A study was conducted to determine if a person\'s agreeability (whether they are

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 Constant Agree Gender x1x2 40977,1 8788.81 4.66 0,0000 -5479.36 2643.95 1.07 0.2409 54225.1 12988.7 4.17 00001 -8708.14 3934.83 -2.21 0,0293 0.7626 Mean Square Error (MSE) 6.047E+07 Adjusted R 0.7552 Standard Deviation 7700.00 Source DF SS MS Regression3 3 1.865E+10 6.217E+09 102.50 .0000 96 5.80SE+09 6.047E+07 99 2.446E+10 Total True or False. Assuming it was determined that the interaction termís) is/are useful for predicting income, the statistician should not use Printout C to perform a t test on the Gender variable in the regression model. True o False

Explanation / Answer

In statistics, an interaction may arise when considering the relationship among three or more variables and describes a situation in which the simultaneous influence of two variables on a third is not additive. Most commonly, interactions are considered in the context of regression analyses.

The presence of interactions can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable. In practice, this makes it more difficult to predict the consequences of changing the value of a variable, particularly if the variables it interacts with are hard to measure or difficult to control.

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