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Incomes of Physicians an Economist Is Analyzing the Incomes of Physicians (General

Question 84

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Incomes of Physicians
An economist is analyzing the incomes of physicians (general practitioners,surgeons,and psychiatrists).He realizes 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 physicians and estimates the multiple regression model y = β0 + β1x1 + β2x2 + β3x3 + ε,where y = annual income (in $1,000),x1 = years of experience,x2 = 1 if physician and 0 if not,and x3 = 1 if surgeons and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 71.65 + 2.07x1 + 10.16x2− 7.44x3 Incomes of Physicians An economist is analyzing the incomes of physicians (general practitioners,surgeons,and psychiatrists).He realizes 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 physicians and estimates the multiple regression model y = β<sub>0</sub> + β<sub>1</sub>x<sub>1</sub> + β<sub>2</sub>x<sub>2</sub> + β<sub>3</sub>x<sub>3</sub> + ε,where y = annual income (in $1,000),x<sub>1</sub> = years of experience,x<sub>2</sub> = 1 if physician and 0 if not,and x<sub>3</sub> = 1 if surgeons and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 71.65 + 2.07x<sub>1</sub> + 10.16x<sub>2</sub>− 7.44x<sub>3</sub> S = 42.6 R−Sq = 30.9% ANALYSIS OF VARIANCE ​ ​ -{Incomes of Physicians Narrative} Do these results allow us to conclude at the 1% significance level that the model is useful in predicting the income of physicians? S = 42.6 R−Sq = 30.9% ANALYSIS OF VARIANCE Incomes of Physicians An economist is analyzing the incomes of physicians (general practitioners,surgeons,and psychiatrists).He realizes 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 physicians and estimates the multiple regression model y = β<sub>0</sub> + β<sub>1</sub>x<sub>1</sub> + β<sub>2</sub>x<sub>2</sub> + β<sub>3</sub>x<sub>3</sub> + ε,where y = annual income (in $1,000),x<sub>1</sub> = years of experience,x<sub>2</sub> = 1 if physician and 0 if not,and x<sub>3</sub> = 1 if surgeons and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 71.65 + 2.07x<sub>1</sub> + 10.16x<sub>2</sub>− 7.44x<sub>3</sub> S = 42.6 R−Sq = 30.9% ANALYSIS OF VARIANCE ​ ​ -{Incomes of Physicians Narrative} Do these results allow us to conclude at the 1% significance level that the model is useful in predicting the income of physicians? ​ ​
-{Incomes of Physicians Narrative} Do these results allow us to conclude at the 1% significance level that the model is useful in predicting the income of physicians?

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H0: β1 = β2 = β3 = 0,H1: At least one βi is no...

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