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 A: Pairwise Correlations:

Income Agree

Agree -0.2785 1.0000

Gender 0.8327 -0.0478

Printout B: Best Subset Regression Models for Income

Forced Independent Variables: (A)Agree (B)Gender (C)x1x2

Unforced Independent Variables: (D)x1sq (E)x1sqx2

Adjusted   AICc -

P Cp R Square Min AICc Resid SS F P(F) Variables

4 4.6 0.7552 1798.32 5.805E+09 A B C

5 4.0 0.7593 1797.84 5.648E+09 2.64 0.1075   A B C D

5 5.3 0.7560 1799.22 5.726E+09 1.30 0.2568   A B C E

6 6.0 0.7568 1800.15 5.648E+09 3.31 0.0356   A B C D E

Cases Included 100    Missing Cases 0

Which of the following statements about multicollinearity is true from Printout A?

The data exhibit very little multicollinearity since there is a low correlation between agreement level (x1) and gender (x2).

No multicollinearity exits since the model is statistically useful for predicting income (y).

There is a high degree of multicollinearity in the data since the R2 for the model is high.

The data exhibit some multicollinearity since there is a moderate correlation between agreement level (x1) and income (y).

Answer 1

here

X₁ (agreeability level) and X₂ (gender) are the independent or regressor or predictor variables

Y ( income ) is the dependent variable or response variable

we consider multiple regression equation of Y on X₁, X₂ .

multicollinearity exists in a multiple regression model when two or more independent variables are moderately or highly correlated

From Printout A, we can see the correlation coefficient between X₁ ( agreeability level) and X₂ ( gender) is -0.0478 which is very low (only 4 % negatively correlated).

so the variables X₁ and X₂ are not correlated significantly.

hence,

the data exhibit very little multicollinearity since there is a low correlation between agreement level (X₁) and gender (X₂)