ISYE 6414 Midterm, Summer Questions and Answers with complete solution

The prediction interval of one member of the population will always be larger than the confidence interval of the mean response for all members of the population when using the same predicting values. - true See 1.7 Regression Line: Estimation & Prediction Examples "Just to wrap up the comparison, the confidence intervals under estimation are narrower than the prediction intervals because the prediction intervals have additional variance from the variation of a new measurement." In ANOVA, the linearity assumption is assessed using a plot of the response against the predicting variable. - false See 2.2. Estimation Method Linearity is not an assumption of ANOVA. If the model assumptions hold, then the estimator for the variance, σ ^ 2, is a random variable. - true See 1.8 Statistical Inference We assume that the error terms are independent random variables. Therefore, the residuals are independent random variables. Since σ ^ 2 is a combination of the residuals, it is also a random variable. The mean sum of squared errors in ANOVA measures variability within groups. - true See 2.4 Test for Equal Means MSE = within-group variability The simple linear regression coefficient, β ^ 0, is used to measure the linear relationship between the predicting and response variables. - falseSee 1.2 Estimation Method β ^ 0 is the intercept and does not tell us about the relationship between the predicting and response variables. The sampling distribution for the variance estimator in simple linear regression is χ 2 (chi-squared) regardless of the assumptions of the data. - false See 1.2 Estimation Method "The sampling distribution of the estimator of the variance is chi-squared, with n - 2 degrees of freedom (more on this in a moment). This is under the assumption of normality of the error terms." β ^ 1 is an unbiased estimator for β 0. - False See 1.4 Statistical Inference "What that means is that β ^ 1 is an unbiased estimator for β 1." It is not an unbiased estimator for β 0. If the pairwise comparison interval between groups in an ANOVA model includes zero, we conclude that the two means are plausibly equal. - true See 2.8 Data Example If the comparison interval includes zero, then the two means are not statistically significantly different, and are thus, plausibly equal. Under the normality assumption, the estimator for β 1 is a linear combination of normally distributed random variables. - true