Question: An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars.

a) Construct a scatter plot.

b) Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.

c) Interpret the meaning of the slope b1 in this problem.

d) Interpret the meaning of the Y-intercept b0 in this problem. Will it make sense to you as far as this model is concerned? Explain why.

e) Find the value of the linear correlation coefficient r.

f) Find the value of the coefficient of determination r2, and interpret the meaning for this problem.

g) Determine the standard error of the estimate.

h) How useful would you think this regression model is for predicting prices of cars?

i) Can you think of other variables that might explain the variation in predicting a price of an aged car?