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?
A. 27.5%
B. 63.8%
C. 71.8%
D. 84.1%

We know that the fraction of the variability in data values accounted by a model is given by [tex]r^2[/tex] , where r is the coefficient of correlation.

We are given , that the correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.

Then, the fraction of the variability in fuel economy is accounted for by the engine size would be [tex]r^2=( - 0.774)^2=0.599076\approx59.91\%[/tex]

[Multiply 100 to convert a decimal into percent]

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

None of the options are correct.

ap8997154 ap8997154 · Answer 2 · 2022-01-22T10:48:01+01:00

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

R- Squared

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.

= r²

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

The correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.

As it is given that the correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.

the variability in fuel economy = r²

= (-0.774)²

= 0.599076

= 59.91%

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

Learn more about R-squared:

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