Consider the simple linear regression model with an intercept:
mpgi = β0 + β1priceki + ui
where mpg is a used car’s mileage per gallon and pricek is the price of the used car in thousands of dollars. Suppose you collect a random sample of size 4 and have the following data: (See photo)
A. Using the formula for the OLS estimators of β0 and β, (See photo)
Compute the numerical values of βˆ0 and βˆ1 using the data in the table.
B. Interpret the OLS estimate of β1 that you just computed in part A. Clearly indicate whether the change in each variable is in dollars, in hundreds of dollars, in percent, or in miles per gallon, etc.
C. Does the fitted regression line in (A) pass through the point of the averages, (pricek, mpg)? First, find the sample average of the variables and then support your answer with numerical evidence.
D. Suppose the natural log of pricek is chosen as the regressor. When estimated, we have
mpg = 29.3 − 5.3 log(pricek)
Interpret the estimated coefficient on log(pricek). Clearly indicate whether the change in each variable is in dollars, in hundreds of dollars, in percent, or in miles per gallon, etc.