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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Definitions:

Obligation

A duty or commitment that an individual is bound to, either legally, morally, or emotionally.

Group Norms

Shared guidelines or rules of behavior that are accepted and followed by members of a group, influencing how they act and interact.

Temperaments

Physiological dispositions to respond to the environment in certain ways; they are present in infancy and in many nonhuman species and are assumed to be innate.

Personalities

The combination of characteristics or qualities that form an individual's distinctive character.