Question

8. (15 pts) A statistics professor was considering the purchase of a Debonair Beechcraft and collected the data shown below the questions from Trade-A-Plane magazine. He ran a regression using year as the predictor and price as the response variable. a. Write the estimated least squares regression equation. b. Conduct an individual t-test for Ho: B1 = 0 vs Hi: B1 # 0 at the a = 0.05 level. c. What is the 95% CI for Bı? How are the test and CI related? d. What would you predict for the price of a 1966 plane? e. How can you quantify the accuracy of the above prediction?

Answer 1

a.

The estimated linear regression equation is,

Price = -4953646 + 2555.6488 Year

b.

Test statistic, t = 4.78

P-value for the test statistic = 0.0002

Since p-value is less than the significance level of 0.05, we reject the null hypothesis H0 and there is sufficient evidence that beta1 is not equal to 0 and the year is a significant variable in the estimated model.

c.

95% CI for beta1 is,

(1421.0974, 3690.2003)

Since the 95% CI for beta1 does not contain the value 0, we are 95% confident that beta1 is not equal to 0.

Both 95% CI and test gave the same conclusions.

d.

Predicted price of a 1966 plane is,

Price = -4953646 + 2555.6488 * 1966 = 70759.54

e.

The standard error of the above prediction is 11682.59