ISYE 6414 Regression Analysis Midterm
Exam 2 - Open Book Section (R) Part 2 |
Concrete Data, Logistic Regression &
Goodness-of-Fit Complete Solutions |
2026/2027 Updated - Georgia Tech
Practice Question Bank & Answer Rationale
THIS PACK CONTAINS
98 exam-style multiple-choice questions. Each question includes the correct answer and a complete rationale
for focused revision.
COVERAGE
This exam covers logistic regression (binary and multinomial), goodness-of-fit testing (Hosmer-Lemeshow,
deviance, Pearson), model diagnostics and remedial measures, variable selection, and regression with time
series data, all analyzed in R with concrete datasets. Emphasis is on interpreting output, assessing model
adequacy, and making correct inferential decisions under open-book conditions.
STUDY GUIDE
Recommended duration: 2 hours 50 minutes (open book, R allowed). Passing target: 70% (B- or higher for
graduate credit).
HIGHP - Page 1 of 33
,1. In a logistic regression with a single continuous predictor, the estimated coefficient is
0.35. What is the correct interpretation of exp(0.35) in terms of odds?
[ ] A. The odds of success increase by 0.35 for a one-unit increase in the predictor.
[ ] B. The odds of success multiply by approximately 1.42 for a one-unit increase in the predictor.
[ ] C. The probability of success increases by 0.35 for a one-unit increase in the predictor.
[ ] D. The log-odds of success increase by 0.35% for a one-unit increase in the predictor.
CORRECT: B. The odds of success multiply by approximately 1.42 for a one-unit increase in the
predictor.
exp(0.35) 1.42, so the odds are multiplied by 1.42 per unit increase. Option A confuses the additive change
in log-odds with odds; C confuses odds with probability; D misstates the log-odds change as a percentage.
2. A logistic regression model yields a deviance of 45.2 on 30 degrees of freedom. Which
conclusion is most appropriate?
[ ] A. The model fits well because deviance is close to the degrees of freedom.
[ ] B. There is evidence of overdispersion because deviance substantially exceeds the degrees of
freedom.
[ ] C. The model is underdispersed because deviance is less than twice the degrees of freedom.
[ ] D. The deviance test is invalid for logistic regression; only Pearson chi-square should be used.
CORRECT: B. There is evidence of overdispersion because deviance substantially exceeds the
degrees of freedom.
For a well-fitting model, deviance df. Here 45.2 is 1.5 times 30, suggesting overdispersion. A is incorrect
because deviance is not close to df; C misinterprets underdispersion; D is false-deviance is a standard
goodness-of-fit measure.
3. In a multiple linear regression, a plot of residuals versus fitted values shows a funnel
shape. Which remedial measure is most appropriate?
[ ] A. Add a quadratic term to the model.
[ ] B. Apply a variance-stabilizing transformation to the response, such as log or square root.
[ ] C. Remove influential outliers and refit the model.
[ ] D. Use weighted least squares with weights proportional to the fitted values.
CORRECT: B. Apply a variance-stabilizing transformation to the response, such as log or square
root.
A funnel shape indicates nonconstant variance (heteroscedasticity). A variance-stabilizing transformation
(e.g., log or Box-Cox) is a standard remedy. Adding a quadratic term addresses curvature, not
heteroscedasticity; removing outliers may not fix systematic variance change; weighted least squares with
weights proportional to fitted values is incorrect (weights should be inversely proportional to variance).
HIGHP - Page 2 of 33
,4. When comparing two nested logistic regression models using a likelihood ratio test, the
test statistic is 6.8 with 2 degrees of freedom. What is the correct conclusion at = 0.05?
[ ] A. Fail to reject the null; the reduced model is preferred.
[ ] B. Reject the null; the full model provides a significantly better fit.
[ ] C. The test is inconclusive because the models are not nested.
[ ] D. Reject the null only if the AIC of the full model is lower.
CORRECT: B. Reject the null; the full model provides a significantly better fit.
The critical value for ²(2) at =0.05 is 5.99; 6.8 > 5.99, so reject the null. The full model is significantly better. A
is incorrect because the statistic exceeds the critical value; C is false-the models are nested; D confuses the
LRT with AIC comparison, which is a different criterion.
5. In a time series regression, the Durbin-Watson statistic is 1.2. What does this indicate
about the errors?
[ ] A. No autocorrelation.
[ ] B. Positive autocorrelation.
[ ] C. Negative autocorrelation.
[ ] D. Heteroscedasticity.
CORRECT: B. Positive autocorrelation.
Durbin-Watson values range from 0 to 4; values below 2 indicate positive autocorrelation. A value of 1.2 is
substantially below 2, suggesting positive autocorrelation. A is incorrect because 1.2 is not near 2; C would
be indicated by values above 2; D is unrelated-DW detects autocorrelation, not heteroscedasticity.
6. Which of the following is a key assumption of logistic regression that distinguishes it
from linear regression?
[ ] A. The errors are normally distributed.
[ ] B. The response variable is continuous.
[ ] C. The log-odds of the response is a linear function of the predictors.
[ ] D. The variance of the response is constant across all predictor levels.
CORRECT: C. The log-odds of the response is a linear function of the predictors.
Logistic regression assumes the logit (log-odds) is linear in the predictors. A is false-errors are binomial, not
normal; B is false-the response is binary; D is false-the variance depends on the mean (p(1-p)), so it is not
constant.
7. In a multiple linear regression with 5 predictors and 40 observations, the VIF for
predictor X is 12. What is the most appropriate action?
[ ] A. Remove X from the model because it is not significant.
[ ] B. Investigate multicollinearity and consider removing or combining correlated predictors.
HIGHP - Page 3 of 33
, [ ] C. Increase the sample size to reduce the VIF.
[ ] D. Ignore it because VIF only matters if the overall F-test is significant.
CORRECT: B. Investigate multicollinearity and consider removing or combining correlated
predictors.
A VIF of 12 exceeds the common threshold of 10, indicating serious multicollinearity. The best action is to
investigate correlations and consider remedial measures. A is incorrect-high VIF does not imply
insignificance; C is impractical and does not directly address the issue; D is false-VIF affects coefficient
stability regardless of the F-test.
8. In a logistic regression with a categorical predictor having 4 levels, how many dummy
variables are needed, and what is the interpretation of the intercept?
[ ] A. 4 dummy variables; intercept is the log-odds for the first level.
[ ] B. 3 dummy variables; intercept is the log-odds for the reference level.
[ ] C. 4 dummy variables; intercept is the average log-odds across all levels.
[ ] D. 3 dummy variables; intercept is the log-odds for the last level.
CORRECT: B. 3 dummy variables; intercept is the log-odds for the reference level.
For a categorical predictor with k levels, k-1 dummy variables are needed. The intercept represents the
log-odds for the reference category. A and C are incorrect because 4 dummies would cause perfect
collinearity; D is incorrect because the intercept corresponds to the reference level (usually the first), not the
last.
9. A Hosmer-Lemeshow test for a logistic regression model yields a p-value of 0.03. What
is the correct interpretation?
[ ] A. The model fits well because the p-value is less than 0.05.
[ ] B. There is evidence of lack of fit; the model may not be adequate.
[ ] C. The test is not valid for large sample sizes.
[ ] D. The model is overdispersed.
CORRECT: B. There is evidence of lack of fit; the model may not be adequate.
The Hosmer-Lemeshow test assesses goodness-of-fit; a small p-value (0.05) indicates significant lack of fit.
A is a common misinterpretation; C is false-the test is valid but sensitive to sample size; D is
unrelated-overdispersion is assessed via deviance or Pearson chi-square.
10. In a time series regression, the errors exhibit autocorrelation. Which remedial measure
is most appropriate?
[ ] A. Add lagged dependent variables or use autoregressive error models.
[ ] B. Apply a log transformation to the response.
[ ] C. Remove outliers and refit the model.
[ ] D. Use robust standard errors to correct for autocorrelation.
HIGHP - Page 4 of 33
Exam 2 - Open Book Section (R) Part 2 |
Concrete Data, Logistic Regression &
Goodness-of-Fit Complete Solutions |
2026/2027 Updated - Georgia Tech
Practice Question Bank & Answer Rationale
THIS PACK CONTAINS
98 exam-style multiple-choice questions. Each question includes the correct answer and a complete rationale
for focused revision.
COVERAGE
This exam covers logistic regression (binary and multinomial), goodness-of-fit testing (Hosmer-Lemeshow,
deviance, Pearson), model diagnostics and remedial measures, variable selection, and regression with time
series data, all analyzed in R with concrete datasets. Emphasis is on interpreting output, assessing model
adequacy, and making correct inferential decisions under open-book conditions.
STUDY GUIDE
Recommended duration: 2 hours 50 minutes (open book, R allowed). Passing target: 70% (B- or higher for
graduate credit).
HIGHP - Page 1 of 33
,1. In a logistic regression with a single continuous predictor, the estimated coefficient is
0.35. What is the correct interpretation of exp(0.35) in terms of odds?
[ ] A. The odds of success increase by 0.35 for a one-unit increase in the predictor.
[ ] B. The odds of success multiply by approximately 1.42 for a one-unit increase in the predictor.
[ ] C. The probability of success increases by 0.35 for a one-unit increase in the predictor.
[ ] D. The log-odds of success increase by 0.35% for a one-unit increase in the predictor.
CORRECT: B. The odds of success multiply by approximately 1.42 for a one-unit increase in the
predictor.
exp(0.35) 1.42, so the odds are multiplied by 1.42 per unit increase. Option A confuses the additive change
in log-odds with odds; C confuses odds with probability; D misstates the log-odds change as a percentage.
2. A logistic regression model yields a deviance of 45.2 on 30 degrees of freedom. Which
conclusion is most appropriate?
[ ] A. The model fits well because deviance is close to the degrees of freedom.
[ ] B. There is evidence of overdispersion because deviance substantially exceeds the degrees of
freedom.
[ ] C. The model is underdispersed because deviance is less than twice the degrees of freedom.
[ ] D. The deviance test is invalid for logistic regression; only Pearson chi-square should be used.
CORRECT: B. There is evidence of overdispersion because deviance substantially exceeds the
degrees of freedom.
For a well-fitting model, deviance df. Here 45.2 is 1.5 times 30, suggesting overdispersion. A is incorrect
because deviance is not close to df; C misinterprets underdispersion; D is false-deviance is a standard
goodness-of-fit measure.
3. In a multiple linear regression, a plot of residuals versus fitted values shows a funnel
shape. Which remedial measure is most appropriate?
[ ] A. Add a quadratic term to the model.
[ ] B. Apply a variance-stabilizing transformation to the response, such as log or square root.
[ ] C. Remove influential outliers and refit the model.
[ ] D. Use weighted least squares with weights proportional to the fitted values.
CORRECT: B. Apply a variance-stabilizing transformation to the response, such as log or square
root.
A funnel shape indicates nonconstant variance (heteroscedasticity). A variance-stabilizing transformation
(e.g., log or Box-Cox) is a standard remedy. Adding a quadratic term addresses curvature, not
heteroscedasticity; removing outliers may not fix systematic variance change; weighted least squares with
weights proportional to fitted values is incorrect (weights should be inversely proportional to variance).
HIGHP - Page 2 of 33
,4. When comparing two nested logistic regression models using a likelihood ratio test, the
test statistic is 6.8 with 2 degrees of freedom. What is the correct conclusion at = 0.05?
[ ] A. Fail to reject the null; the reduced model is preferred.
[ ] B. Reject the null; the full model provides a significantly better fit.
[ ] C. The test is inconclusive because the models are not nested.
[ ] D. Reject the null only if the AIC of the full model is lower.
CORRECT: B. Reject the null; the full model provides a significantly better fit.
The critical value for ²(2) at =0.05 is 5.99; 6.8 > 5.99, so reject the null. The full model is significantly better. A
is incorrect because the statistic exceeds the critical value; C is false-the models are nested; D confuses the
LRT with AIC comparison, which is a different criterion.
5. In a time series regression, the Durbin-Watson statistic is 1.2. What does this indicate
about the errors?
[ ] A. No autocorrelation.
[ ] B. Positive autocorrelation.
[ ] C. Negative autocorrelation.
[ ] D. Heteroscedasticity.
CORRECT: B. Positive autocorrelation.
Durbin-Watson values range from 0 to 4; values below 2 indicate positive autocorrelation. A value of 1.2 is
substantially below 2, suggesting positive autocorrelation. A is incorrect because 1.2 is not near 2; C would
be indicated by values above 2; D is unrelated-DW detects autocorrelation, not heteroscedasticity.
6. Which of the following is a key assumption of logistic regression that distinguishes it
from linear regression?
[ ] A. The errors are normally distributed.
[ ] B. The response variable is continuous.
[ ] C. The log-odds of the response is a linear function of the predictors.
[ ] D. The variance of the response is constant across all predictor levels.
CORRECT: C. The log-odds of the response is a linear function of the predictors.
Logistic regression assumes the logit (log-odds) is linear in the predictors. A is false-errors are binomial, not
normal; B is false-the response is binary; D is false-the variance depends on the mean (p(1-p)), so it is not
constant.
7. In a multiple linear regression with 5 predictors and 40 observations, the VIF for
predictor X is 12. What is the most appropriate action?
[ ] A. Remove X from the model because it is not significant.
[ ] B. Investigate multicollinearity and consider removing or combining correlated predictors.
HIGHP - Page 3 of 33
, [ ] C. Increase the sample size to reduce the VIF.
[ ] D. Ignore it because VIF only matters if the overall F-test is significant.
CORRECT: B. Investigate multicollinearity and consider removing or combining correlated
predictors.
A VIF of 12 exceeds the common threshold of 10, indicating serious multicollinearity. The best action is to
investigate correlations and consider remedial measures. A is incorrect-high VIF does not imply
insignificance; C is impractical and does not directly address the issue; D is false-VIF affects coefficient
stability regardless of the F-test.
8. In a logistic regression with a categorical predictor having 4 levels, how many dummy
variables are needed, and what is the interpretation of the intercept?
[ ] A. 4 dummy variables; intercept is the log-odds for the first level.
[ ] B. 3 dummy variables; intercept is the log-odds for the reference level.
[ ] C. 4 dummy variables; intercept is the average log-odds across all levels.
[ ] D. 3 dummy variables; intercept is the log-odds for the last level.
CORRECT: B. 3 dummy variables; intercept is the log-odds for the reference level.
For a categorical predictor with k levels, k-1 dummy variables are needed. The intercept represents the
log-odds for the reference category. A and C are incorrect because 4 dummies would cause perfect
collinearity; D is incorrect because the intercept corresponds to the reference level (usually the first), not the
last.
9. A Hosmer-Lemeshow test for a logistic regression model yields a p-value of 0.03. What
is the correct interpretation?
[ ] A. The model fits well because the p-value is less than 0.05.
[ ] B. There is evidence of lack of fit; the model may not be adequate.
[ ] C. The test is not valid for large sample sizes.
[ ] D. The model is overdispersed.
CORRECT: B. There is evidence of lack of fit; the model may not be adequate.
The Hosmer-Lemeshow test assesses goodness-of-fit; a small p-value (0.05) indicates significant lack of fit.
A is a common misinterpretation; C is false-the test is valid but sensitive to sample size; D is
unrelated-overdispersion is assessed via deviance or Pearson chi-square.
10. In a time series regression, the errors exhibit autocorrelation. Which remedial measure
is most appropriate?
[ ] A. Add lagged dependent variables or use autoregressive error models.
[ ] B. Apply a log transformation to the response.
[ ] C. Remove outliers and refit the model.
[ ] D. Use robust standard errors to correct for autocorrelation.
HIGHP - Page 4 of 33
