Question

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.

1. 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.

Table 1: T-Test Analysis

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

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; H_A; βp ¹ 0                       Do not reject at the 5% level (P-value > 0.05)

GDP:

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

POP:

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

1. Perform an f-test.

H₀: βp = βgdp = βpop = 0;

H_A: at least one β is not equal to zero

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

Table 2: F-Test Analysis

F = 59.5515

Critical value

Critical F-Value Calculator:

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.

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