The Dean at Cool State San Bernardino wants to see if he could predict the GPA of students using the number of course units and total SAT scores. He takes a sample of students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics egin{tabular}{|l|l|} hline Multiple R & 0.916 \ hline R Square & 0.839 \ hline Adjusted R Square & 0.732 \ hline Standard Error & 0.24685 \ hline Observations & 6 \ hline end{tabular} egin{tabular}{|l|c|l|c|c|} hline & Coeff & multicolumn{1}{|c|}{ Std Error } & T Stat & P-value \ hline Intercept & 4.5939 & 1.1337 & 4.052 & 0.0271 \ hline Units & -0.2473 & 0.0627 & -3.945 & 0.0290 \ hline Total SAT & 0.0014 & 0.0010 & 1.425 & 0.2494 \ hline end{tabular} The estimate of the change in the mean of GPA per unit change in the number of course units, holding SAT score constant, is
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2473. This means that for every one unit increase in the number of course units, the mean GPA is estimated to decrease by 0.2473. Show more…
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Verbal SAT as a Predictor of GPA A scatterplot with a 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 + 0.00189 VerbalSAT. Predictor Coef SE Coef T P Constant 2.0336 0.1621 12.54 0.000 VerbalSAT 0.0018929 0.0002709 6.99 0.000 S = 0.373214 R - Sq = 12.5% R - Sq (adj) = 12.2% Click here for the dataset associated with this question: (a) Use the scatterplot to determine: Are the conditions reasonably met for using a linear model with this data? Yes No
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GPA and SATs A large section of Stat 101 was asked to fill out a survey on grade point average and SAT scores. A regression was run to find out how well Math and Verbal SAT scores could predict academic performance as measured by GPA. The regression was run on a computer package with the following output: $$ \begin{aligned} &\text { RESPONSE GPA }\\ &\begin{array}{lllll} \text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \\ \text { Intercept } & 0.574901 & 0.253819 & 2.27 & 0.0291 \\ \text { SAT Verbal } & 0.001371 & 0.000508 & 2.70 & 0.0104 \\ \text { SAT Math } & 0.001968 & 0.000541 & 3.64 & 0.0008 \end{array} \end{aligned} $$a) What is the regression equation? b) From this model, what is the predicted GPA of a student with an SAT Verbal score of 500 and an SAT Math score of $570 ?$ c) What else would you want to know about this regression before writing a report about the relationship between SAT scores and grade point averages? Why would these be important to know?
It is believed that GPA (grade point average based on a four-point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output for predicting GPA using ACT scores based on a dataset of 8 randomly chosen students from a Big Ten university. Regressing GPA on ACT Regression Statistics: Multiple R: 0.7598 R Square: 0.5774 Adjusted R Square: 0.5069 Standard Error: 0.2691 Observations: 8 ANOVA Significance: 0.0286 Regression: 0.5940 Residual: 0.4347 Total: 0.5940 Coefficients: Standard Error: 0.5681 0.9284 Stat: 0.102 0.0356 P-value: 0.6119 0.5630 Lower 95%: 1.7036 8398 Upper 95%: 2.8633 0.0286 0.0148 1895 Intercept: ACT
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