A Professor of Accounting Wanted to Develop a Multiple Regression $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$

A professor of accounting wanted to develop a multiple regression model to predict the students' grades in her fourth-year accounting course. She decides that the two most important factors are the student's grade point average (GPA) in the first three years and the student's major. She proposes the model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
where
y
= fourth-year accounting course mark (out of 100). $x _ { 1 }$ = GPA in first three years (range 0 to 12). $x _ { 2 }$ = 1 if student's major is accounting.
= 0 if not. $x _ { 3 }$ = 1 if student's major is finance.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS $y =$ $9.14 + 6.73 x _ { 1 } + 10.42 x _ { 2 } + 5.16 x _ { 3 }$ . $$\begin{array} { | c | r c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 9.14 & 7.10 & 1.287 \\x _ { 1 } & 6.73 & 1.91 & 3.524 \\x _ { 2 } & 10.42 & 4.16 & 2.505 \\x _ { 3 } & 5.16 & 3.93 & 1.313 \\\hline\end{array}$$ S = 15.0 R-Sq = 44.2%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | r c c c | } \hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 3 & 17098 & 5699.333 & 25.386 \\\text { Error } & 96 & 21553 & 224.510 & \\\hline \text { Total } & 99 & 38651 & & \\\hline\end{array}\end{array}$$ Do these results allow us to conclude at the 1% significance level that the model is useful in predicting the fourth-year accounting course mark?