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

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

Milestone One Directions

Step 1

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.

· Select Analysis ToolPak and follow the instructions.

*For Mac users, StatPlus is the recommended free program

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. For your submission you will be using the Gasoline data on the adjacent tab.

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.

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.

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 ( 0 Do not reject at the 5% level (P-value > 0.05)

GDP:

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

POP:

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

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 > 2.80, 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 in the Blackboard module.
Evaluate each of the independent variables using a t-test.