Instruction 12 $\text { Regression statistics }$ $\text { ANOVA }$

question 203

Multiple Choice

Instruction 12.33
It is believed that the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Microsoft Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown.
$\text { Regression statistics }$
$\begin{array}{|l|l|}\hline \text { Multiple R } & 0.8857 \\\hline \text { R Square } & 0.7845 \\\hline \begin{array}{l}\text { Adjusted R } \\\text { Square }\end{array} & 0.7801 \\\hline \text { Standard Error } & 1.3704 \\\hline \text { Observations } & 51\\\hline\end{array}$

$\text { ANOVA }$
$\begin{array}{|l|l|l|l|l|l|}\hline & d f & S S & M S & F & \begin{array}{l}\text { Significance } \\F\end{array} \\\hline \text { Regression } & 1 & 335.0472 & 335.0473 & 178.3859 & \\\hline \text { Residual } & & & 1.8782 & & \\\hline \text { Total } & 50 & 427.0798 & & & \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|l|l|} \hline& \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { p-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -1.8940 & 0.4018 & -4.7134 & 2.051 \mathrm{E}-05 & -2.7015 & -1.0865 \\\hline \text { Hours } & 0.9795 & 0.0733 & 13.3561 & 5.944 \mathrm{E}-18 & 0.8321 & 1.1269\\\hline\end{array}$ Note: 2.051E-05 = 2.051 * 10^-0.5 and 5.944E-18 = 5.944 * 10^-18.
-Referring to Instruction 12.33,the p-value of the measured F test statistic to test whether HOURS affects SALARY is

• A) 2.051E-05.
• B) 5.944E-18.
• C) (2.051E-05) / 2.
• D) (5.944E-18) / 2.

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Definitions:

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A numerical expression that represents the likelihood of winning a game, bet, or any situation where there is a competition with a possible outcome.

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A cognitive bias in decision making where the likelihood of an event is judged based on how similar it is to the population it came from, often leading to errors in judgment.