Question 1

Which of the following best describes heteroscedasticity in the context of regression analysis?

Accepted Answer

Errors have different amounts of variation across levels of the explanatory variable.

Question 2

A residual plot from a regression of home price on size shows a fan-shaped pattern. What does this indicate?

Accepted Answer

The variance of errors increases with home size, indicating heteroscedasticity.

Question 3

What is the main consequence of ignoring heteroscedasticity in a regression model?

Accepted Answer

Prediction and confidence intervals may be too narrow or too wide, making hypothesis tests unreliable.

Question 4

Given the regression equation $$	ext{Price} = F + M 	imes 	ext{Size}$$, how can you revise the model to address changing variation in the errors?

Accepted Answer

Use price per square foot as the response and the reciprocal of size as the explanatory variable.

Question 5

In the context of regression diagnostics, what is a leveraged observation?

Accepted Answer

An observation with an extreme value of the explanatory variable that can pull the regression line toward itself.

Question 6

A contractor is analyzing bids for home additions. Including a 900 sq ft project (an outlier) in the regression increases the estimated fixed cost by about 1.5 standard errors. What should the contractor do?

Accepted Answer

Include the outlier only if it represents what is expected in future projects.

Question 7

Which of the following is a correct interpretation of the slope in the regression $$	ext{Price} = 50.599 + 0.159 	imes 	ext{Size}$$?

Accepted Answer

The average increase in home price for each additional square foot.

Question 8

What does the Durbin-Watson statistic test in regression diagnostics?

Accepted Answer

Whether adjacent residuals are uncorrelated (no autocorrelation).

Question 9

If the Durbin-Watson statistic $$D is $$approximately 2, what does this indicate?

Accepted Answer

The residuals are uncorrelated.

Question 10

Suppose you fit a regression model to time series data and the residuals show a clear pattern over time. What is the most appropriate next step?

Accepted Answer

Incorporate the dependence into the regression model.

Question 11

Which of the following is a consequence of positive autocorrelation in regression errors?

Accepted Answer

Estimated standard errors are too small, making slope and intercept estimates less precise.

Question 12

Why might a revised regression model with a lower $$R^2$$ still be preferred over the original model?

Accepted Answer

It provides more reliable and narrower confidence and prediction intervals.

Question 13

Given the following 95% confidence interval for the intercept: $$-4,000 to$$ $$105,000$$, what does this suggest about the estimate of fixed costs?

Accepted Answer

The interval includes zero, so the estimate is not precise.

Question 14

Which of the following best describes homoscedastic errors?

Accepted Answer

Errors have equal amounts of variation across all levels of the explanatory variable.

Question 15

A boxplot of residuals by home size category shows increasing spread as size increases. What does this indicate?

Accepted Answer

The errors are heteroscedastic.

Question 16

If a prediction interval for a small home is much wider than for a large home, what problem might this indicate in the regression model?

Accepted Answer

Heteroscedasticity.

Question 17

Which of the following is NOT a recommended way to address an outlier in regression analysis?

Accepted Answer

Exclude the outlier without justification.

Question 18

What is the null hypothesis tested by the Durbin-Watson statistic?

Accepted Answer

$$H_0$$: \rho_\varepsilon = 0$$

Question 19

A regression model for home prices has $$R^2 = 0.6545$ and s_e = 91.05$. What does s_e$ represent?

Accepted Answer

The estimated standard deviation of the residuals.

Chapter 22: Regression Diagnostics – Business Statistics Study Notes

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