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 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

To within what amount would we expect to be able to predict income level if we use this model?

Explanation / Answer

we know that the coefficient of determination is defined as the variation that can be explained using the regression model

here the coefficient of determination (R squared) = 0.7626 or 0.7626*100 = 76.26%

This shows us that 76.26% variation in the income level can be explained using the regression model.

So, we can explain income level within 76.26% using the regression model

Option A is correct

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