Answer all questions. Show all of your work. Turn in all relevant computer STATA printouts. Problem...

Answer all questions. Show all of your work. Turn in all relevant computer STATA printouts.

Problem 1 (20 points). Show work

Consider the following regression on the average miles per gallon achieved by a random sample of 500 automobiles:

MPGi = 20.4 + 2.5 FOREIGNi – 3.1 WEIGHTi + 1.2 (FOREIGNi*WEIGHTi)

Where:

MPGi is the average miles per gallon achieved by the ith car

FOREIGNi is a dummy variable equal to 1 if the ith car is made outside the United States, zero otherwise.

WEIGHTi is the weight of the ith car, in thousands of pounds.

FOREIGNi*WEIGHTi is the interaction between FOREIGN and WEIGHT

a. Interpret the meaning of the coefficient on FOREIGN*WEIGHT.

b. If the weight of a foreign car increases 3000 pounds, what is the change in miles per gallon?

Solutions

Expert Solution

a) The coefficient in linear regression is a mathematical constant which indicates the relation between the variable and the outcome. The coefficient indicates the change in outcome when variable is altered by a unit. This coefficient could be either positive or negative. A positive coefficient means the change in outcome will be in the direction of variable. A rise in the value of variable will show a rise in value of the outcome while a negative coefficient indicates the change in opposite direction.

The equation suggests the average miles per gallon by the car. The average miles per gallon is the function of many variables.
Such variables include manufacturing design which vary by company to company and also its weight. The higher weight means a lower miles per gallon.

b) The equation is given as

MPGi = 20.4 + 2.5 FOREIGNi – 3.1 WEIGHTi + 1.2 (FOREIGNi*WEIGHTi)

The data for weight is not given. However, if we plug some values in that equation by considering earlier weight of 2500 pounds then

20.4 + 2.5 - ( 3.1 * ( 2.5 ) ) + 1.2 ( 2.5 ) = 18.15

If the weight is increased by 3000 pounds then

20.4 + 2.5 - ( 3.1 * ( 5.5 ) ) + 1.2 ( 5.5 ) = 12.45

18.15 - 12.45 = 5.7

The decrease in average miles per gallon will be 5.7.

Rahul Sunny answered 1 year ago

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