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 100

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 the1% significant level to conclude that physicians earn more on average than lawyers?

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Definitions:

Sensitization

An increase in behavioral response after exposure to a stimulus, often leading to an exaggerated response to a later stimulus.

Habituation

The process by which an organism decreases or ceases its responses to a repetitive stimulus over time.

Behavioral Contrast

A phenomenon where the rate of response to a stimulus changes significantly when the conditions of reinforcement for another stimulus are altered.

Higher-order Conditioning

A form of learning in which a stimulus is first made meaningful or consequential for an organism through an initial step of learning, and then that stimulus is used as a basis for learning about some new stimulus.