Regression - Middle Units

Question 1

In multiple regression, we need the linearity assumption to hold for at least one of the predicting variables

Answer 1

False

Question 2

Multicollinearity in the predicting variables will impact the standard deviations of the estimated coefficients

Answer 2

True

Question 3

The presence of certain types of outliers can impact the statistical significance of some of the regression coefficients

Answer 3

True

Question 4

When making a prediction for predicting variables on the “Edge” of the space of predicting variables, then its uncertainty level is high

Answer 4

True

Question 5

The prediction of the response variable and the estimation of the mean response have the same interpretation

Answer 5

False (prediction has higher uncertainty than estimation)

Question 6

In multiple linear regression, a VIF value of 6 for a predictor means that 80% of the variation in that predictor can be modeled by the other predictors

Answer 6

False

Question 7

We can use a t-test to test for the statistical significance of a coefficient given all predicting variables in a multiple regression model

Answer 7

True

Question 8

Multicollinearity can lead to less accurate statistical significance of some of the regression coefficients

Answer 8

True

Question 9

The estimator of the mean response is unbiased

Answer 9

True

Question 10

The sampling distribution of the prediction of the response variable is a chi-squared distribution

Answer 10

False (In multiple linear regression, the sampling distribution of the prediction of the response variable is a t-distribution since the variance of the error term is not known.)

Question 11

Multicollinearity in multiple linear regression means that the rows in the design matrix are (nearly) linearly dependent

Answer 11

False

Question 12

A linear regression model has high predictive power if the coefficient of determination is close to 1

Answer 12

False

Question 13

In multiple linear regression, if the coefficient of a quantitative predicting variable is negative, that means the response variable will decrease as this predicting variable increases

Answer 13

False

Question 14

Cooks distance measures how much the fitted values (response) in the multiple linear regression model change when the ith observation is removed

Answer 14

True

Question 15

The prediction of the response variable has the same levels of uncertainty compared with the estimation of the mean response

Answer 15

False

Question 16

The coefficient of variation is used to evaluate goodness-of-fit

Answer 16

False

Question 17

Influential point in multiple linear regression are outliers

Answer 17

True

Question 18

We could diagnose the normality assumption using the normal probability plot

Answer 18

True

Question 19

If the VIF for each predicting variable is smaller than a certain threshold, then we can say that multicollinearity does not exist in this model

Answer 19

False

Question 20

If the residuals are not normally distributed, then we can model instead the transformed response variable where the common transformation for normality is the Box-Cox transformation

Answer 20

True

Question 21

If a logistic regression model provides accurate classification, then we can conclude that it is a good fit for the data

Answer 21

False

Question 22

The logit function is the log of the ratio of the probability of success to the probability of failure. It is also known as the log odds function

Answer 22

True

Question 23

We interpret logistic regression coefficients with respect to the response variable

Answer 23

False

Question 24

The likelihood function is a linear function with a closed-form solution

Answer 24

False

Question 25

In logistic regression, there is not a linear relationship between the probability of success and the predicting variables

Answer 25

True

Question 26

We can use a z-test to test for the statistical significance of a coefficient given all predicting variables in a Poisson regression model

Answer 26

True

Question 27

The number of parameters that need to be estimated in a logistic regression model with 5 predicting variables and an intercept is the same as the number of parameters that need to be estimated in a standard linear regression model with an intercept and same predicting variables.

Answer 27

False

Question 28

Although there are no error terms in a logistic regression model using binary data with replications, we can still perform residual analysis

Answer 28

True

Question 29

A goodness-of-fit test should always be conducted after fitting a logistic regression model without repetition

Answer 29

False

Question 30

For a classification model, training error tends to underestimate the true classification error rate of the model

Answer 30

True

Question 31

The binary response variable in logistic regression has a bernoulli distribution

Answer 31

True and false

Question 32

For logistic regression, if the p-value of the deviance test for goodness-of-fit is large, then it is an indication that the model is a good fit

Answer 32

True

Question 33

The error term in logistic regression has a normal distribution

Answer 33

False (the error term does not exist!)

Question 34

The estimated regression coefficients in Poisson regression are approximate

Answer 34

True

Question 35

In Poisson regression, there is a linear relationship between the log rate and the predicting variables

Answer 35

True

Question 36

Under logistic regression, the sampling distribution used for a coefficient estimator is a chi-square distribution

Answer 36

False (normal distribution)

Question 37

An over dispersion parameter close to 1 indicates that the variability of the response is close to the variability estimated by the model

Answer 37

True

Question 38

When testing a subset of coefficients, deviance follows a chi-square distribution with degrees of freedom, where q is the number of regression coefficients in the reduced model

Answer 38

False (q is the number of discarded coefficients)

Question 39

For both logistic and poisson regression, both the pearson and deviance residuals should approximately follow the standard normal distribution if the model is a good fit for the data

Answer 39

True

Question 40

The logit link function is the best link function to model binary response data because the models produced always fit the data better than other link functions

Answer 40

False

Question 41

If the non-constant variance assumption does not hold in multiple linear regression, we apply a transformation to the predicting variables

Answer 41

False (we apply a transformation to the response)

Question 42

Multicollinearity in multiple linear regression means that the columns in the design matrix are (nearly) linearly dependent

Answer 42

True

Question 43

In logistic regression, R_2 could be used as a measure of explained variation in the response variable

Answer 43

False

Question 44

The interpretation of the regression coefficients is the same for both logistic and poisson regression

Answer 44

False

Question 45

We estimate the regression coefficients in Poisson regression using the MLE approach

Answer 45

true

Question 46

The f-test can be used to test for the overall regression in poisson regression

Answer 46

False (perhaps chi-square)

Question 47

A logistic regression model may not be a good fit if the responses are correlated or if there is heterogeneity in the success that hasn’t been modeled

Answer 47

True

Question 48

Trying all three link functions for a logistic regression model (C-In-In, probit, logit) will produce models with the same goodness of fit for a dataset

Answer 48

False

Question 49

A poisson regression model fit to a dataset with a small sample size will have a hypothesis testing procedure with more Type I errors than expected

Answer 49

True

Question 50

If poisson regression model does not have a good fit, the relationship between the log of the expected rate and the predicting variables might not be linear

Answer 50

True

Question 51

R-squared decreases as more predictors are added to a multiple linear regression model, given that the predictors added are unrelated to the response variable

Answer 51

False

Question 52

In a multiple linear regression model, an observation should always be discarded when its Cook’s distance is greater than 4/n where n is the sample size

Answer 52

False

Question 53

A linear regression model is a good fit to the data set if the adjusted R-squared is above 0.85

Answer 53

False

Question 54

The sum or squares regression (SSR) measures the explained variability captured by the regression model given the explanatory variables used in the model

Answer 54

True

Question 55

The hypothesis testing procedure for subsets of regression coefficients is not used for GoF assessment in logistic regression

Answer 55

True

Question 56

Statistical inference for logistic regression is not reliable for small sample size

Answer 56

True

Question 57

In logistic regression, we can perform residual analysis for binary data with replications

Answer 57

True

Question 58

When assessing GoF for a logistic regression model on binary data with replications, the assumption is that the response variables come from a normal distribution

Answer 58

False (what dist?) (EH: I think they’re going for binomial/bernoulli here)

Question 59

The null hypothesis for the GoF test of a logistic regression model is that the model does not fit the data

Answer 59

False

Question 60

The threshold to calculate the classification error rate of a logistic regression model should always be set at 0.5

Answer 60

False

Question 61

Using leave one out cross validation is equivalent to k-fold cross validation where the number of folds is equal to the sample size of the training set

Answer 61

True

Question 62

the assumption of constant variance will always hold for standard linear regression models with poisson distributed response data

Answer 62

False

Question 63

since there are no error terms in poisson model, we cannot perform residual analysis for evaluating the model’s goodness of fit

Answer 63

False

Question 64

We can diagnose the constant variance assumption in Poisson regression using the normal probability plot

Answer 64

False

Question 65

In poisson regression, the expectation of the response variable given the predictors is equal to the linear combination of the predicting variables

Answer 65

False (the natural log of y is a linear combination)

Question 66

The variance of the response is equal to the expected value of the response in Poisson regression with no overdispersion

Answer 66

True

Question 67

A poisson regression model with p predictors and the intercept with have p+2 parameters to estimate

Answer 67

False (it’s p+1 because there’s no error term)

Question 68

If a Poisson regression model is found to be overdispersed, there is an indication that the variability of the response variable implied by the model is larger than the variability present in the observed response variable

Answer 68

False (overdispersion means the variability in the response variable is larger than the model indicates)

Question 69

In all the regression models we have considered (including multiple linear, logistic, and Poisson), the response variable is assumed to have a distribution from the exponential family of distributions.

Answer 69

True

Question 70

When considering using generalized linear models, it’s important to consider the impact of Simpson’s paradox when interpreting relationships between explanatory variables and the response. This paradox refers to the reversal of these associations when looking at a marginal relationship compared to a conditional one.

Answer 70

True