Question

a. Assuming a linear relationship between year and salaries by gender, determine when the median annual salary for women will exceed men. Justify your answer. Include in the discussion the regression analysis you performed. b. Based on the answer you found in the above step, provide an argument pro or con to the statement “As the number of women exceed men in the number of bachelor degrees received, expect there to be a corresponding change in the median annual salaries for each gender

Answer 1

First We have to find the tendency for both cases individually. Let's calculate the equation of the line for each one.

For Men we take two points (year, salary) ( 2 , 35,308) ( 4 , 37076) With these points we are going to calculate the slope of the line.

$m=\frac{y2-y1}{x2-x1}=\frac{37076-35308}{4-2}=884$

Then, we have to calculate the intercept of the line with the slope and point (2, 35,308)

y= mx+ b

35,308 = 884*(2)+b

Isolating b,

35,308 - 1768 = b

33540=b

The first equation must be y = 884x +33540

For Women we take two points (year, salary) ( 2 , 27,508) ( 4 , 29,796 ) With these points we are going to calculate the slope of the line

$m=\frac{y2-y1}{x2-x1}=\frac{29,796-27,508}{4-2}=1144$

Then, we have to calculate the intercept of the line with the slope and point (2, 27,508)

y= mx+ b

27,508 = 1144*(2)+b

Isolating b,

27,508 - 2288 = b

25220=b

The second equation must be y = 1144x +25220

Now We are going to find the incercept of these equations, we are going to formulate the following equation

884x+33540 = 1144x+25220

33540-25220=1144x-884x ( Isolating terms with x)

8320=260x (Solving on each side)

8320/260 = x =32 ( Isolating x)

It implies that after 32 years Women would exceed men.

B. It seems that as the number of bachelor degrees of women exceeds men's number, the salary increases at a higher rate. So , the change would be greater for women than men every year.