A subsample from the Current Population Survey is taken, on weekly earnings of individuals, their age, and their gender. You have read in the news that women make 70 cents to the $1 that men earn. To test this hypothesis, you first regress earnings on a constant and a binary variable, which takes on a value of 1 for females and is 0 otherwise. The results were: $\widehat { E a m }$
= 570.70 - 170.72 × Female, $R ^ { 2 }$ =0.084, SER = 282.12.
(a)There are 850 females in your sample and 894 males. What are the mean earnings of males and females in this sample? What is the percentage of average female income to male income?
(b)You decide to control for age (in years)in your regression results because older people, up to a point, earn more on average than younger people. This regression output is as follows: $\widehat { E a m }$
= 323.70 - 169.78 × Female + 5.15 × Age, $R ^ { 2 }$ =0.135, SER = 274.45.
Interpret these results carefully. How much, on average, does a 40-year-old female make per year in your sample? What about a 20-year-old male? Does this represent stronger evidence of discrimination against females?

Question

A subsample from the Current Population Survey is taken, on weekly earnings of individuals, their age, and their gender. You have read in the news that women make 70 cents to the $1 that men earn. To test this hypothesis, you first regress earnings on a constant and a binary variable, which takes on a value of 1 for females and is 0 otherwise. The results were: $\widehat { E a m }$
 = 570.70 - 170.72 × Female, $R ^ { 2 }$ =0.084, SER = 282.12.
(a)There are 850 females in your sample and 894 males. What are the mean earnings of males and females in this sample? What is the percentage of average female income to male income?
(b)You decide to control for age (in years)in your regression results because older people, up to a point, earn more on average than younger people. This regression output is as follows: $\widehat { E a m }$
 = 323.70 - 169.78 × Female + 5.15 × Age, $R ^ { 2 }$ =0.135, SER = 274.45.
Interpret these results carefully. How much, on average, does a 40-year-old female make per year in your sample? What about a 20-year-old male? Does this represent stronger evidence of discrimination against females?

Quizplus · Accepted Answer

The Answer of A subsample from the Current Population Survey is taken, on weekly earnings of individuals, their age, and their gender. You have read in the news that women make 70 cents to the $1 that men earn. To test this hypothesis, you first regress earnings on a constant and a binary variable, which takes on a value of 1 for females and is 0 otherwise. The results were: $\widehat { E a m }$
 = 570.70 - 170.72 × Female, $R ^ { 2 }$ =0.084, SER = 282.12.
(a)There are 850 females in your sample and 894 males. What are the mean earnings of males and females in this sample? What is the percentage of average female income to male income?
(b)You decide to control for age (in years)in your regression results because older people, up to a point, earn more on average than younger people. This regression output is as follows: $\widehat { E a m }$
 = 323.70 - 169.78 × Female + 5.15 × Age, $R ^ { 2 }$ =0.135, SER = 274.45.
Interpret these results carefully. How much, on average, does a 40-year-old female make per year in your sample? What about a 20-year-old male? Does this represent stronger evidence of discrimination against females?

A Subsample from the Current Population Survey Is Taken, on Weekly