Final Exam – Part 1 Solutions

Final Exam – Part 1 Solutions

1. We should always use mean squared error to determine the best value of lambda in lasso
regression.
a. True
b. False

Sol: False. The criterion used is a choice we make.

2. Standard linear regression is an example of a generalized linear model where the response is
normally distributed and the link is the identity function.
a. True
b. False

Sol: True. See Unit 4.4.1.

3. Goodness-of-fit assessment for logistic regression involves checking for the independence,
constant variance, and normality of the deviance residuals.
a. True
b. False

Sol: False. We don’t have constant variance in binomial regression.

4. You are interested in understanding the relationship between stress level and exercise, with
stress as the response. In your model, the number of hours a person spends exercising per week
would be considered an explanatory variable while the person’s age would be a controlling
variable.
a. True
b. False

Sol: True. Time spent exercising is part of the relationship you are trying to understand while age
could act as a confounding variable that you need to control.

5. The hypothesis test for goodness-of-fit using Pearson residuals and the test using deviance
residuals will always reach the same conclusion.
a. True
b. False

Sol: False. One test may conclude plausibly good fit while the other rejects it.

6. A logistic regression model with high goodness of fit can have low predictive power.
a. True
b. False

Sol: True. See Unit 4.2.3.




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, 7. If we apply a Poisson regression model using a small sample size, the estimators of the
regression coefficient may not follow an approximate Normal distribution, affecting the
reliability of the statistical inference on the coefficients.
a. True
b. False

Sol: True. See Unit 4.2.1.

8. You fit a regression model using three predictors. You notice the estimated coefficient for
predictor X1 is an order of magnitude larger than the estimated coefficient for predictor X2. It is
correct to conclude that X1 has a greater effect on the response than X2.
a. True
b. False

Sol: False. We do not know that the variables are on the same scale in order to directly compare
them. We can only conclude that a 1-unit change in X1 is associated with a greater change in the
response than a 1-unit change in X2 holding other variables constant.

9. Regularized regression with a lambda value equal to 0 is equivalent to regression model
estimation without penalization.
a. True
b. False

Sol: True. See Unit 5.2.2.

10. In a Poisson regression model, the difference between the null deviance and residual deviance
follows a normal distribution.
a. True
b. False

Sol: False. It follows a Chi-square distribution (this is used to check the overall regression
significance).

11. You want to examine the relationship between study time and score on exams. You create five
exams and recruit 50 participants. For each participant in your study, you record their time
studying for and grade on each of those five exams. If you were to use all the data you recorded
to build a simple linear regression model, you would violate the independence assumption.
a. True
b. False

Sol: True. Because you are collecting 5 observations from each person, the observations coming
from the same person would be correlated. Similarly, all observations from the same test may
be correlated.

12. Maximum likelihood estimation produces unbiased coefficient estimates for logistic and Poisson
regression.
a. True
b. False




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