ISYE6414 FINAL EXAM / ISYE6414 FINAL EXAM REAL EXAM QUESTIONS AND 100% CORRECT ANSWERS PLUS RATIONALES/ GRADED A

ISYE6414 FINAL EXAM / ISYE6414 FINAL EXAM REAL EXAM QUESTIONS AND 100% CORRECT ANSWERS PLUS RATIONALES/ GRADED A 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. -ANSWER-- 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 becausethe 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- false See 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER- - 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. -ANSWER-- true See 1.4 Statistical Inference "Under the normality assumption, β 1 is thus a linear combination of normally distributed random variables... β ^ 0 is also linear combination of random variables" An ANOVA model with a single qualitative predicting variable containing k groups will have k + 1 parameters to estimate. -ANSWER-- true See 2.2 Estimation Method We have to estimate the means of the k groups and the pooled variance estimator, s p o o l e d 2. In simple linear regression models, we lose three degrees of freedom when estimating the variance because of the estimation of the three model parameters β 0 , β 1 , σ 2. -ANSWER-- false See 1.2 Estimation Method "The estimator for σ 2 is σ ^ 2, and is the sum of the squared residuals, divided by n - 2." The pooled variance estimator, s p o o l e d 2, in ANOVA is synonymous with the variance estimator, σ ^ 2, in simple linear regression because they both use mean squared error (MSE) for their calculations. -ANSWER-- true See 1.2 Estimation Method for simple linear regression See 2.2 Estimation Method for ANOVA The pooled variance estimator is, in fact, the variance estimator. The normality assumption states that the response variable is normally distributed. -ANSWER-- false See 1.8 Diagnostics "Normality assumption: the error terms are normally distributed." The response may or may not be normally distributed, but the error terms are assumed to be normally distributed. If the constant variance assumption in ANOVA does not hold, the inference on the equality of the means will not be reliable. -ANSWER-- true See 2.8 Data Example "This is important since without a good fit, we cannot rely on the statistical inference." Only when the model is a good fit, i.e. all model assumptions hold, can we rely on the statistical inference. A negative value of β 1 is consistent with an inverse relationship between the predictor variable and the response variable. -ANSWER-- true See 1.2 Estimation Method "A negative value of β 1 is consistent with an inverse relationship" The p-value is a measure of the probability of rejecting the null hypothesis. - ANSWER-- false See 1.5 Statistical Inference Data Example "p-value is a measure of how rejectable the null hypothesis is... It's not the probability of rejecting the null hypothesis, nor is it the probability that the null hypothesis is true." We assess the constant variance assumption by plotting the error terms, ϵ i, against fitted values. -ANSWER-- false See 1.2 Estimation M