ISYE 6414 Regression Modules 1-2, Top Questions and answers, 100% Accurate. Verified

ISYE 6414 Regression Modules 1-2, Top Questions and answers, 100% Accurate. Verified Assuming that the data are normally distributed, under the simple linear model, the estimated variance has the following sampling distribution: - -Chi-squared with n-2 degrees of freedom. The fitted values are defined as? - -The regression line with parameters replaced with the estimated regression coefficients. The estimators fo the linear regression model are derived by? - -Minimizing the sum of squared differences between the observed and expected values of the response variable. The estimators for the regression coefficients are: - -Unbiased regardless of the distribution of the data. The assumption of normality: - -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* - -have the same expectation. The variability in the prediction comes from - -the variability due to a new measurement and due to estimation. Residual analysis can only be used to assess uncorrelated errors. - -False Independence assumption can be assess using the normal probability plot. - -False Independence assumption can be assessed using the residuals vs fitted values. - -False We detect departure from the assumption of constant variance - -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. - -False If a departure from the independence assumption is detected, we transform the response variable to improve upon the independence assumption. - -False The Box-Cox transformation is commonly used to improve upon the linearity assumption. - -False In evaluating a simple linear model - -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 - -residual analysis R-squared (the coefficient of variation) is interpreted as - -the percentage of variability in the response variable explained by the model. The parameters of ANOVA are - -the k sample means and the population variance. The pooled variance estimator is - -the sample variance estimator assuming equal variances. In ANOVA, the mean sum of squares divided by N-1 is - -the sample variance estimator assuming equal means and equal variances. MSE measures - -the within-treatment variability. MSSTr measures - -the between treatment variability. If we reject the test of equal means, we conclude that at least one pair of means are different. - -True If we do not reject the test of equal means, we conclude that means are definitely all equal. - -False If we reject the test of equal means, we conclude that all treatment means are not equal. - -False In ANOVA, the objective of residual analysis is to - -evaluate departures from the model assumptions. In ANOVA, the objective of the pairwise comparison is - -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. - -False The constant variance assumption is diagnosed using the histogram? - -False The estimator sigma^2 is a random variable? - -True The regression coefficients are used to measure the linear dependence between two variables? - -False The mean sum of square errors in ANOVA measures variability within groups - -True Beta 1 is an unbiased estimator for Beta 0. - -False Under the normality assumptions, the estimator for B1 is a linear combindation of randomly distributed random variables? - -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? - -False The assumptions to diagnose with a linear regression model are independence, linearity, constant variance, and normality? - -True