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

question 198

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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, the interpretation of the coefficient of determination in this regression is

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Definitions:

Rational Model

A decision-making model based on logically working through options and choosing the most logical, efficient, and rational outcome.

Rational Model

A decision-making framework that assumes logical, systematic identification of goals, evaluation of alternatives, and selection based on maximizing utility.

Decision Errors

Mistakes made in the process of choosing between alternatives, often due to biases, inadequate information, or errors in judgment.

Decision Making

The process of selecting a course of action from among multiple alternatives to achieve a desired outcome.

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