Consider the following regression based on hypothetical data. We hypothesize tha

Question

Consider the following regression based on hypothetical data. We hypothesize that age, height, and income affect people’s weight. So we run a regression analysis of data from a random sample of 25 people, with weight (in pounds) as the dependent variable and age (x variable 1, in years), height (x variable 2, in inches), and income (x variable 3, in $1,000) as the independent variables. Here is part of the regression output from Excel:

Regression Statistics

Multiple R

0.84897499

R Square

0.72075853

Adjusted R Square

0.68086689

Standard Error

8.1862544

Observations

25

Which of the following statement is true?

Regression Statistics

Multiple R

0.84897499

R Square

0.72075853

Adjusted R Square

0.68086689

Standard Error

8.1862544

Observations

25

Explanation / Answer

What Is R-squared?

R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.

The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or:

R-squared = Explained variation / Total variation

R-squared is always between 0 and 100%:

Therefore from the statements above we can say that the 5th option is correct: Both a and b are correct

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