Question

) The correlation between a car’s engine size and its fuel economy (in mpg) is r= -0.774. What fraction of the variability in fuel economy is accounted for by the engine size?

Answer 1

The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

Given that, r= -0.774.

To solve such problems we must know about the fraction of the variability in data values or R-squared.

What fraction of the variability in fuel economy is accounted for by the engine size?

The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.

It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r”  in a simple regression model.

Fraction of the variability in data values = (coefficient of correlation)²= r²

Now, the variability in fuel economy = r²= (-0.774)²

= 0.599076%= 59.91%

Hence, the fraction of the variability in fuel economy accounted for by the engine size is 59.91%.

To learn more about the fraction of the variability visit:

brainly.com/question/2516132.

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