I need help with my regression analysis homework.

Step 1

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Download the Regression Analysis Practice document (Excel file).

 

Step 2

Make sure you have the Data Analysis ToolPak add-in for your Excel. You can do that by going to the Data tab and searching for Data Analysis. If it does not appear, you will need to download it. The steps to download add-ins varies with each version of Excel. Here are the steps for the 2007 version:

 

·         Click on the Excel icon in the upper-left corner of your spreadsheet.

·         Click on Excel Options.

·         Along the left-side menu, click on Add-Ins.

·         Select Analysis ToolPak and follow the instructions.

 

Step 3

At the bottom, click on the “Demand for Jet Fuel” tab. The sample demand equation is estimated using this data set, and the results are shown.

 

Step 4

Use the procedure described to estimate the demand for gasoline using the same steps identified in the example below. Sample answers are based on the “Demand for Jet Fuel” data.

 

 

1.     Evaluate adjusted R2.

The adjusted R2 is 0.778421. It indicates that approximately 78% of the variation in the demand for jet fuel across states is explained by the three independent variables—price, state GDP, and state population.

 

 

2.     Evaluate each of the independent variables using a t-test.

Table 1 provides the results of the t-tests for each of the independent variables.

 

 

Coefficients

Standard Error

T-Stat

P-Value

Intercept

-18.4498

45.28617

-0.40741

0.68556

Price

0.138429

2.788582

0.049641

0.960619

GDP

0.170079

0.039165

4.342646

7.45E-05

Population

0.005281

0.001791

2.948036

0.004967

Table 1: T-Test Analysis

 

To assist use the Student t-Value Calculator:  http://www.danielsoper.com/statcalc3/calc.aspx?id=10

The degrees of freedom are 47, and the probability is 0.05. The critical value is approximately 2. If the absolute value of the t-statistic is greater than 2, the null hypothesis can be rejected. The P-value results can be used to determine whether to reject each of the following hypotheses.

 

Using the null hypothesis that each of the estimated coefficients is not significantly different from zero, and a 5% probably level (or a 5% probability of obtaining the test statistic as large or larger as the one obtained if the true value is in fact zero), the coefficients for GDP and Population are significant (reject the null hypothesis that the true values are 0), while coefficients for the intercept and price are not significant (do not reject the null hypothesis that the true values of the coefficients are zero).

 

Price:

(a)          H0: βp = 0; HA; βp ¹ 0                       Do not reject at the 5% level (P-value > 0.05)

 

GDP:

(b)          H0: βgdp = 0; HA; βgdp ¹ 0             Reject at the 5% level (P-value < 0.05)

 

POP:

(c)           H0: βpop = 0; HA; βpop ¹ 0            Reject at the 5% level (P-value < 0.05)

 

3.     Perform an f-test.

 

H0: βp = βgdp = βpop = 0;

HA: at least one β is not equal to zero

 

                Use the analysis of variance (ANOVA) information given in the table below.

 

ANOVA

 

 

 

 

 

 

df

SS

MS

F

Significance F

Regression

3

368163.7

122721.2

59.55115

4.83988E-16

Residual

47

96856.2

2060.77

 

 

Total

50

465019.9

 

 

 

Table 2: F-Test Analysis

 

F = 59.5515

 

Critical value

Critical F-Value Calculator:

http://www.danielsoper.com/statcalc3/calc.aspx?id=4

 

F(3,47) = 2.80235519

 

Since the 59.5515 > 4.00, reject the null hypothesis. At least one of the β’s is not equal to zero. You can also use the “Significance of F” information, which indicates that the critical value would need to be essentially zero to not reject the null hypothesis.

 

Step 5

 

Submit your regression results and answers to the questions given using the Assignment link. 

 

 

 

 

Trillions of BTUs

Price per Million BTU

Billions of Dollars

Millions

 

Quantity

Price

GDP

Population

Alabama

325,2

21,09

154,1

4 785

Alaska

34,8

27,17

45

714

Arizona

323,6

21,85

228,5

6 413

Arkansas

176,2

21,34

91,8

2 922

California

1 835,70

24,05

1 731,80

37 338

Colorado

260,8

21,35

235,2

5 048

Connecticut

184,7

22,99

211,3

3 575

Delaware

54,7

21,95

56,2

605

Dist. of Col.

12,7

23,08

90,7

605

Florida

998,3

21,17

673,4

18 839

Georgia

599,9

20,41

362

9 712

Hawaii

50,3

27,17

59,3

1 363

Idaho

82

23,01

50,7

1 571

Illinois

600,3

21,92

581,3

12 842

Indiana

369,6

21,18

245,4

6 491

Iowa

195,1

21,54

127,7

3 050

Kansas

146,1

21,39

114

2 859

Kentucky

272,9

21,9

144,6

4 347

Louisiana

280,4

21,2

195,2

4 545

Maine

83,2

22,85

46

1 327

Maryland

329,3

22,05

264,9

5 786

Massachusetts

344,3

22,17

342,1

6 555

Michigan

558,9

21,4

344,9

9 877

Minnesota

310,7

22,32

243,4

5 311

Mississippi

201,7

21,16

87,1

2 970

Missouri

392,4

20,9

217,3

5 996

Montana

60,2

22,91

31,8

991

Nebraska

103,8

22,13

79,7

1 830

Nevada

134

22,75

111,6

2 704

New Hampshire

88,5

22,19

54,6

1 317

New Jersey

517,6

21,26

438,7

8 800

New Mexico

110,9

22,01

72,8

19 395

New York

712,4

22,32

1 034,30

9 560

North Carolina

544,5

21,99

380,6

675

North Dakota

45,6

22,87

31,3

675

Ohio

618

22,01

426,1

11 538

Oklahoma

232,4

20,95

133,5

3 760

Oregon

187

23,33

166,7

3 838

Pennsylvania

633,9

22,54

505,9

1 053

Rhode Island

48,1

22,79

44

1 053

South Carolina

325,6

20,69

145,1

4 637

South Dakota

51,7

22,29

36,3

817

Tennessee

387,9

21,26

228,7

6 357

Texas

1 511,20

21,08

1 106,20

25 253

Utah

125,3

22,9

102,8

2 775

Vermont

40,5

22,96

23,1

626

Virginia

499,9

21,35

380,6

8 024

Washington

328,6

24,05

306,6

6 743

West Virginia

105,4

23,05

56

1 854

Wisconsin

313,9

22,63

221,3

5 692

Wyoming

40,1

21,45

34,4

565

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