Question 1

Suppose you are analyzing the effect of advertising spending (in $$1000s) and number of salespeople on monthly sales (in 1000s) $$using a multiple regression model. The estimated regression equation is $$\hat{y} = 50 + 2x_1 + 3x_2$$, where $$x_1 is $$advertising and $$x_2 is $$number of salespeople. What is the correct interpretation of the coefficient 2 for $$x_1$$?

Accepted Answer

For each additional $1000 spent on advertising, monthly sales are expected to increase by 2 units, holding the number of salespeople constant.

Question 2

In a multiple regression model, what happens to the sum of squared errors (SSE) when you add an additional regressor to the model?

Accepted Answer

SSE will either decrease or stay the same, but never increase.

Question 3

Which of the following best describes the purpose of the adjusted $$R^2 in $$multiple regression?

Accepted Answer

It adjusts the $$R^2$$ value to account for the number of predictors in the model, penalizing the addition of unnecessary variables.

Question 4

You are testing the significance of a single regressor in a multiple regression model. Which test statistic should you use?

Accepted Answer

The t-test statistic: $$t = \frac{b_1$}{S_{b_1$}}$$

Question 5

A company wants to model the effect of education (in years), experience (in years), and gender (male=1, female=0) on salary. Which of the following is the correct way to include gender in the regression model?

Accepted Answer

Add a dummy variable for gender, where male=1 and female=0.

Question 6

Which of the following is a correct interpretation of the coefficient of a dummy variable for 'School of Major' (Business=1, Other=0) in a regression predicting starting salary?

Accepted Answer

It represents the expected difference in starting salary between business majors and other majors, holding other variables constant.

Question 7

When should you consider adding a quadratic term (e.g., $$x^2) to a $$regression model?

Accepted Answer

When the relationship between the independent variable and the dependent variable appears to be non-linear.

Question 8

Suppose your regression model includes an interaction term $$x_1$$ $$x_2. $$What does the coefficient of this term represent?

Accepted Answer

The change in the effect of $$x_1 on$$ $$y$$ for a one-unit increase in $$x_2 ($$and vice versa), holding other variables constant.

Question 9

What is multicollinearity (collinearity) in the context of multiple regression?

Accepted Answer

A situation where two or more independent variables are highly correlated with each other.

Question 10

What is a potential consequence of multicollinearity in a regression model?

Accepted Answer

It can make it difficult to determine the individual effect of correlated predictors, leading to unstable coefficient estimates.

Question 11

Given the regression output: $$\hat{y} = 10 + 4x_1 - 2x_2$$, where $$x_1 is $$years of experience and $$x_2 is a $$dummy variable for gender (male=1, female=0), what is the predicted value of $$y$$ for a male with 5 years of experience?

Accepted Answer

$$10 + 4 	imes 5 - 2 	imes 1 = 28$$

Question 12

Which of the following is the correct formula for the total sum of squares (SST) in regression analysis?

Accepted Answer

$$SST = SSR + SSE$$

Question 13

You are testing the overall significance of a regression model with three predictors. Which test should you use?

Accepted Answer

The full F-test.

Question 14

Suppose you have a regression model with $$R^2 = 0.80$ and adjusted R^2$ = 0.75. $$What does this suggest about your model?

Accepted Answer

Some predictors may not be contributing much explanatory power, and the model may include unnecessary variables.

Question 15

A regression model includes the term $$0.5x - 0.02x^2$. What does the negative coefficient on x^2$ indicate about the relationship between x$ and y$?

Accepted Answer

The relationship is quadratic and opens downward, indicating diminishing returns as $$x$$ increases.

Question 16

Which of the following is NOT a correct step in conducting an individual significance test for a regression coefficient?

Accepted Answer

Calculate the F-statistic for the overall model.

Question 17

If you want to test whether the effect of education on salary differs by gender, which term should you add to your regression model?

Accepted Answer

An interaction term: education $$	imes$$ gender

Question 18

A regression model is estimated as $$\hat{y} = 5 + 2x_1 + 3x_2 + 1.5x_1x_2. If$$ $$x_1 = 2$ and x_2$ = 1$$, what is the predicted value of $$y$$?

Accepted Answer

$$5 + 2 	imes 2 + 3 	imes 1 + 1.5 	imes 2 	imes 1 = 12$$

Question 19

Which of the following statements about $$R^2$$ and adjusted $$R^2 is $$correct?

Accepted Answer

Adjusted $$R^2$$ can decrease when a new variable is added to the model if the variable does not improve the model sufficiently.

Multiple Regression and Model Building: Study Notes for Business Statistics

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