A study was conducted to determine if a person’s agreeability (whether they are
ID: 2910050 • Letter: A
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-testExplanation / Answer
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.
Answer:
A t-test
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