A regression was performed on test data for 37 car models to examine the associa

Question

A regression was performed on test data for 37 car models to examine the association between the weight (thousands of pounds) of the car and the fuel efficiency (miles per gallon (MPG)). A partial output from the simple linear regression analysis is given below. A hypothesis test is to be performed to determine if weight of cars is a significant predictor of fuel efficiency of cars. Determine the correct conclusion based on the results of the hypothesis test. Variable Constant Weight SE(C Coefficient 46.08 -4.87 3.412 1.339 Choose the correct answer below. O A. There is strong evidence to indicate fuel efficiency is a significant predictor of weight of cars since the p-value from the hypothesis test is quite small 0.001). 0 B. There is no evidence to indicate fuel efficiency is a significant predictor of weight of cars since the p-value from the hypothesis test is quite large ( > 0.10). O C. There is strong evidence to indicate weight of cars is not a significant predictor of fuel efficiency since the p-value from the hypothesis test is quite small0.10).

Explanation / Answer

Here we have 37 observations and 1 predictor.
So Degrees of freedom = n - k - 1 = 37 - 1 - 1 = 35

t value can be calculated by dividing the Coefficient value by SE = -4.87/1.339 = -3.637043
Now we can look at the t table as see the p value correponding to t value of -3.637043 and 35 degrees of freedom.
From t table we can see the p value is 0.0009

So there is a strong evidence to indicate weight of cars is a significant predictor of fuel efficiency since the p value from the hypothesis test is quite small(<0.001)

So option D is correct.

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