Consider the following regression based on hypothetical data. We hypothesize tha
ID: 3224630 • Letter: C
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