The following table shows the annual maintenance costs for several cars, as well
ID: 2964993 • Letter: T
Question
The following table shows the annual maintenance costs for several cars, as well as their age.
age of car
annual expenses ($)
1
150
2
425
2
375
3
505
3
570
4
535
4
580
5
645
5
565
6
750
6
850
7
1050
7
1000
(a) Develop a regression model that relates maintenance costs (dependent variable) as a function of age (independent variable). What are the regression-equation parameters?
(b) Predict the annual cost of maintaining an eight-year-old car.
age of car
annual expenses ($)
1
150
2
425
2
375
3
505
3
570
4
535
4
580
5
645
5
565
6
750
6
850
7
1050
7
1000
Explanation / Answer
let the model be : maintenance cost ( Y_i ) = b0 +b1* age_i(X_i) +error_i
using ols estimators we can find regression coefficients :b1 = sum(x_i*y_i)/sum(x_i^2)
where x_i and y_i are in deviance form
computing above value we get
b1 = 120.68 , b0 = Ybar - b1*Xbar = 104.775
b) predict value for age 8 =b0 + b1*(8) = 1070.291 $ answer
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