A statistics professor investigated some of the factors that affect an individual student's final grade in his or her course. He proposed the multiple regression model:

y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon

.
Where:
y = final mark (out of 100).

x _ { 1 }

= number of lectures skipped.

x _ { 2 }

= number of late assignments.

x _ { 3 }

= mid-term test mark (out of 100).
The professor recorded the data for 50 randomly selected students. The computer output is shown below.
THE REGRESSION EQUATION IS
ŷ =

41.6 - 3.18 x _ { 1 } - 1.17 x _ { 2 } + .63 x _ { 3 }

\begin{array} { | c | c c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } \\\hline \text { Constant } & 41.6 & 17.8 & 2.337 \\x _ { 1 } & - 3.18 & 1.66 & - 1.916 \\x _ { 2 } & - 1.17 & 1.13 & - 1.035 \\x _ { 3 } & 0.63 & 0.13 & 4.846 \\\hline\end{array}

se = 13.74, R2 = 30.0%.

\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \mathrm { df } & \text { SS } & \text { MS } & \text { F } \\\hline \text { Regression } & 3 & 3716 & 1238.667 & 6.558 \\\text { Error } & 46 & 8688 & 188.870 & \\\hline \text { Total } & 49 & 12404 & & \\\hline\end{array}\end{array}

Interpret the coefficients

\hat { \beta } _ { 1 }

and

\hat { \beta } _ { 3 }

Which of the Following Best Describes the Ratio MSR/MSE in a Multiple

Multiple Choice

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