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A Professor of Accounting Wanted to Develop a Multiple Regression y=β0+β1x1+β2x2+β3x3+εy = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon

question 44

Essay

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=β0+β1x1+β2x2+β3x3+εy = \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). x1x _ { 1 } = GPA in first three years (range 0 to 12). x2x _ { 2 } = 1 if student's major is accounting.
= 0 if not. X3X _ { 3 } = 1 if student's major is finance.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS y=y = 9.14+6.73x1+10.42x2+5.16x39.14 + 6.73 x _ { 1 } + 10.42 x _ { 2 } + 5.16 x _ { 3 } .  Predictor  Coef  SDev T Constant 9.147.101.287x16.731.913.524x210.424.162.505x35.163.931.313\begin{array} { | c | r r c | } \hline \text { Predictor } & \text { Coef } & \text { SDev } & 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%.  ANALYSIS OF VARIANCE  Source of Variation df SS  MS F Regression 3170985699.33325.386 Error 9621553224.510 Total 9938651\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | r r r r | } \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 on average accounting majors outperform those whose majors are not accounting or finance?

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