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# Coefficients/Significance Level for Fuel Efficiency

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3. Fuel efficiency
We got a sample of 50 used cars sold in an auction and defined the following variables.
MPG Fuel efficiency, in miles per gallon
HP Strength of the engine, in horsepower
Repair Number of times the car was repaired before the auction
Foreign Equals 1 if the car is foreign made, 0 otherwise
We ran a regression to find out how certain characteristics of the car affect its fuel efficiency.
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MPG | Coef. Std. Err. t P>|t|
-------------+----------------------------------------------------------------
HP | -0.2034169 0.02846808 -7.1454 0.0000
Foreign | 3.09772802 0.71535252 4.3304 0.0001
Repair | -3.132985 1.79280832 -1.7474 0.0874
_cons | 60.3810185 2.76109585 21.8685 0.0000
------------------------------------------------------------------------------
(a) Which coefficients are significant at the 5% level?
(b) What is the estimated coefficient of Foreign? Interpret this number (be precise).
(c) You are comparing two cars, the first one is US-made with a 150 hp engine, which has been repaired once, and the second one is a Japanese car with a 200 hp engine, which has not been repaired. Which car do you expect to have higher MPG, and by how much?
(d) A car auction specialist tells you that you forgot to include the car's AGE among the explanatory variables - after all, these are used cars. She says that in her experience (holding HP and Foreign fixed), older cars that come up on auctions tend to have been repaired more often, and age has a negative effect on fuel efficiency. Suppose that you include AGE in your regression, and the (new) coefficient on Repair turns out to be 1.19. Would this contradict her story? How about a coefficient of -4.67 (on Repair); would that contradict her story?