Question

A regional car rental company is interested in estimating weekly costs of maintenance of a particular model of its rental cars based on the following 4 variables: number of miles driven during the week; the number of renters during the week; the car's total mileage; and the car's age. The company conducts a regression analysis (n = 45 cars) and the results produce: SSR = 7768; and SST = 15673.

1- Test for the existence of a linear regression relationship between weekly maintenance costs and any of the 4 independent variables considered. Use alpha = .01.

Answer 1

1.

H1: Not all coefficients of the predictor variables are zero.

R square for the model = = SSR / SST = 7768 / 15673 = 0.4956294

Test statistic,

The test statistic F follow F distribution with numerator df = k = 4 and denominator df = n-k-1 = 45-4-1 = 40

Critical value of F at 0.01 significance level and df = 4, 40 is  3.828

We reject H0 if F > 3.828

Test statistic,

Since the observed test statistic (9.827) is greater than the critical value (3.828) , we reject H0 and conclude that there is a significant linear regression relationship between weekly maintenance costs and any of the 4 independent variables considered at alpha = 0.01.