Question

The correlation coefficient between the age of a vehicle and the money spent to repair it is 0.9. Which of the following statement is true? Group of answer choices 81% of the variation in the money spent on repairs is explained by the age of the vehicle 90% of the repair cost will be explained by the age of the vehicle 90% of the money spent on repair is explained by the age of the vehicle 81% of money spent on repairs is explained by the age of the vehicle

Answer 1

Answer:

Option A) 81% of the variation in the money spent on repairs is explained by the age of the vehicle.          

Step-by-step explanation:

We are given the following information:

The correlation coefficient between the age of a vehicle and the money spent to repair it is 0.9

• The coefficient of determination is used to explain how much variability of one factor can be caused by its relationship to another factor.
• It helps to explain the change in the dependent variable due to independent variable.
• The coefficient of determination is the square of the correlation coefficient

Then,

$\text{Coefficient of Determination} = \text{(Correlation Coefficient)}^2 = (0.9)^2 = 0.81 = 81\%$

Thus, it could be said  81% of the variation in the money spent on repairs is explained by the age of the vehicle.

Thus, Option A) is the correct explanation.

Answer 2

Coefficient of correlation shows the correlation degree from -1 to 1 interval.

The true statement is

Option A: 81% of the variation in the money spent on repairs is explained by the age of the vehicle.

How can we get to know the variability of one variable to other from correlation coefficient?

For that, we can use the coefficient of determination.

The coefficient of determination is square of correlation coefficient and thus, ranges from 0 to 1.

The coefficient of determination tells for unit variation in one variable will lead to how much variation in other variable and vice versa.

Since for the given case, let

X = Age of vehicle

Y = Money spent on repair

Then

Correlation coefficient (X, Y) =  0.9

Coefficient of determination = square of correlation coefficient =  $(0.9)^2 = 0.81$

Thus, as coefficient of determination ranges from 0 to 1, increasing its range to be same as percentage (0 to 100), we get that 0.81 times 100 = 81% of the variation in the money spent on repairs is explained by the age of the vehicle.

Thus,

The true statement is

Option A: 81% of the variation in the money spent on repairs is explained by the age of the vehicle.

Learn more about coefficient of determination here:

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