ISYE6414 (Regression) Midterm 2 Real Exam Questions With All Complete Answers.

What is cooks distance used for? - correct answer It measures how much all of the values in the regression model change with the ith observation is removed. Basically its a test for outliers Rule of thumb: D denotes cooks distance, if D is 4/n OR D 1 or any large D then it may be an outlier and should be removed. If the normality assumption does not hold, we can pursue a transformation in the response variable. T/F - correct answer True If the linearity assumption does not hold, we can pursue a transformation in the response variable. T/F - correct answer False, we pursue a transformation in the predictor variables. R^2 will always increase if we add more predicting variables. T/F - correct answer True If we want to compare models with different numbers of predicting variables, what statistic should we use? - correct answer Adjusted R^2 because it adjusts for the number of predicting variables. It doesn't increase when we add more predicting variables. A statistic that effectively summarizes how well the X's are linearly related to Y is the correlation coefficient. T/F - correct answer True T/F - The correlation coefficient cannot be used to evaluate the correlation between the predicting variables for detecting (near) linear dependence among the variables (or multicolinearity) - correct answer False, it CAN How do you diagnose multicolinearity? - correct answer Calculate the VIF (variance inflation factor) for each predicting variable VIF = 1 / (1 - R^2j) If VIF max(10, 1 / (1- R^2)) then we got a problem If a variable is correlated but does not have multicolinearity, is this a problem? - correct answer Not necessarily bruh What does the VIF measure - correct answer the VIF measures the proportional increase in the variance of beta hat compared to what it would have been if the predicting variables had been completely uncorrelated. True/False: The response variable in logistic regression is a binary response? - correct answer True True/False: In logistic regression, we model the probability of a success given the predicting variables, not the response itself. - correct answer True What are the assumptions for logistic regression? - correct answer Linearity Assumption Independence Assumption The G-Link function is a logit function Assumption What is the logit function? - correct answer ratio between the probability of success over probability of a failure. So basically ratio between log of P over 1-p What is the interpretation of the logistic regression coefficient? - correct answer The log of the odds ratio for an increase of one unit in the predicting variable. We do not interpret beta with respect to the response variable but with respect to the odds of success. How many regression coefficients are there for logistic regression? - correct answer Since there is no error time, you have P + 1 with intercept. Logistic regression is different from standard linear regression in that a) It does not have an error term b) The response variable is not normally distributed. c) It models probability of a response and not the expectation of the response. d) All of the above. - correct answer d) all of the above Which one is correct? a) The logit link function is the only link function that can be used for modeling binary response data. b) Logistic regression models the probability of a success given a set of predicting variables. c) The interpretation of the regression coefficients in logistic regression is the same as for standard linear regression assuming normality. d) None of the above. - correct answer b) Logistic regression models the probability of a success given a set of predicting variables. In logistic regression, a) The estimation of the regression coefficients is based on maximum likelihood estimation. b) We can derive exact (close form expression) estimates for the regression coefficients. c) The estimations of the regression coefficients is based on minimizing the sum of least squares. d) All of the above. - correct answer a) The estimation of the regression coefficients is based on maximum likelihood estimation. Using the R statistical software to fit a logistic regression, a) We can use the lm() command. b) The input of the response variable is exactly the same if the binary response data are with or without replications. c) We can obtain both the estimates and the standard deviations of the estimates for the regression coefficients. d) None of the above. - correct answer c) We can obtain both the estimates and the standard deviations of the estimates for the regression coefficients. The maximum likelihood estimator can be approximated by the normal distribution. T/F - correct answer True What is the test for statistical significance given all predictors in a logistic regression model? - correct answer Z-test (wald test) Statistical inference is reliable on logistic regression models with a small N. T/F - correct answer False How do you calculate the deviance statistic for a model with a subset of predictors in logistic regression? - correct answer The deviance is calculated as the difference in the log likliehood under the reduced model and the log liklihood under the full model. The distribution of the deviance test statistic is a chi-squared distribution. T/F - correct answer True