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.

Correlation coefficient is the measure of the correlation that exists between two variables.

Option c and e are correct.

Given that the coefficient of determination is  equals to 0.158.

Convert into percentage.

        %

It means that nearly 16 % variation between two variable.

It represent that  About 16% of the variation in value of the car is explained by a linear relationship with the age of the car.

correlation coefficient,

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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