ISYE6414 REGRESSION SUMMER MIDTERM 1 AND 2 EXAM / ISYE6414 MIDTERM 1 AND 2 REAL EXAM QUESTIONS AND 100% CORRECT ANSWERS/ GRADED A

ISYE6414 REGRESSION SUMMER MIDTERM 1 AND 2 EXAM / ISYE6414 MIDTERM 1 AND 2 REAL EXAM QUESTIONS AND 100% CORRECT ANSWERS/ GRADED A If the confidence interval for a regression coefficient contains the value zero, we interpret that the regression coefficient is definitely equal to zero. ---ANSWER-- False The larger the coefficient of determination or R-squared, the higher the variability explained by the simple linear regression model. ---ANSWER-- True The estimators of the error term variance and of the regression coefficients are random variables. ---ANSWER-- True The one-way ANOVA is a linear regression model with one qualitative predicting variable. ---ANSWER-- True We can assess the assumption of constant-variance in multiple linear regression by plotting the standardized residuals against fitted values. ---ANSWER-- True If one confidence interval in the pairwise comparison includes zero under ANOVA, we conclude that the two corresponding means are plausibly equal. --- ANSWER-- True We do not need to assume normality of the response variable for making inference on the regression coefficients. ---ANSWER-- False Assuming the model is a good fit, the residuals in simple linear regression have constant variance. ---ANSWER-- True We cannot estimate a multiple linear regression model if the predicting variables are linearly independent. ---ANSWER-- False If a predicting variable is categorical with 5 categories in a linear regression model without intercept, we will include 5 dummy variables in the model. ---ANSWER-- True In the ANOVA, the number of degrees of freedom of the chi-squared distribution for the variance estimator is N-k-1 where k is the number of groups. ---ANSWER-- False The prediction of the response variable has higher uncertainty than the estimation of the mean response. ---ANSWER-- True In linear regression, outliers do not impact the estimation of the regression coefficients. ---ANSWER-- False Multicolinearity in multiple linear regression means that the columns in the design matrix are (nearly) linearly dependent. ---ANSWER-- True The statistical inference for linear regression under normality relies on large size of sample data. ---ANSWER-- False If the non-constant variance assumption does not hold in multiple linear regression, we apply a transformation to the predicting variables. ---ANSWER-- False The only assumptions for a linear regression model are linearity, constant variance, and normality. ---ANSWER-- False In the regression model, the variable of interest for study is the predicting variable. ---ANSWER-- False The constant variance is diagnosted using the quantile-quantile normal plot. --- ANSWER-- False β 1 is an unbiased estimator for β 0 . ---ANSWER-- False The estimator σ ^ 2 is a fixed variable. ---ANSWER-- False The linear regression model with a qualitative predicting variable with k levels/classes will have k + 1 parameters to estimate ---ANSWER-- True Under the normality assumption, the estimator for β 1 is a linear combination of normally distributed random variables. ---ANSWER-- True A negative value of β 1 is consistent with an inverse relationship between x and y . ---ANSWER-- True In the simple linear regression model, we lose three degrees of freedom because of the estimation of the three model parameters β 0 , β 1 , σ 2 . ---ANSWER-- False The regression coefficient is used to measure the linear dependence between two variables. ---ANSWER-- False If the constant variance assumption in ANOVA does not hold, the inference on the equality of the means will not be reliable. ---ANSWER-- True If one confidence interval in the pairwise comparison does not include zero, we conclude that the two means are plausibly equal. ---ANSWER-- False The mean sum of square errors in ANOVA measures variability within groups. --- ANSWER-- True Only the log-transformation of the response variable can be used when the normality assumption does not hold. ---ANSWER-- False If one confidence interval in the pairwise comparison includes only positive values, we conclude that the difference in means is statistically significantly positive. ---ANSWER-- True The number of degrees of freedom of the χ 2 (chi-square) distribution for the variance estimator is N − k + 1 where k is the number of samples. ---ANSWER-- False For assessing the normality assumption of the ANOVA model, we can use the quantile-quantile normal plot and the historgram of the residuals. ---ANSWER-- True The ANOVA is a linear regression model with one or more qualitative predicting variables. ---ANSWER-- True The sampling distribution for the variance estimator in ANOVA is χ 2 (chi-square) regardless of the assumptions of the data. ---ANSWER-- False We assess the assumption of constant-variance by plotting the residuals against fitted values. ---ANSWER-- True Prediction is the only objective of multiple linear regression. ---ANSWER-- False The number of parameters to estimate in the case of a multiple linear regression model containing 5 predicting variables and no intercept is 6. ---ANSWER-- True The equation to find the estimated variance of the error terms can be obtained by summing up the squared residuals and dividing that by n - p - 1, where n is the sample size and p is the number of predictors. ---ANSWER-- True