Question

A college admission s counselor was interested in finding out how well high school grade point averages (HS GPA) predict first-year college GPAs (FY GPA). A random sample of data from first-year students was reviewed to obtain high school and first-year college GPAs. The data are shown below:
   
  


Given the following computer output. Determine what percent of the variation in FY GPA is explained by HS GPA.
Computer output for this regression might look like this:
The regression equation is
FY GPA = - 1.56 + 1.31 HS GPA
  
Predictor Coef SE Coef T P
Constant -1.5641 0.7306 -2.14 0.050
HS GPA 1.3053 0.1993 6.55 0.000
S = 0.211773 r-Sq = .754 r = 0.8683

		High school GPA seems to account for 21.1% of the variation in first-year college GPA.
		High school GPA seems to account for 86.8% of the variation in first-year college GPA.
		High school GPA seems to account for 5% of the variation in first-year college GPA.
		High school GPA seems to account for 75.4% of the variation in first-year college GPA.

Answer 1

The regression equation is FY GPA = - 1.56 + 1.31 HS GPA

FY GPA is the dependent variable and HS GPA is the independent variable

The % of the variation in the dependent variable explained by the independent variable is nothing but the R2 measure

As per the computer output, we have R2= 0.754

Hence, we can say that 75.4% of the variation in first-year college GPA is explained by High school GPA

So, 4th option is our answer choice- High school GPA seems to account for 75.4% of the variation in first-year college GPA.

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