test3_1_(533)_solution - DS 533 Fall 2004 Exam 3 Name Show...

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DS 533 Fall 2004 Exam # 3 Name: ___________________ Show All your Work An automobile rental company wants to predict the yearly maintenance expense ( Y ) for an automobile using the number of miles driven during the year ( 1 X ) and the age of the car ( 2 X , in years) at the beginning of the year. The company has gathered the data on 10 automobiles and the regression information from Excel is presented below. Use this information to answer the following questions. Summary measures Multiple R 0.9689 R-Square 0.9387 Adj R-Square 0.9212 Standard Error 72.218 Regression coefficients Coefficient Std Err t-value p-value Constant 33.796 48.181 0.7014 0.5057 Miles Driven 0.0549 0.0191 2.8666 0.0241 Age of car 21.467 20.573 1.0434 0.3314 a. Use the information above to estimate the linear regression model. Car of Age driven Miles 467 . 21 0549 . 796 . 33 ˆ 2 1 2 1 x x x x y b. Interpret each of the estimated regression coefficients of the regression model in Question a. For every extra 100 miles driven, the maintenance cost goes up by $5.49, given the age of the car is fixed. As the age of the car goes up by one year the maintenance cost goes up by $21.467, give the miles driven is fixed. c. Identify and interpret the coefficient of determination ( 2 R ), and the standard error of the estimate (S y.x ) for the model in Question 3. R 2 = .9387. 93.87% of the variability in maintenance cost can be explained by the age of the car and the miles driven.
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