1
ISYE 6414 - All Units 2025| COMPLETE EXAM SET
(questions and verified answers)frequently most
tested questions | already passed!!
response (dependent) variables - (ANSWER)one particular variable that we are
interested in understanding or modeling (y)
predicting or explanatory (independent) variables - (ANSWER)a set of other
variables that might be useful in predicting or modeling the response variable (x1,
x2)
What kind of variable is a response variable and why? - (ANSWER)random,
because it varies with changes in the predictor/s along with other random
changes.
What kind of variable is a predicting variable and why? - (ANSWER)fixed, because
it does not change with the response but it is fixed before the response is
measured.
linear relationship - (ANSWER)a simple deterministic relationship between 2
factors, x and y
what are three things that a regression analysis is used for? - (ANSWER)1.
Prediction of the response variable, 2. Modeling the relationship between the
response and explanatory variables, 3. Testing hypotheses of association
relationships
, 2
B0 = ? - (ANSWER)intercept
B1 = ? - (ANSWER)slope
for our linear model where: Y = B0 + B1 + EPSILON (E), what does the epsilon
represent? - (ANSWER)deviance of the data from the linear model (error term)
what are the 4 assumptions of linear regression? - (ANSWER)Linearity/Mean
Zero, Constant Variance, Independence, Normality
Linearity/Mean zero assumption - (ANSWER)Means that the expected value
(deviances) of errors is zero. This leads to difficulties in estimating B0 and means
that our model does not include a necessary systematic component
Constant variance assumption - (ANSWER)Means that it cannot be true that the
model is more accurate for some parts of the population, and less accurate for
other parts of the populations. This can result in less accurate parameters and
poorly-calibrated prediction intervals.
Assumption of Independence - (ANSWER)Means that the deviances, or in fact the
response variables ys, are independently drawn from the data-generating
process. (this most often occurs in time series data) This can result in very
misleading assessments of the strength of regression.
, 3
Normality assumption - (ANSWER)This is needed if we want to do any confidence
or prediction intervals, or hypothesis test, which we usually do. If this assumption
is violated, hypothesis test and confidence and prediction intervals and be very
misleading.
what are the 3 parameters we estimated in regression? - (ANSWER)B0, B1, sigma
squared (variance of the one pop.)
What do we mean by model parameters in statistics? - (ANSWER)Model
parameters are unknown quantities, and they stay unknown regardless how much
data are observed. We estimate those parameters given the model assumptions
and the data, but through estimation, we're not identifying the true parameters.
We're just estimating approximations of those parameters.
What is the estimated sampling distribution of s^2? - (ANSWER)chi-square with
n-1 DF
Why do we lose 1 DF for s^2? - (ANSWER)we replace mu with zbar
what is the relationship between s^2 and sigma^2? - (ANSWER)S^2 estimates
sigma^2
What is the estimated sampling distribution of sigma^2? - (ANSWER)chi-square
with n-2 DF (~ equivalent to MSE)
, 4
Why do we lose 2 DF for sigma^2? - (ANSWER)we replaced two parameters, B0
and B1
In SLR, we are interested in the behavior of which parameter? - (ANSWER)B1
If we have a positive value for B1,.... - (ANSWER)then that's consistent with a
direct relationship between the predicting variable x and the response variable y.
If we have a negative value for B1,.... - (ANSWER)is consistent with an inverse
relationship between x and y
When B1 is close to zero... - (ANSWER)we interpret that there is not a significant
association between predicting variables, between the predicting variable x, and
the response variable y.
How do we interpret B1? - (ANSWER)It is the estimated expected change in the
response variable associated with one unit of change in the predicting variable.
How we interpret ^B0? - (ANSWER)It is the estimated expected value of the
response variable, when the predicting variable equals zero.
What is the sampling distribution of ^B1? - (ANSWER)t distribution with N-2 DF
What can we use to test for statistical significance? - (ANSWER)t-test
ISYE 6414 - All Units 2025| COMPLETE EXAM SET
(questions and verified answers)frequently most
tested questions | already passed!!
response (dependent) variables - (ANSWER)one particular variable that we are
interested in understanding or modeling (y)
predicting or explanatory (independent) variables - (ANSWER)a set of other
variables that might be useful in predicting or modeling the response variable (x1,
x2)
What kind of variable is a response variable and why? - (ANSWER)random,
because it varies with changes in the predictor/s along with other random
changes.
What kind of variable is a predicting variable and why? - (ANSWER)fixed, because
it does not change with the response but it is fixed before the response is
measured.
linear relationship - (ANSWER)a simple deterministic relationship between 2
factors, x and y
what are three things that a regression analysis is used for? - (ANSWER)1.
Prediction of the response variable, 2. Modeling the relationship between the
response and explanatory variables, 3. Testing hypotheses of association
relationships
, 2
B0 = ? - (ANSWER)intercept
B1 = ? - (ANSWER)slope
for our linear model where: Y = B0 + B1 + EPSILON (E), what does the epsilon
represent? - (ANSWER)deviance of the data from the linear model (error term)
what are the 4 assumptions of linear regression? - (ANSWER)Linearity/Mean
Zero, Constant Variance, Independence, Normality
Linearity/Mean zero assumption - (ANSWER)Means that the expected value
(deviances) of errors is zero. This leads to difficulties in estimating B0 and means
that our model does not include a necessary systematic component
Constant variance assumption - (ANSWER)Means that it cannot be true that the
model is more accurate for some parts of the population, and less accurate for
other parts of the populations. This can result in less accurate parameters and
poorly-calibrated prediction intervals.
Assumption of Independence - (ANSWER)Means that the deviances, or in fact the
response variables ys, are independently drawn from the data-generating
process. (this most often occurs in time series data) This can result in very
misleading assessments of the strength of regression.
, 3
Normality assumption - (ANSWER)This is needed if we want to do any confidence
or prediction intervals, or hypothesis test, which we usually do. If this assumption
is violated, hypothesis test and confidence and prediction intervals and be very
misleading.
what are the 3 parameters we estimated in regression? - (ANSWER)B0, B1, sigma
squared (variance of the one pop.)
What do we mean by model parameters in statistics? - (ANSWER)Model
parameters are unknown quantities, and they stay unknown regardless how much
data are observed. We estimate those parameters given the model assumptions
and the data, but through estimation, we're not identifying the true parameters.
We're just estimating approximations of those parameters.
What is the estimated sampling distribution of s^2? - (ANSWER)chi-square with
n-1 DF
Why do we lose 1 DF for s^2? - (ANSWER)we replace mu with zbar
what is the relationship between s^2 and sigma^2? - (ANSWER)S^2 estimates
sigma^2
What is the estimated sampling distribution of sigma^2? - (ANSWER)chi-square
with n-2 DF (~ equivalent to MSE)
, 4
Why do we lose 2 DF for sigma^2? - (ANSWER)we replaced two parameters, B0
and B1
In SLR, we are interested in the behavior of which parameter? - (ANSWER)B1
If we have a positive value for B1,.... - (ANSWER)then that's consistent with a
direct relationship between the predicting variable x and the response variable y.
If we have a negative value for B1,.... - (ANSWER)is consistent with an inverse
relationship between x and y
When B1 is close to zero... - (ANSWER)we interpret that there is not a significant
association between predicting variables, between the predicting variable x, and
the response variable y.
How do we interpret B1? - (ANSWER)It is the estimated expected change in the
response variable associated with one unit of change in the predicting variable.
How we interpret ^B0? - (ANSWER)It is the estimated expected value of the
response variable, when the predicting variable equals zero.
What is the sampling distribution of ^B1? - (ANSWER)t distribution with N-2 DF
What can we use to test for statistical significance? - (ANSWER)t-test
