Question 1

A company wants to predict monthly sales (in thousands of dollars) based on advertising expenditure (in thousands of dollars). The regression output in EXCEL gives the following equation: $$	ext{Sales} = 50 + 8 	imes 	ext{Advertising}. $$What does the coefficient 8 represent in this context?

Accepted Answer

For every additional $$1,000 spent on advertising, sales increase by 8$$,000.

Question 2

Suppose the regression output for predicting house prices based on square footage gives an $$R^2$$ value of 0.85. What does this $$R^2$$ value indicate?

Accepted Answer

$$85\% of $$the variation in house prices is explained by the variation in square footage.

Question 3

A regression analysis is performed to predict employee productivity (Y) from years of experience (X). The 95% confidence interval for the slope coefficient is $$[1.2, 2.8]. $$What does this interval mean?

Accepted Answer

We are 95% confident that each additional year of experience increases productivity by between 1.2 and 2.8 units.

Question 4

Which of the following is NOT an assumption of the classical linear regression model?

Accepted Answer

The independent variable is normally distributed.

Question 5

You run a regression and obtain the following residual plot: the residuals fan out as the predicted values increase. What does this suggest?

Accepted Answer

The assumption of constant variance (homoscedasticity) is violated.

Question 6

A regression model is used to predict exam scores based on hours studied. The p-value for the overall F-test is 0.002. What does this indicate?

Accepted Answer

There is strong evidence that the regression model explains a significant amount of variation in exam scores.

Question 7

In a regression output, the p-value for the slope coefficient of a variable is 0.45. What is the correct interpretation?

Accepted Answer

There is insufficient evidence to conclude that this variable is a significant predictor of the dependent variable.

Question 8

A company wants to predict employee salary based on education level (Bachelor's, Master's, PhD). How should education level be included in a regression model?

Accepted Answer

By creating dummy variables for each education category (except one as the reference group).

Question 9

Suppose you have the regression equation $$\hat{Y} = 10 + 3X_1 + 5X_2$$, where $$X_1 is $$years of experience and $$X_2 is a $$dummy variable for gender (1 = male, 0 = female). What is the predicted value for a female with 4 years of experience?

Accepted Answer

$$\22$

Question 10

A regression model is used to predict the number of defective products based on machine age. The 95% confidence interval for the predicted number of defects for a 5-year-old machine is $$[8, 12]. $$What does this interval mean?

Accepted Answer

We are 95% confident that the mean number of defects for all 5-year-old machines is between 8 and 12.

Question 11

Which of the following best describes the purpose of residual analysis in regression?

Accepted Answer

To check whether the assumptions of the regression model are satisfied.

Question 12

A regression model is built to predict monthly electricity usage based on temperature and number of occupants. The $$R^2 is 0.60. $$What does this mean in practical terms?

Accepted Answer

60% of the variation in monthly electricity usage is explained by temperature and number of occupants.

Question 13

You are testing whether the variable 'training hours' is a significant predictor of employee performance. The null hypothesis is $$H_0$$: \$$beta_1 = 0$. The t-statistic is 3.5 and the p-value is 0.001. What is the correct conclusion at the 5% significance level?

Accepted Answer

Reject $$H_0$$; training hours is a significant predictor of employee performance.

Question 14

A regression model is used to predict car price based on mileage and age. The regression output shows a negative coefficient for mileage. What does this mean?

Accepted Answer

As mileage increases, the predicted car price decreases, holding age constant.

Question 15

Suppose you want to predict the sales of a new product using a regression model. The model's 95% prediction interval for a single new observation is $$[120, 180]. $$What does this interval mean?

Accepted Answer

We are 95% confident that the sales of a single new product will fall between 120 and 180.

Question 16

A regression model is used to predict the time to complete a project based on the number of team members and project complexity. The F-test for the overall model has a p-value of 0.08. What is the correct interpretation at the 5% significance level?

Accepted Answer

There is insufficient evidence to conclude that the model explains a significant amount of variation in project completion time.

Question 17

You are building a regression model to predict customer satisfaction (Y) from service speed (X1) and friendliness (X2). The regression equation is $$\hat{Y} = 2 + 0.5X_1 + 1.2X_2. $$What is the predicted satisfaction score for a customer who rates service speed as 4 and friendliness as 3?

Accepted Answer

$$7.6$$

Question 18

Which of the following statements about dummy variables in regression is TRUE?

Accepted Answer

A dummy variable takes the value 0 or 1 to indicate the absence or presence of a categorical effect.

Question 19

A regression model is used to predict monthly rent based on apartment size and location (urban or suburban). The dummy variable for location is coded as 1 for urban and 0 for suburban. The coefficient for location is 200. What does this mean?

Accepted Answer

Urban apartments are predicted to have $$\200$ higher rent than suburban apartments, holding size constant.

Exam Review: Regression Analysis and Chi-Square/Nonparametric Tests

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