An Economist Is Analysing the Incomes of Professionals (Physicians, Dentists $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$

question 78

Essay

An economist is analysing the incomes of professionals (physicians, dentists and lawyers). He realises that an important factor is the number of years of experience. However, he wants to know if there are differences among the three professional groups. He takes a random sample of 125 professionals and estimates the multiple regression model: $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \varepsilon$ .
where
y
= annual income (in $1000). $x _ { 1 }$ = years of experience. $x _ { 2 }$ = 1 if physician.
= 0 if not. $x _ { 3 }$ = 1 if dentist.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS $y =$ $71.65 + 2.07 x _ { 1 } + 10.16 x _ { 2 } - 7.44 x _ { 3 }$ . $$\begin{array} { | c | r r c | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 71.65 & 18.56 & 3.860 \\x _ { 1 } & 2.07 & 0.81 & 2.556 \\x _ { 2 } & 10.16 & 3.16 & 3.215 \\x _ { 3 } & - 7.44 & 2.85 & - 2.611 \\\hline\end{array}$$ S = 42.6 R-Sq = 30.9%. $$\begin{array}{l}\text { ANALYSIS OF VARIANCE }\\\begin{array} { | l | r c c c | } \hline \text { Source of Variation } & \text { df } & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 3 & 98008 & 32669.333 & 18.008 \\\text { Error } & 121 & 219508 & 1814.116 & \\\hline \text { Total } & 124 & 317516 & & \\\hline\end{array}\end{array}$$ Is there enough evidence at the 5% significance level to conclude that income and experience are linearly related?

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Definitions:

Monopoly Behavior

The actions of a firm that is the sole provider of a good or service, often involving price setting and market control.

Monopoly Structure

A market structure characterized by a single seller that controls the whole industry, leading to a lack of competition and high prices for consumers.

Relevant Market

The market in which a particular product or service is sold, considering the competition and the demand of consumers.

Rule Of Reason

A legal doctrine that determines the legality of certain business practices based on their harm or benefit to competition.