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SCENARIO 12-8
It Is Believed That GPA (Grade Point Average

question 178

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SCENARIO 12-8
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 a data set 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 Qbservations 8\begin{array}{l}\begin{array} { l r } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\text { Adjusted R Square } & 0.5069 \\\text { Standard Error } & 0.2691 \\\text { Qbservations } & 8 \\\hline\end{array}\\\end{array}
ANOVA
 df  SS  MS  F  Significance.F  Regression 10.59400.59408.19860.0286 Error 60.43470.0724 Total 71.0287\begin{array}{lrrrcc} \hline & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Significance.F } \\\hline\text { Regression } & 1 & 0.5940&0.5940&8.1986&0.0286 \\\text { Error } & 6 & 0.4347&0.0724\\\text { Total } & 7 &1.0287\\\hline\end{array}
 Coefficients  Standard Error t Stat P-value  Lower 95%  Upper 95%  Intercept 0.56810.92840.61190.56301.70362.8398 ACT 0.10210.03562.86330.02860.01480.1895\begin{array}{l}\begin{array} { l c r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 0.5681 & 0.9284 & 0.6119 & 0.5630 & - 1.7036 & 2.8398 \\\text { ACT } & 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}\end{array}
-Referring to Scenario 12-8, what is the predicted value of GPA when ACT = 20?

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