Question

A study was conducted to determine if a person’s agreeability (whether they are generally an agreeable person or not) affects their income level. It also looked at the person’s gender to see if it was a factor as well. The variables are shown below:

Income:    y = annual income in dollars

Agree:      x1 = agreeability level with higher scores indicating a person is more aggregable and lower scores indicating less agreeable

Gender:   x2 = 1 if male, 0 if female

Use the following information to answer the multiple regression questions.

Printout C: Least Squares Linear Regression of Income

Predictor

Variables Coefficient Std Error T P  

Constant 40977.1    8788.81 4.66 0.0000  

Agree -5479.36    2643.95 -1.07 0.2409  

Gender 54225.1    12988.7 4.17 0.0001  

x1x2 -8708.14    3934.83 -2.21 0.0293  

R² 0.7626 Mean Square Error (MSE)              6.047E+07

Adjusted R²   0.7552 Standard Deviation 7700.00

Source DF          SS MS F P

Regression 3   1.865E+10    6.217E+09    102.50 0.0000

Residual 96   5.805E+09    6.047E+07

Total 99   2.446E+10

Suppose we consider Printout C to be the printout we should use after the quadratics test (May or may not be accurate. Please don’t change your answer to the last question). What type of test should be used to determine if an interaction exists between the agreement and gender variables?

A t-test

A Global F-test

A Partial F-test (called a Best Subset test in Statistix)

Answer 1

Result:

A study was conducted to determine if a person’s agreeability (whether they are generally an agreeable person or not) affects their income level. It also looked at the person’s gender to see if it was a factor as well. The variables are shown below:

Income:    y = annual income in dollars

Agree:      x1 = agreeability level with higher scores indicating a person is more aggregable and lower scores indicating less agreeable

Gender:   x2 = 1 if male, 0 if female

Use the following information to answer the multiple regression questions.

Printout C: Least Squares Linear Regression of Income

Predictor

Variables Coefficient Std Error T P  

Constant 40977.1    8788.81 4.66 0.0000  

Agree -5479.36    2643.95 -1.07 0.2409  

Gender 54225.1    12988.7 4.17 0.0001  

x1x2 -8708.14    3934.83 -2.21 0.0293  

R² 0.7626 Mean Square Error (MSE)              6.047E+07

Adjusted R²   0.7552 Standard Deviation 7700.00

Source DF          SS MS F P

Regression 3   1.865E+10    6.217E+09    102.50 0.0000

Residual 96   5.805E+09    6.047E+07

Total 99   2.446E+10

Suppose we consider Printout C to be the printout we should use after the quadratics test (May or may not be accurate. Please don’t change your answer to the last question). What type of test should be used to determine if an interaction exists between the agreement and gender variables?

Answer:

A t-test

A Global F-test

A Partial F-test (called a Best Subset test in Statistix)

Note: In the printout, the variables x1, x2 and the interaction x1x2 are used to build the model. To test the significance of the interaction term, the t test to be used. This is used to test the significance of the interaction term regression coefficient. From the print out, calculated t = 2.21, P=0.0293   which is < 0.05 level of significance. The interaction is significant.