Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

There is evidence of heteroscedasticity.

Question 3

Given the regression equation $$	ext{Price} = F + M 	imes 	ext{SqFt} + \varepsilon$$, what does the intercept $$F$$ represent in the context of home prices?

Accepted Answer

The fixed cost of a home.

Question 4

Why might the 95% confidence interval for the intercept in a regression model be considered unreliable if it includes zero?

Accepted Answer

Because it suggests the fixed cost could be negative or not significantly different from zero.

Question 5

If a regression model’s residuals show increasing variance with the explanatory variable, what is a recommended way to revise the model?

Accepted Answer

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

Question 6

What is the main consequence of ignoring heteroscedasticity in regression analysis?

Accepted Answer

Prediction and confidence intervals may be too narrow or too wide, leading to unreliable inference.

Question 7

In the revised home price model, $$	ext{Estimated } \$$/	ext{SqFt} = 157.753 + \frac{53,887}{	ext{SqFt}}$, what does the slope represent?

Accepted Answer

The fixed cost associated with the home.

Question 8

A contractor’s data set contains one project much larger than the others, which pulls the regression line toward it. This observation is best described as:

Accepted Answer

A leveraged outlier.

Question 9

What is the effect of including a leveraged outlier in a regression analysis?

Accepted Answer

It can shift the estimated intercept and slope by more than one standard error, making predictions less reliable.

Question 10

Which of the following is the correct formula for the Durbin-Watson statistic used to detect autocorrelation in regression residuals?

Accepted Answer

$$D = \frac{\sum_{i=2}^n (e_i - e_{i-1})^2$}{\sum_{i=1}^n e_i^2$}$$

Question 11

If the Durbin-Watson statistic is much less than 2, what does this indicate about the regression residuals?

Accepted Answer

There is positive autocorrelation among the residuals.

Question 12

In a time series regression, what is a consequence of positive autocorrelation in the errors?

Accepted Answer

Estimated standard errors are too small, making confidence intervals and hypothesis tests unreliable.

Question 13

Why might a model with a lower $$R^2$$ still be preferred over one with a higher $$R^2 in $$the context of regression diagnostics?

Accepted Answer

Because it provides more reliable and sensible confidence and prediction intervals when model assumptions are met.

Question 14

A company wants to estimate home prices for budgeting. Why is it important to distinguish between fixed and marginal costs in the regression model?

Accepted Answer

To separately estimate the base cost of a home and the additional cost per square foot, aiding in more accurate budgeting.

Question 15

Which of the following is NOT a recommended diagnostic step when evaluating a regression model?

Accepted Answer

Ignoring outliers if $$R^2 is $$high.

Question 16

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

Accepted Answer

An observation with an extreme value of the explanatory variable that can strongly influence the regression line.

Question 17

Suppose you fit a regression model to predict cell phone subscribers over time, but the residuals show a clear pattern when plotted against time. What should you conclude?

Accepted Answer

There is evidence of dependence (autocorrelation) in the errors, so statistical inference may not be reliable.

Question 18

If a 95% prediction interval for a 1,000 sq ft home is much wider than for a 3,000 sq ft home in a regression model, what does this suggest about the model?

Accepted Answer

The model may have heteroscedastic errors, with prediction intervals not reflecting true uncertainty.

Question 19

Which of the following is a correct interpretation of a 95% confidence interval for the slope in a regression model?

Accepted Answer

We are 95% confident that the true marginal cost per unit increase in the explanatory variable lies within the interval.

Regression Diagnostics: Changing Variation, Outliers, and Dependent Errors

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