Section 2: Regression Analysis (13 pts)

Problem 1: Imagine that you have created a regression to predict annual salaries for graduates leaving Excelsior with Bachelors and Masters degrees and entering the job market. You have and created two regressions that take the following form:

Salary = ₀+ ₁GPA + ₂Age+ ₃Gender + ₄MastersDegree

Where both Gender and Masters Degree are binary varables: Gender = 1 for a female, 0 for males; Masters Degree = 1 for students graduating with a Masters degree, 0 for students without

Using data you have collected from graduating students over several years you find the following fitted regression results:

Regression (1)

Regression (2)

Coefficient

Fitted Value

Fitted Value

GPA

500

-

Age

-

250

Gender

-2000

-1500

Masters Degree

12,000

8,000

Constant

30,000

35,000

R²

0.876

0.667

In the first regression, you decide not to use age because you hypothesize that it may not have any impact on salaries, while in the second you test leaving out GPA because you think that it may not have any impact on salaries. This is why you see a "-" in these boxes. Anytime you see this, it means that this variable is not included in that regression.

Example Problem: Using Regression 1, what salary would you predict for a 23 year old male with a masters degree and a GPA of 3.5?

Step 1: Set up the equation for regression 1

Salary = (500 * GPA) - (2000 * Gender) + (12,000 * Masters) + 30,000

Step 2: Plug in the values you are given to solve for the predicted salary:

Salary = (500 * 3.5) - (2000 * 0) + (12,000 * 1) + 30,000 = $43,750

Note that even though you were given a value for age, you don't does anything with it when you are working with regression 1.

Using Regression 1:

a.What salary would you expect for a female with a GPA of 2.5 and a bachelors degree ____ (1 pt)

b.What salary would you expect for a male with a GPA of 2.0 and a masters degree _______ (1 pt)

c.How much more will you expect someone make if they graduate with a GPA of 4.0 instead of 2.0 ________ (1 pt)

Using Regression 2: Follow the same steps above to set up and solve the questions below

d.what salary would you expect for a 40 year old male with a bachelors degree and a GPA of 4.0 ____________ (1 pt)

e.what salary would you expect for a 33 year old female with a masters degree? _________ (1 pt)

f.How much higher would you expect the salary of a 50 year old be than that of a 30 year old? _________ (1 pt)

g.Which Regression is a better fit for the data used to create it (1 pt)

a.Regression 1

b.Regression 2

c.Both are equal