ISYE 6414 Midterm Exam | Verified
Questions and Correct Answers
The predicti0n interval 0f 0ne member 0f the p0pulati0n will always be larger than the
c0nfidence interval 0f the mean resp0nse f0r all members 0f the p0pulati0n when using
the same predicting values. - ANSWER-true
See 1.7 Regressi0n Line: Estimati0n & Predicti0n Examples
"Just t0 wrap up the c0mparis0n, the c0nfidence intervals under estimati0n are narr0wer
than the predicti0n intervals because the predicti0n intervals have additi0nal variance
fr0m the variati0n 0f a new measurement."
In AN0VA, the linearity assumpti0n is assessed using a pl0t 0f the resp0nse against the
predicting variable. - ANSWER-false
See 2.2. Estimati0n Meth0d
Linearity is n0t an assumpti0n 0f AN0VA.
If the m0del assumpti0ns h0ld, then the estimat0r f0r the variance, σ ^ 2, is a rand0m
variable. - ANSWER-true
See 1.8 Statistical Inference
We assume that the err0r terms are independent rand0m variables. Theref0re, the
residuals are independent rand0m variables. Since σ ^ 2 is a c0mbinati0n 0f the residuals,
it is als0 a rand0m variable.
The mean sum 0f squared err0rs in AN0VA measures variability within gr0ups. -
ANSWER-true
See 2.4 Test f0r Equal Means
MSE = within-gr0up variability
The simple linear regressi0n c0efficient, β ^ 0, is used t0 measure the linear relati0nship
between the predicting and resp0nse variables. - ANSWER-false
See 1.2 Estimati0n Meth0d
β ^ 0 is the intercept and d0es n0t tell us ab0ut the relati0nship between the predicting
and resp0nse variables.
The sampling distributi0n f0r the variance estimat0r in simple linear regressi0n is χ 2 (chi-
squared) regardless 0f the assumpti0ns 0f the data. - ANSWER-false
See 1.2 Estimati0n Meth0d
, "The sampling distributi0n 0f the estimat0r 0f the variance is chi-squared, with n - 2
degrees 0f freed0m (m0re 0n this in a m0ment). This is under the assumpti0n 0f n0rmality
0f the err0r terms."
β ^ 1 is an unbiased estimat0r f0r β 0. - ANSWER-False
See 1.4 Statistical Inference
"What that means is that β ^ 1 is an unbiased estimat0r f0r β 1." It is n0t an unbiased
estimat0r f0r β 0.
If the pairwise c0mparis0n interval between gr0ups in an AN0VA m0del includes zer0, we
c0nclude that the tw0 means are plausibly equal. - ANSWER-true
See 2.8 Data Example
If the c0mparis0n interval includes zer0, then the tw0 means are n0t statistically
significantly different, and are thus, plausibly equal.
Under the n0rmality assumpti0n, the estimat0r f0r β 1 is a linear c0mbinati0n 0f n0rmally
distributed rand0m variables. - ANSWER-true
See 1.4 Statistical Inference
"Under the n0rmality assumpti0n, β 1 is thus a linear c0mbinati0n 0f n0rmally distributed
rand0m variables... β ^ 0 is als0 linear c0mbinati0n 0f rand0m variables"
An AN0VA m0del with a single qualitative predicting variable c0ntaining k gr0ups will
have k + 1 parameters t0 estimate. - ANSWER-true
See 2.2 Estimati0n Meth0d
We have t0 estimate the means 0f the k gr0ups and the p00led variance estimat0r, s p 0 0
l e d 2.
In simple linear regressi0n m0dels, we l0se three degrees 0f freed0m when estimating
the variance because 0f the estimati0n 0f the three m0del parameters β 0 , β 1 , σ 2. -
ANSWER-false
See 1.2 Estimati0n Meth0d
"The estimat0r f0r σ 2 is σ ^ 2, and is the sum 0f the squared residuals, divided by n - 2."
The p00led variance estimat0r, s p 0 0 l e d 2, in AN0VA is syn0nym0us with the variance
estimat0r, σ ^ 2, in simple linear regressi0n because they b0th use mean squared err0r
(MSE) f0r their calculati0ns. - ANSWER-true
See 1.2 Estimati0n Meth0d f0r simple linear regressi0n
See 2.2 Estimati0n Meth0d f0r AN0VA
The p00led variance estimat0r is, in fact, the variance estimat0r.
Questions and Correct Answers
The predicti0n interval 0f 0ne member 0f the p0pulati0n will always be larger than the
c0nfidence interval 0f the mean resp0nse f0r all members 0f the p0pulati0n when using
the same predicting values. - ANSWER-true
See 1.7 Regressi0n Line: Estimati0n & Predicti0n Examples
"Just t0 wrap up the c0mparis0n, the c0nfidence intervals under estimati0n are narr0wer
than the predicti0n intervals because the predicti0n intervals have additi0nal variance
fr0m the variati0n 0f a new measurement."
In AN0VA, the linearity assumpti0n is assessed using a pl0t 0f the resp0nse against the
predicting variable. - ANSWER-false
See 2.2. Estimati0n Meth0d
Linearity is n0t an assumpti0n 0f AN0VA.
If the m0del assumpti0ns h0ld, then the estimat0r f0r the variance, σ ^ 2, is a rand0m
variable. - ANSWER-true
See 1.8 Statistical Inference
We assume that the err0r terms are independent rand0m variables. Theref0re, the
residuals are independent rand0m variables. Since σ ^ 2 is a c0mbinati0n 0f the residuals,
it is als0 a rand0m variable.
The mean sum 0f squared err0rs in AN0VA measures variability within gr0ups. -
ANSWER-true
See 2.4 Test f0r Equal Means
MSE = within-gr0up variability
The simple linear regressi0n c0efficient, β ^ 0, is used t0 measure the linear relati0nship
between the predicting and resp0nse variables. - ANSWER-false
See 1.2 Estimati0n Meth0d
β ^ 0 is the intercept and d0es n0t tell us ab0ut the relati0nship between the predicting
and resp0nse variables.
The sampling distributi0n f0r the variance estimat0r in simple linear regressi0n is χ 2 (chi-
squared) regardless 0f the assumpti0ns 0f the data. - ANSWER-false
See 1.2 Estimati0n Meth0d
, "The sampling distributi0n 0f the estimat0r 0f the variance is chi-squared, with n - 2
degrees 0f freed0m (m0re 0n this in a m0ment). This is under the assumpti0n 0f n0rmality
0f the err0r terms."
β ^ 1 is an unbiased estimat0r f0r β 0. - ANSWER-False
See 1.4 Statistical Inference
"What that means is that β ^ 1 is an unbiased estimat0r f0r β 1." It is n0t an unbiased
estimat0r f0r β 0.
If the pairwise c0mparis0n interval between gr0ups in an AN0VA m0del includes zer0, we
c0nclude that the tw0 means are plausibly equal. - ANSWER-true
See 2.8 Data Example
If the c0mparis0n interval includes zer0, then the tw0 means are n0t statistically
significantly different, and are thus, plausibly equal.
Under the n0rmality assumpti0n, the estimat0r f0r β 1 is a linear c0mbinati0n 0f n0rmally
distributed rand0m variables. - ANSWER-true
See 1.4 Statistical Inference
"Under the n0rmality assumpti0n, β 1 is thus a linear c0mbinati0n 0f n0rmally distributed
rand0m variables... β ^ 0 is als0 linear c0mbinati0n 0f rand0m variables"
An AN0VA m0del with a single qualitative predicting variable c0ntaining k gr0ups will
have k + 1 parameters t0 estimate. - ANSWER-true
See 2.2 Estimati0n Meth0d
We have t0 estimate the means 0f the k gr0ups and the p00led variance estimat0r, s p 0 0
l e d 2.
In simple linear regressi0n m0dels, we l0se three degrees 0f freed0m when estimating
the variance because 0f the estimati0n 0f the three m0del parameters β 0 , β 1 , σ 2. -
ANSWER-false
See 1.2 Estimati0n Meth0d
"The estimat0r f0r σ 2 is σ ^ 2, and is the sum 0f the squared residuals, divided by n - 2."
The p00led variance estimat0r, s p 0 0 l e d 2, in AN0VA is syn0nym0us with the variance
estimat0r, σ ^ 2, in simple linear regressi0n because they b0th use mean squared err0r
(MSE) f0r their calculati0ns. - ANSWER-true
See 1.2 Estimati0n Meth0d f0r simple linear regressi0n
See 2.2 Estimati0n Meth0d f0r AN0VA
The p00led variance estimat0r is, in fact, the variance estimat0r.
