ISYE 6414 Midterm, Summer 2025
questions well answered passed
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. - correct 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 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. - correct 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. -
correct 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. - correct 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. - correct 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. - correct 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. - correct 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. - correct 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. - correct 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. - correct 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. - correct
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. - correct answer ✔✔true
questions well answered passed
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. - correct 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 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. - correct 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. -
correct 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. - correct 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. - correct 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. - correct 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. - correct 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. - correct 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. - correct 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. - correct 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. - correct
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. - correct answer ✔✔true
