Question

A researcher found a study relating the value of a car, y, to the age of the car, x. When researchers looked at the association of x and y, they found that the coefficient of determination was r squared equals 0.158. Select two conclusions that the researcher can make from this data.
a) About 40% of the variation in the age of the car is explained by a linear relationship with the value of the car.
b) The correlation coefficient, r, is 0.025.
c) About 16% of the variation in value of the car is explained by a linear relationship with the age of the car.
d) About 84% of the variation in the value of the car is explained by a linear relationship with the age of the car.
e) The correlation coefficient, r, is 0.397. f.) The correlation coefficient, r, is 0.842.

Answer 1

Answer: c) About 16% of the variation in value of the car is explained by a linear relationship with the age of the car.

e) The correlation coefficient, r, is 0.397.

Step-by-step explanation:

Given that:

Coefficient of determination (r²) between two variables, age of car (x) and value of car (y) = 0.158

Correlation of determination (r²) of 0.158 = (0.158 × 100% = 15.8% of the variation between the two variables can be explained by the regression line). Hence, about 16% of the variation between age and value of car can be explained by the linear relationship.

Coefficient of correlation (r) = sqrt(r²) = sqrt(0.158) = 0.397