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 68

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 $y =$ $9.14 + 6.73 x _ { 1 } + 10.42 x _ { 2 } + 5.16 x _ { 3 }$ . $\begin{array} { | c | r c c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 9.14 & 7.10 & 1.287 \\x _ { 1 } & 6.73 & 1.91 & 3.524 \\x _ { 2 } & 10.42 & 4.16 & 2.505 \\x _ { 3 } & 5.16 & 3.93 & 1.313 \\\hline\end{array}$ 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 on average accounting majors outperform those whose majors are not accounting or finance?

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Definitions:

Poisson Distribution

A discrete frequency distribution that expresses the probability of a given number of events happening in a fixed interval of time or space.

Probability

The calculation of how likely an event is to occur, with its value determined to be between 0 and 1.

Insulin-Dependent Diabetes

A chronic condition where the pancreas produces little or no insulin, requiring the person to administer insulin through injections or a pump; also known as Type 1 diabetes.

Poisson Distribution

A probability distribution that models the number of times an event occurs within a fixed interval of time or space.