Question

In a comprehensive road test on new car models, one variable measured is the time it takes the car to accelerate from 0 to 60 miles per hour. To model acceleration time, a regression analysis is conducted on a random sample of 129 new cars. TIME60: y = Elapsed time (in seconds) from 0 mph to 60 mph MAX x = Maximum speed attained (miles per hour) The simple linear model E(y) = Bo + Bjx was fit to the data. Computer printouts for the analysis are given below: NWEIGHTED LEAST SQUARES LINEAR REGRESSION OF TIME60 PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S TP CONSTANT 18.7171 0.63708 29.38 0.0000 MAX -0.08365 0.00491 - 17.05 0.0000 R-SQUARED ADJUSTED R-SQUARED 0.6960 0.6937 RESID. MEAN SQUARE (MSE) STANDARD DEVIATION 1.28695 1.13444 DF SOURCE REGRESSION RESIDUAL TOTAL FLP 290.83 0.0000 SS 374.285 163.443 537.728 MS 374.285 1.28695 128 CASES INCLUDED 129 MISSING CASES O Approximately what percentage of the sample variation in acceleration time can be explained by the simple linear model? A) 8% B) 0% C) 70% D) -17%

Answer 1

Option(C): 70%

>> Coefficient of determination,

r^{​​​​​​2}​​​ = SS(Regression)/SS(Total) = 374.285/537.728 = 0.69604 ≈ 0.70

Approximately 70% of the sample variation in acceleration time can be explained by the simple linear model.