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

ISYE6414 FINAL EXAM 2022-2024 / 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