ISYE 6414 Regression Modules 1-2 Study Guide Exam With Detailed Answers.

Assuming that the data are normally distributed, under the simple linear model, the estimated variance has the following sampling distribution: - correct answer Chi-squared with n-2 degrees of freedom. The fitted values are defined as? - correct answer The regression line with parameters replaced with the estimated regression coefficients. The estimators fo the linear regression model are derived by? - correct answer Minimizing the sum of squared differences between the observed and expected values of the response variable. The estimators for the regression coefficients are: - correct answer Unbiased regardless of the distribution of the data. The assumption of normality: - correct answer Is needed for the sampling distribution of the estimators of the regression coefficients and hence for inference. The estimated versus predicted regression line for a given x* - correct answer have the same expectation. The variability in the prediction comes from - correct answer the variability due to a new measurement and due to estimation. Residual analysis can only be used to assess uncorrelated errors. - correct answer False Independence assumption can be assess using the normal probability plot. - correct answer False Independence assumption can be assessed using the residuals vs fitted values. - correct answer False We detect departure from the assumption of constant variance - correct answer when the residuals vs fitted values are larger in the ends but smaller in the middle. If a departure from normality is detected, we transform the predicting variable to improve upon the normality assumption. - correct answer False If a departure from the independence assumption is detected, we transform the response variable to improve upon the independence assumption. - correct answer False The Box-Cox transformation is commonly used to improve upon the linearity assumption. - correct answer False In evaluating a simple linear model - correct answer there is a direct relationship between the coefficient of determination and the correlation between the predicting and response variables. Goodness of fit assessment is done by - correct answer residual analysis R-squared (the coefficient of variation) is interpreted as - correct answer the percentage of variability in the response variable explained by the model. The parameters of ANOVA are - correct answer the k sample means and the population variance. The pooled variance estimator is - correct answer the sample variance estimator assuming equal variances. In ANOVA, the mean sum of squares divided by N-1 is - correct answer the sample variance estimator assuming equal means and equal variances. MSE measures - correct answer the within-treatment variability. MSSTr measures - correct answer the between treatment variability. If we reject the test of equal means, we conclude that at least one pair of means are different. - correct answer True If we do not reject the test of equal means, we conclude that means are definitely all equal. - correct answer False If we reject the test of equal means, we conclude that all treatment means are not equal. - correct answer False In ANOVA, the objective of residual analysis is to - correct answer evaluate departures from the model assumptions. In ANOVA, the objective of the pairwise comparison is - correct answer To identify the statistically significant different means For assessing the normality assumption of the ANOVA model, we can only use the quantile-quantile normal plot of the residuals. - correct answer False The constant variance assumption is diagnosed using the histogram? - correct answer False The estimator sigma^2 is a random variable? - correct answer True The regression coefficients are used to measure the linear dependence between two variables? - correct answer False The mean sum of square errors in ANOVA measures variability within groups - correct answer True Beta 1 is an unbiased estimator for Beta 0. - correct answer False Under the normality assumptions, the estimator for B1 is a linear combindation of randomly distributed random variables? - correct answer True In simple linear regression models, we loose three degrees of freedom because of the estimation of the three model parameters, B0, B1, and Sigma^2? - correct answer False The assumptions to diagnose with a linear regression model are independence, linearity, constant variance, and normality? - correct answer True The sampling distribution for the variance estimator in ANOVA is chi-squared regardless of the assumptions of data? - correct answer False If the constant variance assumption in ANOVA does not hold, the inference on the equality of the means will not be reliable. - correct answer True A negative value of B1 is consistent with an inverse relationship between x and y. - correct answer True