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

Which of the following problems would cause us to transform the income variable and begin our model building again?

A plot of the residuals vs. y-hat values indicates a cone pattern.

A plot of the stem-and-leaf display of the residuals indicates extreme skewness.

A plot of the residuals vs. agreeability levels indicates a quadratic trend.

We discover a high level of multicollinearity is present between agreeability level and gender.

Answer 1

Here' the answer to the question with full concept. Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

What causes us to transform income variable and begin our model again:

-- a residual vs. y^ ( y predicted) values indicate a spread out ( a cone) pattern

The same case is given in option A -- A plot of the residuals vs. y^ values indicates a conce pattern,

For your understanding when we see cone pattern, then its clear that we have heteroscedasticity in the data and we need to transform the independent variable to solve for this.

Option A is correct.