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Instruction 12  Regressing average grade on university entrance exam score \text { Regressing average grade on university entrance exam score }

question 200

Multiple Choice

Instruction 12.32
It is believed that average grade (based on a four-point scale) should have a positive linear relationship with university entrance exam scores. Given below is the Microsoft Excel output from regressing average grade on university entrance exam scores using a data set of eight randomly chosen students from a large university.
 Regressing average grade on university entrance exam score \text { Regressing average grade on university entrance exam score }

 Regression statistics \text { Regression statistics }
 MultipleR 0.7598 R Square 0.5774 Adjusted R  Square 0.5069 Standard Error 0.2691 Observations 8\begin{array}{|l|l|}\hline\text { MultipleR } & 0.7598 \\\hline \text { R Square } & 0.5774 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.5069 \\\hline \text { Standard Error } & 0.2691 \\\hline \text { Observations } & 8\\\hline\end{array}

 ANOVA \text { ANOVA }
df55MSF Significance F Regression 10.59400.59408.19860.0286 Residual 60.43470.0724 Total 71.0287\begin{array}{|l|l|l|l|l|l|}\hline & d f & 55 & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\\hline \text { Residual } & 6 & 0.4347 & 0.0724 & & \\\hline \text { Total } & 7 & 1.0287 & & & \\\hline\end{array}

 Coefficients  Standard  Error  tStat  p-value  Lower 95%  Upper 95%  Intercept 0.56810.92840.61190.56301.70362.8398 University  entrance exam  score 0.10210.03562.86330.02860.01480.1895\begin{array}{|l|l|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { tStat } & \text { p-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\\hline \begin{array}{l}\text { University } \\\text { entrance exam } \\\text { score }\end{array} & 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895 \\\hline\end{array}
-Referring to Instruction 12.32,the value of the measured test statistic to test whether there is any linear relationship between average grade and university entrance exam score is


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