Question

8. 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: Bi= 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. Price = -4953646 + 2555.649*Year

b. H₀: β₁ = 0, Year is not a significant predictor of price

H₁: β₁ ≠ 0, Year is a significant predictor of price

p-value (Prob > |t| of year) = 0.0002

Level of significance = 0.05

Since p-value is less than 0.05, we reject the null hypothesis and conclude that β₁ ≠ 0.

So, year is a significant predictor of price.

c. 95% confidence interval for β₁: (1421.0974, 3690.2003)

t-test tells us that the coefficient for year is not zero. Confidence interval tells us the possible range in which the value of coefficient will lie.

d. Year = 1966

Price = -4953646 + 2555.649*Year = -4953646 + 2555.649*1966 = -4953646 + 5024405.934 = 70759.934

e. Accruracy = R-square = 0.587658 = 58.7658%