Question

1) In a comprehensive road test on all new car models, one variable measured is the time it takes a 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. Given: R^2= 0.6960 Approximately what percentage of the sample variation in acceleration time can be explained by the simple linear model? (Points : 1) 8% -17% 0% 70%

2)The coefficient of correlation between x and y is r = 0.59. Calculate the coefficient of determination R^2

Answer 1

1) 70%

2) 34,81%

Explanation:

Hello!

1)

The coefficient of determination R² is the percentage of the variability of the dependent variable (Yi) that is explained by the independent variable (Xi) under the simple linear model.

So your coefficient is R²= 0.6960 ≅ 0.70

70% of the sample variation in acceleration time is explained by the simple linear model.

2)

There is a mathematical coincidence between the coefficient of determination and the correlation coefficient (Person's r) if the correlation coefficient is squared, the coefficient of determination is obtained.

(r)²=R²

R²=(0.59)²= 0.3481

The coefficient of determination between Y and X is 34,81%.

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