Question

The correlation r between the age of a car x , and the cars mileage, y is 0.768. what percent of the variation in mieage cannot be explained by diffrences in the cars ages?

A-23.2%
b-41.0%
C-59.0%
B-76.8%

Answer 1

C-59.0%

Explanation:

The percentage of variation of a variable Y explained by a variable X, in a simple linear regression model, is given by the coefficient of determination that is calculated through r^2.

In this case, r = 0.768, whereby
`r^2 = 0.768^2 = 0.5898`. That is, 58.98% of the variation in the number of miles traveled by a car is explained by the age of the car.

Answer 2

The correlation r between the age of a car x , and the cars mileage, y is 0.768. this means that 76.8 % of the variation in mileage can be explained by the differences in the cars ages, 100 – 76.8 = 23.2% of the variation cannot be explained