Question

A least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 46.8 and the sum of squares of regression (SSR) was 14.55. Use these values to calculate the percent of the variability in y that can be explained by variability in the regression model. Round your answer to the nearest integer.

Answer 1

Answer: 31%

Step-by-step explanation:

Formula : Percent of the variability = $R^2\times100=\dfrac{SSR}{SST}\times100$

, where $R^2$ = Coefficient of Determination.

SSR =  sum of squares of regression

SST = total sum of squares

$R^2$  is the proportion of the variation of Y that can be attributed to the variation of x.

As per given , we have

SSR = 14.55

SST=  46.8

Then, the percent of the variability in y that can be explained by variability in the regression model =$\dfrac{14.55}{46.8}\times100=31.0897435897\%\approx31\%$

Hence, the percent of the variability in y that can be explained by variability in the regression model  = 31%