a) What is the slope of the regression line? What does this mean in terms of the

Question

a) What is the slope of the regression line? What does this mean in terms of the story?

b) What is the correlation between vehicle weight and MPG?

c) What percent of the variation in MPG is not explained by the regression on weight?

d) Predict the MPG for vehicles that weigh 2800, 3900 and 4200 pounds. Are these predictions valid?

Explain your reasoning.

e) Determine the residual for the vehicle that weighs 3700 pounds.

A vehicle company's auditors want to understand how the vehicle weight affects its gas mileage. A simple random sample of 30 vehicles in the North American fleet of this company produced the following data, pairing vehicle weight (in hundreds of pounds) and miles per gallon (MPG) of the vehicle. The data and scatterplot are below 6. Vehicle Vehicle Vehicle WeightMPG 13.96 34 17.16 18.24 20.28 38 14.58 19.96 20.97 12.49 15.8 17.59 WeightMPG 20.18 26 23.85 13.61 17.56 22.32 23.43 15.23 37 13.27 17.62 18.61 WeightMPG 14.07 17.88 18.7 20.78 18.24 11.34 18.91 12.85 12.5 12.07 36 35 31 26 35 39 36 31 21 2 23 24 25 26 27 28 29 30 30 27 13 39 4 26 29 35 30 34 35 34 39 36 38 35 29 20 MPG vs Vehicle Weight in Hundreds of Pounds 275 300 3s.o 375 40.0 Weight The least squares regression line is -0.7713x + 42.821. R20.7692

Explanation / Answer

Answer based on equation and graph:

a. Coefficient of x is the slope = .7713

b. Correlation is basically the square root of coefficient of determination or r square. so, that's sqrt(.7692)= .8770

c. The predicted MPG for :

Ycap.for x= 2800 , -.7713*28+42.821= 21.23

Ycap for x= 3900 will also be -.7713*39+42.821= 12.74

Ycap for x= 4200 will be = -.7713*42+42.821= 10.43

These are valid except the one for weight 4200 as it not within the range of data points on which this regression line was built.

e. Residual is y-ycap = 13.37 - (-.7713*37+42.821) = -.91

This means we have under estimated MPG for weight 3709 pound car by 91.0 MPG

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