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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.
Age (x)
8
3
6
9
2
5
Price (y)
16
74
40
19
124
36
33
89
a) Set up a scatter diagram for age and price.
b) At the 0.05 level of significance, determine whether there is a significant linear relationship between age and price.
c) State the linear regression equation.
d) Predict the average price obtained when the age of the car is 7 years old.
e) Determine the coefficient of determination, r^{2}, and interpret its meaning.
f) How useful do you think this regression model is for predicting price?
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