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:

Inductive Perceptions

The cognitive process of making generalized conclusions or theories based on specific observations or experiences.

Subliminal Perception

The capacity to perceive and respond to stimuli that are presented below the threshold of awareness.

Selective Perception

The process by which individuals perceive what they want to in media messages while ignoring opposing viewpoints due to personal attitudes and beliefs.

Stroboscopic Perception

The visual phenomenon where continuous motion is represented by a series of short or instantaneous samples, as seen in motion pictures.