ISYE 6414 Regression Modules 1-2 Exam Study Questions and Answers UPDATED 2024

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.