The following regression model of gas mileage was estimated: Where Y is the gas mileage ( miles per gallon) and X is the weight of the car (pounds) The results from a sample of 74 cars are reported below:
MPG
Coefficient Standard Error
Weight- .0060087 .0005179
Cons 39.44028 1.614003
You were asked to analyze individually, the effects first of changing the units of gasoline, and then for weight. Gasoline was changed to pints, which meant MPG was in miles per pint, and the model was describing miles per pint against the weight of the car in pounds. Then, gas was left as MPG, but weight was measured in tons (2000 pounds) rather than pounds. In this case, the model described MPG against the weight of the car in tons. In this problem, you are asked to change both gallons to pints and weight from pounds to tons.
a) Interpret the estimates of the slope and intercept. Do these make intuitive sense? Why or why not?
b) The population mean automobile weight is 3000 pounds. What is the predicted value of the gas mileage of a car with average weight? You must show your work to receive credit.
c) What is the formula for an 80% confidence interval for B, ? Using this formula, construct an 80% confidence interval for Bj.
d) At the 5% level of significance, test the null hypothesis that the weight of a car does not have a positive effect on gas mileage. You must show all eight steps to receive credit. How does this result compare to your results from the problem set?