal to the variance of the Process Workers, Gas Prices, and Truckers.

 

New York

 

     The variance of the New York profits was not equal to the variance of the poultry prices. However, the variance of the New York profits were equal to the variance of the Process Workers, Gas Prices, and Truckers.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Two Sample T-Test of the Means (Small Sample)

 

The following T-tests were performed on a small sample of the data.  In this case the sample chosen was the data from the year 1993 (12 data points).  Comparisons of the variances were first performed, followed by the T-test.  The results are shown below.

 

 

Test for Equal Variances, Diesel Prices

 

Level1     WC GAS

Level2     EC GAS

ConfLvl    95.0000

 

Bonferroni confidence intervals for standard deviations

 

 

 

  Lower     Sigma     Upper     N  Factor Levels

 

1.36E-02  2.01E-02  3.71E-02    12  WC GAS

1.05E-02  1.56E-02  2.88E-02    12  EC GAS

 

 

F-Test (normal distribution)

 

 

Test Statistic: 1.659

P-Value       : 0.414

 

 

Levene's Test (any continuous distribution)

 

 

Test Statistic: 0.401

P-Value       : 0.533

 

 

The results of this test suggest that assumption of equal variances is correct with a probability of .533.

 

 

Two-Sample T-Test and CI: West Coast Diesel, East Coast Diesel

 

 

Two-sample T for WC GAS vs EC GAS

 

         N      Mean     StDev   SE Mean

WC GAS  12    1.1775    0.0201    0.0058

EC GAS  12    1.0533    0.0156    0.0045

 

Difference = mu WC GAS - mu EC GAS

Estimate for difference:  0.12417

95% CI for difference: (0.10897, 0.13937)

T-Test of difference = 0 (vs not =): T-Value = 16.94 

P-Value = 0.000  DF = 22

Both use Pooled StDev = 0.0180

 

The conclusion is that the means are not equal, this is based on the P-value of 0.

 

 

 

Test for Equal Variances Process Workers

 

Level1     PNY

Level2     PCA

ConfLvl    95.0000

 

Bonferroni confidence intervals for standard deviations

 

 

  Lower     Sigma     Upper     N  Factor Levels

 

 21.0906   31.1891   57.6533    12  PNY

 22.1087   32.6947   60.4364    12  PCA

 

 

F-Test (normal distribution)

 

 

Test Statistic: 0.910

P-Value       : 0.879

 

 

Levene's Test (any continuous distribution)