ISYE 6414 Regression Modules 1-2 (2023/2024) Already Passed

ISYE 6414 Regression Modules 1-2 (2023/2024) Already Passed 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 The sampling distribution for the variance estimator in ANOVA is chi-squared regardless of the assumptions of data? False If the constant variance assumption in ANOVA does not hold, the inference on the equality of the means will not be reliable. True A negative value of B1 is consistent with an inverse relationship between x and y. True In one confidence interval in the pairwise comparison does not include zero, we conclude that the two means are plausibly equal. False The mean sum of square errors in ANOVA measures the variability between groups? False THe linear regression model with a qualitative predicting variable with k levels/classes will have k+1 parameters to estimate? True We assess the assumption of constant-variance by plotting the response variable against fitted values? False In ANOVA number of degrees of freedom of the chi-square distribution for the pooled variance estimator is N-k where k is the number of groups? True Only the log-transformation of the response variable can be used with the normality assumption does not hold. False The prediction interval will never be smaller than the confidence interval for data points with identical predictor values? True If one confidence interval in the pairwise comparison includes only positive values, we conclude that the difference in means is statistically significantly positive? True In regression we are interested in one particular variable's response to one or more predictor variables. True In regression, a response variable is a random variable. True In regression, predicting variables are random variables. False Linear regression can have terms where the predicting variable is raised to some exponential power. True We cannot estimate a polynomial relationship of X in linear regression. False What is regression analysis used for? Prediction, modeling relationships and testing hypothesis Violation of the linearity/mean 0 assumption in SLR can lead to problems with what? Intercepts Violations of constant variance assumptions in SLR can lead to what? Poor prediction intervals Time series data typically results in violations of what assumption? Independence The Mean Squared Error in SLR is an estimator for what? Sample Variance. What equation is SSE/(n-2) Mean squared error What is another name for the sum of the residuals squared? SSE In SLR, MSE is distributed how? chi-squared with n-2 degrees of freedom. What happens to R2 if we add more predicting variables? It will increase. Adjuisted R2 is adjusted for what? different number of predictive variables. Conducting T tests on each beta parameter in a multiple regression model is the best way of testing the overall significance of the model. False In the case of a MLR model containing 6 quantitative predicting variables and an intercept, thje number of parameters to estimate is 7. False The regression coefficient corresponding to one predictor in MLR is interpreted in terms of the estimated expected change in the response variable when there is a change of one unit in the corresponding predicting variables holding all other predictors fixed. True The proportion of variability in the response variable that is explained by the predicting variables is called correlation. False Predicting values of the response variable for values of the predictors that are within the data range is known as extrapolation. False In MLR we study the relationship between a single response variable and several predicting quantitative and/or qualitative variables. True The sampling distribution used for estimating the confidence intervals for the regression coefficients is the normal distribution. False A partial F-test can be used to test whether a subset of regression coefficients are all equal to zero. True Prediction is the only objective of MLR. False The equation to find the estimated variance of the error terms of a MLR model with intercept can be obtained by summing up the squared residuals and dividing that by n-p, where n is the sample size and p is the number of predictors? False For a given predicting variable, the estimated coefficient of regression associated with it will likely be different in a model with other predicting variables or in the model with only the predicting variable alone. True Observational studies allow us to make causal inference. False In the case of MLR, controlling variables are used to control for sample bias. True In the case of a multiple regression model with 10 predictors, the error term variance estimator follows a chi-squared distribution with n - 10 degrees of freedom. False The estimated coefficients obtained by using the method of least squares are unbiased estimators of the true coefficients. True Before making statistical inference on regression coefficients, estimation of the variance of the error terms is necessary. True An example of a multiple regression model is Analysis of Variance. (ANOVA). True Given a qualtitative predicting variable with 7 categories in a linear regression model with intercept, 7 dummy variables need to be included in the model. False It is a good practice to create a multiple linear regression model using linearly dependent set of predictor variables. False The causation of a predicting variable to the response variable can be captured using multiple linear regression, conditional of the other predicting variables in the model. False