Question

It is known that several factors effect the gas mileage of cars. Complete the F-test below that was performed on 25 sedans measuring (3 factors): weight, horsepower, and number of cylinders, and their respective gas mileage. Use alpha = 0.05.

F-Test and A t-Test Multiple Regression

Source                   SS                        DF                          MS               F(stat)

Regression            250

Error               

Total                    400

Given the regression equation below, perform three t-tests to determine if each variable is significant at the 0.05 level. STATE WHICH VARIABLES HAVE A SIGNIFICANT EFFECT ON GAS MILEAGE.

y = 8.7 - 7.1 x₁ - 5.9 x₂ + 1.2 x₃

(weight)Sb₁ = .9 , (horsepower)Sb₂ = 1.7, and (cylinders)Sb₃ = 1.3

Answer 1

ANOVA
	df	SS	MS	F	Significance F
Regression	3	250	250/3 = 83.3333	11.6667	0.0001
Residual	21	400-250 = 150	150/21 = 7.1429
Total	25-1 = 24	400

F = MSR/MSE = 83.3333/7.1429 = 11.6667

p-value = F.DIST.RT(11.6667, 3, 21) =  0.0001

As p-value < 0.05, we reject the null hypothesis.

The model is significant.

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For weight:

t = -7.1/0.9 = -78.8889

p-value = T.DIST.2T( ABS(-78.8889), 21) = 0.000

As p-value < 0.05, we reject the null hypothesis.

The variable is significant.

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For horsepower:

t = -5.9/1.7 = -3.4706

p-value = T.DIST.2T( ABS(-3.4706), 21) = 0.0023

As p-value < 0.05, we reject the null hypothesis.

The variable is significant.

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For cylinder:

t = 1.2/1.3 = 0.9231

p-value = T.DIST.2T( ABS(0.9231), 21) = 0.3664

As p-value > 0.05, we fail to reject the null hypothesis.

The variable cylinder is not significant.