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

question 89

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: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
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 $y =$ $9.14 + 6.73 x _ { 1 } + 10.42 x _ { 2 } + 5.16 x _ { 3 }$ . $\begin{array}{|c|rrc|}\hline \text { Predictor } & \text { Coef } & \text { SDev } & \text { T } \\\hline \text { Constant } & 9.14 & 7.10 & 1.287 \\x_{1} & 6.73 & 1.91 & 3.524 \\x_{2} & 10.42 & 4.16 & 2.505 \\x_{3} & 5.16 & 3.93 & 1.313 \\\hline\end{array}$ S = 15.0 R-Sq = 44.2%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | r c c c | } \hline \text { Source of Variation } & d f & S S & M S & F \\\hline \text { Regression } & 3 & 17098 & 5699.333 & 25.386 \\\text { Error } & 96 & 21553 & 224.510 & \\\hline \text { Total } & 99 & 38651 & & \\\hline\end{array}\end{array}$$ Do these results allow us to conclude at the 1% significance level that grade point average in the first three years is linearly related to fourth-year accounting course mark?

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SIP

An acronym that can refer to several concepts, including Systematic Investment Plan, which allows investors to contribute small amounts periodically into a mutual fund.

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An Environmental Impact Statement, a document prepared to describe the effects for proposed activities on the environment, often required for major projects to assess their environmental consequences.

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A government body in the United States created by the Congress to enforce laws and regulations in a specific area of responsibility.

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The Council on Environmental Quality, a federal agency coordinating federal environmental efforts and advising the president on environmental policy.