ISYE6414 FINAL EXAM 2022-2024 / ISYE6414 FINAL EXAM
REAL EXAM QUESTIONS AND 100% CORRECT ANSWERS
PLUS RATIONALES/ ALREADY 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 Method
"We use ϵ ^ i as proxies for the deviances or the error terms. We don't have the
deviances because we don't have β 0 and β 1.
With the Box-Cox transformation, when λ = 0 we do not transform the
response. -ANSWER-- false
See 1.8 Diagnostics
When λ = 0, we transform using the normal log.
The sampling distribution of β ^ 0 is a
t-
distribution
chi-squared distribution
normal distribution
REAL EXAM QUESTIONS AND 100% CORRECT ANSWERS
PLUS RATIONALES/ ALREADY 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 Method
"We use ϵ ^ i as proxies for the deviances or the error terms. We don't have the
deviances because we don't have β 0 and β 1.
With the Box-Cox transformation, when λ = 0 we do not transform the
response. -ANSWER-- false
See 1.8 Diagnostics
When λ = 0, we transform using the normal log.
The sampling distribution of β ^ 0 is a
t-
distribution
chi-squared distribution
normal distribution
