Chapter 9, Section 1, Exercise 017 Verbal SAT as a Predictor of GPA A scatterplo

Question

Chapter 9, Section 1, Exercise 017 Verbal SAT as a Predictor of GPA A scatterplot with regression line is shown below for a regression model using Verbal SAT score, VerbalSAT, to predict grade point average in college, GPA, using the data in Studentsurvey. We also show computer output of the regression analysis below. The regression equation is GPA = 2.03 + 0.00 189 Verba!SAT. Predictor Constant2.0336 0.1621 12.54 0.000 VerbalSAT 0.0018929 0.0002709 6.99 0.000 Coef SE Coef TP S-0373214 R-Sq-12.5% R-Sq (adj)-12.2% 4.0 3.5 2.5 2.0 500 600 00 VerbaISAT 400 800 Click here for the dataset associated with this question

Explanation / Answer

Answer

(A) yes, because there is no outlier and scatter plot is showing a good line of linear model to predict dependent variable using the independent variable

(B) Regression equation is GPA = 2.03+0.00189Verbal SAT

putting verbal sat = 690, we get

GPA = 2.03+0.00189*690 = 2.03 + 1.304 = 3.33

so, the GPA associated with verbal SAT score of 690 is 3.33

(C) b1 = 0.00189 (rounded to five decimals)

Interpretation

For every 1 unit increase in the VerbalSAT score, there will be 0.00189 units increase in the GPA

(D) test statistic is 6.99 and p value is 0.000

This shows that the p value is significant, which means that the verbalSAT has effect on the GPA

so, we will reject the null hypothesis

Thus, the conclusion will be "Reject the null hypothesis Ho"

(E) R^2 is 12.5%

This means that 12.5 percent of variation in the GPA can be explained by the verbalSAT

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