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ISYE 6414 Final Exam Review with complete solution Least Square Elimination (LSE) cannot be applied to GLM models. ✔✔ False - it is applicable but does not use data distribution information fully. In multiple linear regression with idd and equal variance, the least squares estimation of regression coefficients are always unbiased. ✔✔ True - the least squares estimates are BLUE (Best Linear Unbiased Estimates) in multiple linear regression. Maximum Likelihood Estimation is not applicable for simple linear regression and multiple linear regression. ✔✔ False - In SLR and MLR, the SLE and MLE are the same with normal idd data. The backward elimination requires a pre-set probability of type II error ✔✔ False - Type I error The first degree of freedom in the F distribution for any of the three procedures in stepwise is always equal to one. ✔✔ True MLE is used for the GLMs for handling complicated link function modeling in the X-Y relationship. ✔✔ True In the GLMs the link function cannot be a non linear regression. ✔✔ False - It can be linear, non linear, or parametric When the p-value of the slope estimate in the SLR is small the r-squared becomes smaller too. ✔✔ False - When P value is small, the model fits become more significant and R squared become larger. In GLMs the main reason one does not use LSE to estimate model parameters is the potential constrained in the parameters. ✔✔ False - The potential constraint in the parameters of GLMs is handled by the link function. The R-squared and adjusted R-squared are not appropriate model comparisons for non linear regression but are for linear regression models. ✔✔ TRUE - The underlying assumption of R-squared calculations is that you are fitting a linear model. The decision in using ANOVA table for testing whether a model is significant depends on the normal distribution of the response variable ✔✔ True When the data may not be normally distributed, AIC is more appropriate for variable selection than adjusted R-squared ✔✔ True The slope of a linear regression equation is an example of a correlation coefficient. ✔✔ False - the correlation coefficient is the r value. Will have the same + or - sign as the slope. In multiple linear regression, as the value of R-squared increases, the relationship between predictors becomes stronger ✔✔ False - r squared measures how much variability is explained by the model, NOT how strong the predictors are. When dealing with a multiple linear regression model, an adjusted R-squared can be greater than the corresponding unadjusted R-Squared value. ✔✔ False - the adjusted rsquared value take the number and types of predictors into account. It is lower than the r squared value. In a multiple regression problem, a quantitative input variable x is replaced by x − mean(x). The R-squared for the fitted model will be the same ✔✔ True The estimated coefficients of a regression line is positive, when the coefficient of determination is positive. ✔✔ False - r squared is always positive. If the outcome variable is quantitative and all explanatory variables take values 0 or 1, a logistic regression model is most appropriate. ✔✔ False - More research is necessary to determine the correct model. After fitting a logistic regression model, a plot of residuals versus fitted values is useful for checking if model assumptions are violated. ✔✔ False - for logistic regression use deviance residuals. In a greenhouse experiment with several predictors, the response variable is the number of seeds that germinate out of 60 that are planted with different treatment combinations. A Poisson regression model is most appropriate for modeling this data ✔✔ False - poisson regression models rate or count data. For Poisson regression, we can reduce type I errors of identifying statistical significance in the regression coefficients by increasing the sample size. ✔✔ True Both LASSO and ridge regression always provide greater residual sum of squares than that of simple multiple linear regression. ✔✔ True If data on (Y, X) are available at only two values of X, then the model Y = \beta_1 X + \beta_2 X^2 + \epsilon provides a better fit than Y = \beta_0 + \beta_1 X + \epsilon. ✔✔ False - nothing to determine of a quadratic model is necessary or required. If the Cook's distance for any particular observation is greater than one, that data point is definitely a record error and thus needs to be discarded. ✔✔ False - must see a comparison of data points. Is 1 too large? We can use residual analysis to conclusively determine the assumption of independence ✔✔ False - we can only determine uncorrelated errors. It is possible to apply logistic regression when the response variable Y has 3 classes. ✔✔ True . A correlation coefficient close to 1 is evidence of a cause-and-effect relationship between the two variables. ✔✔ False- cause and effect can only be determined by a well designed experiment. Multiplying a variable by 10 in LASSO regression, decreases the chance that the coefficient of this variable is nonzero. ✔✔ False - I am not sure why anyone would think this would be true. In regression inference, the 99% confidence interval of coefficient \beta_0 is always wider than the 95% confidence interval of \beta_1. ✔✔ False- can only compare beta1 with beta1 and beta0 with beta0 The regression coefficients for the Poisson regression model can be estimated in exact/closed form. ✔✔ False - MLE is NOT closed form. Mean square error is commonly used in statistics to obtain estimators that may be biased, but less uncertain than unbiased ones. And that's preferred. ✔✔ True Regression models are only appropriate for continuous response variables. ✔✔ False - logistic and poisson model probability and rate The assumptions in logistic regression are - Linearity, Independence of response variable, and the link function is the logit function. ✔✔ True - linearity is measured through the link, , the g of the probability of success and the predicted variable. The log odds function, also called the logit function, which is the log of the ratio between the probability of a success and the probability of a failure ✔✔ True In logistic regression we interpret the Betas in terms of the response variable. ✔✔ False - we interpret it in terms of the odds of success or the log odds of success In logistic regression we have an additional error term to estimate. ✔✔ False - there is not error term in logistic regression. The least square estimation for the standard regression model is equivalent with Maximum Likelihood Estimation, under the assumption of normality. ✔✔ True The variance estimator in logistic regression has a closed form expression. ✔✔ False - use statistical software to obtain the variance-co-variance matrix We can use the z value to determine if a coefficient is equal to zero in logistic regression. ✔✔ True - z value = (Beta-0)/(SE of Beta) In testing for a subset of coefficients in logistic regression the null hypothesis is that the coefficient is equal to zero ✔✔ True Like standard linear regression we can use the F test to test for overall regression in logistic regression. ✔✔ False - It's 1-pchisq(null deviance-residual deviance, DFnull-DFresidual) For logistic regression we can define residuals for evaluating model goodness of fit for models with and without replication. ✔✔ False - can only be with replication under the assumption that Yi is binary and n1 is greater than 1 The deviance residuals are the signed square root of the log-likelihood evaluated at the saturated model ✔✔ True From the binomial approximation with a normal distribution using the central limit theorem, the Pearson residuals have an approximately standard chi-squared distribution. ✔✔ False - Normal distribution Visual Analytics for logistic regression Normal probability plot of residuals Residuals vs predictors Logit of success rate vs predictors ✔✔ True Normal probability plot of residuals - Normality Residuals vs predictors - Linearity/Independence Logit of success rate vs predictors - Linearity Under the null hypothesis of good fit for logistic regression, the test statistic has a Chi-Square distribution with n- p- 1 degrees of freedom ✔✔ True - don't forget, we want large P values For the testing procedure for subsets of coefficients, we compare the likelihood of a reduced model versus a full model. This is a goodness of fit test ✔✔ False - it provides inference of the predictive power of the model Predictive power means that the predicting variables predict the data even if one or more of the assumptions do not hold. ✔✔ True

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