ISYE 6414 Regression Analysis - Solution_Endterm Closed Book Section - Part 1_ Regression Analysis -

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Endterm Closed Book Section - Part 1 Due Jul 28 at 10:59pm Points 40 Questions 30 Available Jul 22 at 7am - Jul 28 at 10:59pm 7 days Time Limit 90 Minutes

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Each question in the closed book portion of the exam (including the multiple choice) has exactly 1 correct answer. You may use your computer's onscreen calculator app but may not use your phone calculator.

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Attempt History Attempt

Time

Score

LATEST

Attempt

Time

Score

Attempt 1

34 minutes

24 out of 40

Score for this quiz: 24 out of 40 Submitted Jul 24 at 9:10pm This attempt took 34 minutes.

Question 1

1 / 1 pts

We should always use mean squared error to determine the best value of lambda in lasso regression.

True Correct!

False

Question 2

1 / 1 pts

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

Correct!

True False

Question 3

0 / 1 pts

Goodness-of-fit assessment for logistic regression with replications involves checking for the independence, constant variance, and normality of the deviance residuals.

You Answered

True

orrect Answer

False

Question 4

1 / 1 pts

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.

Correct!

True False

Question 5

1 / 1 pts

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

True Correct!

False

Question 6

1 / 1 pts

A logistic regression model with high goodness of fit can have low predictive power.

Correct!

True False

Question 7

1 / 1 pts

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.

Correct!

True False

Question 8

1 / 1 pts

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.

True Correct!

False

Question 9

0 / 1 pts

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

orrect Answer

True

You Answered

False

Question 10

0 / 1 pts

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

You Answered

True

orrect Answer

False

Question 11

1 / 1 pts

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.

Correct!

True False

Question 12

1 / 1 pts

Maximum likelihood estimation produces unbiased coefficient estimates for logistic and Poisson regression.

Correct!

True False

Question 13

1 / 1 pts

If considering only BIC for the model selection criterion, a model with lower BIC is preferred over a model with higher BIC. Correct!

True False

Question 14

0 / 1 pts

If we do not penalize the training risk, our variable selection method would always prefer more complex models. orrect Answer

True

You Answered

False

Question 15

1 / 1 pts

One goal of variable selection is to balance the bias-variance tradeoff when making predictions.

Correct!

True False

Question 16

1 / 1 pts

Forward stepwise selection is computationally more expensive than backward stepwise selection because it takes more iterations to terminate.

True Correct!

False

Question 17

0 / 1 pts

When testing for the significance of a subset of predictors, the null hypothesis is that all coefficients for variables in that subset are 0 and the alternative is that all those coefficients are not 0.

You Answered

True

orrect Answer

False

Question 18

1 / 1 pts

Classification error estimated from leave-one-out cross validation tends to have higher bias but lower variability than classification error estimated from 2-fold cross validation.

True Correct!

False

Question 19

0 / 1 pts

One reasonable method for variable selection is to fit the full model and then drop all variables with a high p-value in that full model.

You Answered

True

orrect Answer

False

Question 20

1 / 1 pts

The logit link is the only link function that yields s-shaped curves.

True Correct!

False

Question 21 Recall the formula for adjusted R-squared is

2 / 2 pts

Which of the following is TRUE about adjusted R-squared?

Correct!

The adjusted R2 can be used to compare models, and its value will always be less than or equal to that of R2.

The adjusted R2 cannot be used to compare models, and its value will always be less than or equal to that of R2.

The adjusted R2 can be used to compare models, and its value will always be greater than or equal to that of R2.

The adjusted R2 cannot be used to compare models, and its value will always be greater than or equal to that of R2.

Question 22

0 / 2 pts

Mary has a dataset with height (in inches), weight (in lbs), and math_score (final exam score out of 100) of 300 students in an undergraduate math course. She creates another field called BMI (Body Mass Index) calculated as BMI=703*(weight/height2). She wants to examine if math_score is related to height, weight and BMI. She plans to use a linear regression model math_score ~ height+weight+BMI to study this relationship.

Leonard hears about Mary’s plan and tells Mary that BMI should not be used in her experiment because it is created from the height and weight variables which are already included in the model. He says this leads to an issue called multicollinearity in linear regression.

Which of the below options is TRUE?

Leonard is right; retaining height, weight, BMI in the model will definitely lead to multicollinearity.

orrect Answer Leonard is wrong because BMI is not a linear combination of weight and height.

You Answered Leonard is wrong; it is impossible to say whether multicollinearity is a problem in a proposed model without first fitting the model.

Leonard is right, but the correct name for this issue is homoscedasticity.

Question 23

0 / 2 pts

When working to create a logistic regression model, an analyst is considering two models: Model one with only one predicting variable A. Model two includes predicting variable B in addition to variable A. The analyst notices that the sign of the estimated coefficient for A is negative in model one and positive in model two. This is most likely because:

A is significant in Model two B is significant on Model two You Answered

A is a confounding variable

orrect Answer

B is correlated with A

2 / 2 pts

Question 24

The regression glm(Y~X, family=poisson) was fitted to count data, resulting in the estimate of

to be 16 and the estimate of

to be 9.4. For a one unit

increase in X,

the rate increases by 9.4 units.

Correct!

the log rate increases by 9.4 units.

the log rate increases by exp(9.4) units.

the rate increases by exp(9.4) percent

Question 25

2 / 2 pts

Which of the following is correct?

Correct!

Lasso regression uses the L1 norm.

Ridge regression uses the L0 norm.

Ridge regression performs variable selection.

Elastic net does not perform variable selection.

Question 26

0 / 2 pts

A data point with predictor and response values three orders of magnitude higher than the corresponding values of all other observations is for certain

orrect Answer

an outlier with respect to the data

You Answered

an influential point but not an outlier

an erroneous data point None of the above

Question 27

0 / 2 pts

In simple linear regression, what is the relation between the correlation coefficient

and R-squared?

= R-squared orrect Answer

= sqrt(R-squared)

= R-squared + Adjusted R-squared You Answered

There is no relation between the two

Question 28 High VIF (> 10) value for predictors in linear regression suggests

homoscedasticity. orrect Answer

multicollinearity.

You Answered

autocorrelation.

0 / 2 pts

non-Linear relation between dependent and independent variables.

Question 29

2 / 2 pts

Which of the following is true regarding logistic regression?

Logistic regression can also be replaced by standard linear regression if with repetitions

Logistic regression can only be used with continuous predicting variables.

Logistic regression can only be used when the response variable is binary.

Correct!

The logit link is the canonical link function.

Question 30

2 / 2 pts

Which of the following is correct?

Overdispersion is a concern for Poisson regression but not for logistic regression.

For both logistic and Poisson regression, the variance of the response equals the expectation of the response given the predicting variables.

Correct!

Overdispersion affects the reliability of our statistical inferences if not modeled correctly.

Under overdispersion, the observed variance is smaller than the variance implied by our model.

Quiz Score: 24 out of 40