Question

5. Use the figure below to answer the remaining questions. The figure is excel output of a regression meant to find the relationship between college students' grade point average (univGPA) and the same students' high school grade point average (highGPA). SUMMARY OUTPUT Regression Statistics Multiple R 0.779563121 R Square 0.607718659 Adjusted R Square 0.603910102 Standard Error 0.281444322 Observations 105 ANOVA Regression Residual Total 159.5666562 SS MS 12.63941949 12.63941949 8 158723372 0.079210907 20.79814286 1 103 104 Intercept highGPA Coefficients Standard Error State P-value 1.096823282 0.166626896 6.582510432 1.97668E-09 0.674829903 0.0534223821263196961 1.17561E-22 Figure 3: Grade point averages

Answer 1

Q5) f) The coefficient of determination R2 is defined as the percentage of variation in the dependent variable that is explained by the independent variable. As the R2 here is given to be 0.6077 ( from the regression statistics ) , therefore 60.77% of the variation in college grade point average is explained by variation in high school grade point average.

g) The correlation between high school grade point average and the high school grade point average here is given to be the value of R from the regression statistics that is R = 0.7796. Therefore 0.7796 is the required correlation here. This means that there is a strong positive correlation between the 2 variables.

h) We first compute the predicted value from the coefficients column here as:

University GPA = 1.0968 + 0.6748*High School GPA

= 1.0968 + 0.6748*2.3 = 2.64884

Now the error residual here is computed as:

= Observed Value - Predicted Value

= 2.3 - 2.64884

= -0.34884

Therefore -0.3488 is the required error term here.