Question

EXERCISES FOR CHAPTERS 18 – 19

1. (Ch. 18 – Interaction Effects)  Below is Minitab output for a regression model using the Teen Gambling data from Chapter 18.   Use it to answer the questions below.

Regression Analysis: Gambling Amount ($) versus Sex, Status, Sex:Status, Income ($100)

Model Summary

      S    R-sq  R-sq(adj)  

21.7798  56.39%     52.24%      

Coefficients

Term          Coef  SE Coef  T-Value  P-Value  

Constant      30.1     16.7     1.80    0.079

Sex          -68.2     20.1    -3.40    0.002  

Status      -0.481    0.269    -1.79    0.081

Sex:Status   1.088    0.460     2.37    0.023

Income ($)   4.970    0.984     5.05    0.000

Regression Equation

Gambling Amount($) = 30.1 - 68.2 Sex - 0.481 Status + 1.088 Sex:Status + 4.970 Income

1. What is the predicted Gambling Amount for a female with income of $250 whose parents have a Status score of 60? (Recall that in the Sex variable, females are coded with a 1; males with 0. Status is recorded on a scale of 1 to 100 and note that Income is recorded in $100s.)

2. What is the predicted Gambling Amount for a female with income of $250 whose parents have a Status score of 70?

3. What is the predicted Gambling Amount for a male with income of $250 whose parents have a Status score of 70?

4. What is the predicted Gambling Amount for a male with income of $250 whose parents have a Status score of 60?

5. Interpret the slope of the Sex:Status (interaction) predictor for a female teenager. (Remember to account for the slope of Status.)
6. Interpret the slope of the Status predictor for a male teenager.

2. (Ch. 19 – Logistic Regression)  In a famous research paper, econometrics researchers investigated the effectiveness of a teaching method known as the Personalized System of Instruction (PSI) for the teaching of economics.  They randomly selected 32 students from two intermediate econ classes.  Students from one of the classes were being taught using PSI; in the other class, the traditional lecture method was used.  The researchers then recorded 1) whether or not the students’ grades had Improved  (Yes or No) from their introductory econ class, 2) their performance in the introductory class assessed using the Test for the Understanding of College Economics (TUCE), and 3) their overall GPA upon entering the intermediate course.  Using Minitab, a binary logistic regression was done to assess the probability of grade improvement from the other variables.  The output is below.  Use it to answer the questions that follow.

1. Using this model, what is the predicted probability of grade improvement for a student in the PSI class who had a 20 score on the TUCE and a GPA of 3.2?

2. Using this model, what is the predicted probability of grade improvement for a student not in the PSI class who had a 20 score on the TUCE and a GPA of 3.2?
3. Interpret the slope of the PSI predictor.  (PSI was recorded as 0 (No) or 1 (Yes).)

4. Which of the factors recorded appears to have little effect on the probability of grade improvement?  Upon what in the output is your answer based?  (FOOD FOR THOUGHT: What implications might this have for these researchers?)

Answer 1

Note : Allowed to answer only 4 questions per post.

regression equation
Gambling Amount($) = 30.1 - 68.2 Sex - 0.481 Status + 1.088 Sex:Status + 4.970 Income

What is the predicted Gambling Amount for a female with income of $250 whose parents have a Status score of 60?

We are given the following

Sex = 1 (since it is female)
income = 250
status = 60

We subsititute these values in the regression equation as given below

Gambling Amount($) = 30.1 - 68.2 Sex - 0.481 Status + 1.088 Sex:Status + 4.970 Income

Gambling Amount($) = 30.1 - 68.2*(1) - 0.481*(60) + 1.088 (1*60) + 4.970*(250)=1240.82

What is the predicted Gambling Amount for a female with income of $250 whose parents have a Status score of 70?

Sex = 1 (since it is female)
income = 250
status = 70

We subsititute these values in the regression equation as given below

Gambling Amount($) = 30.1 - 68.2 Sex - 0.481 Status + 1.088 Sex:Status + 4.970 Income

Gambling Amount($) = 30.1 - 68.2*(1) - 0.481*(70) + 1.088 (1*70) + 4.970*(250)=1246.89

What is the predicted Gambling Amount for a male with income of $250 whose parents have a Status score of 70?

Sex = 0 (since it is Male)
income = 250
status = 60

We subsititute these values in the regression equation as given below

Gambling Amount($) = 30.1 - 68.2 Sex - 0.481 Status + 1.088 Sex:Status + 4.970 Income

Gambling Amount($) = 30.1 - 68.2*(0) - 0.481*(60) + 1.088 (0*60) + 4.970*(250)=1243.74

What is the predicted Gambling Amount for a male with income of $250 whose parents have a Status score of 60?

Sex = 0 (since it is Male)
income = 250
status = 60

We subsititute these values in the regression equation as given below

Gambling Amount($) = 30.1 - 68.2 Sex - 0.481 Status + 1.088 Sex:Status + 4.970 Income

Gambling Amount($) = 30.1 - 68.2*(0) - 0.481*(70) + 1.088 (0*70) + 4.970*(250)=1238.93