A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below:

Also SSR (X1 ∣ X2) = 36400.6326 and SSR (X2 ∣ X1) = 3297.7917

What fraction of the variability in house size is explained by income and size of family?

A. 84.79%
B. 71.89%
C. 17.56%
D. 70.69%

R-squared is a statistical quantity that measures, just how near the values are to the fitted regression line. It is also known as the coefficient of determination.

The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent variable).

The coefficient of determination R² can be computed by the formula,

[tex]R^{2}=\frac{SSR}{SST}[/tex]

Here,

SSR = sum of squares of regression

SST = sum of squares of total

From the output attached below the value of SSR and SST are:

SSR = 37043.3236

SST = 51531.0863

Compute the value of R² as follows:

[tex]R^{2}=\frac{SSR}{SST}[/tex]

[tex]=\frac{37043.3236 }{51531.0863}[/tex]

[tex]=0.7188539\\\approx 0.7189[/tex]

Thus, the fraction of the variability in house size is explained by income and size of family is 71.89%.

The correct option is (B).