ISYE 6414 – Georgia Institute of Technology – All Units Exam Guide (2025 Edition) –
Actual Exam Questions with 100% Verified Answers
This comprehensive exam document covers all units of the ISYE 6414 course (Georgia
Tech), providing fully verified questions and answers for the 2025 edition. Topics
include simple and multiple linear regression, ANOVA, logistic regression, Poisson
regression, model assumptions, variable selection, regularization techniques (Ridge,
LASSO, Elastic Net), and statistical inference methods. It is structured for clarity,
with extensive true/false, multiple-choice, and open-answer format, making it a
reliable resource for mastering exam material.
100% Verified Exam Study Guide 2025/2026.
response (dependent) variables - ansone particular variable that we are interested in
understanding or modeling (y)
predicting or explanatory (independent) variables - ansa 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? - ansrandom, because it varies with
changes in the predictor/s along with other random changes.
What kind of variable is a predicting variable and why? - ansfixed, because it does not
change with the response but it is fixed before the response is measured.
linear relationship - ansa simple deterministic relationship between 2 factors, x and y
what are three things that a regression analysis is used for? - ans1. Prediction of the response
variable, 2. Modeling the relationship between the response and explanatory variables, 3.
Testing hypotheses of association relationships
B0 = ? - ansintercept
B1 = ? - ansslope
for our linear model where: Y = B0 + B1 + EPSILON (E), what does the epsilon represent? -
ansdeviance of the data from the linear model (error term)
what are the 4 assumptions of linear regression? - ansLinearity/Mean Zero, Constant
Variance, Independence, Normality
Linearity/Mean zero assumption - ansMeans 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 - ansMeans 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 - ansMeans 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.
Normality assumption - ansThis 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? - ansB0, B1, sigma squared (variance
of the one pop.)
What do we mean by model parameters in statistics? - ansModel 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? - anschi-square with n-1 DF
Why do we lose 1 DF for s^2? - answe replace mu with zbar
what is the relationship between s^2 and sigma^2? - ansS^2 estimates sigma^2
,ISYE 6414 – Georgia Institute of Technology – All Units Exam Guide (2025 Edition) –
Actual Exam Questions with 100% Verified Answers
This comprehensive exam document covers all units of the ISYE 6414 course (Georgia
Tech), providing fully verified questions and answers for the 2025 edition. Topics
include simple and multiple linear regression, ANOVA, logistic regression, Poisson
regression, model assumptions, variable selection, regularization techniques (Ridge,
LASSO, Elastic Net), and statistical inference methods. It is structured for clarity,
with extensive true/false, multiple-choice, and open-answer format, making it a
reliable resource for mastering exam material.
100% Verified Exam Study Guide 2025/2026.
What is the estimated sampling distribution of sigma^2? - anschi-square with n-2 DF (~
equivalent to MSE)
Why do we lose 2 DF for sigma^2? - answe replaced two parameters, B0 and B1
In SLR, we are interested in the behavior of which parameter? - ansB1
If we have a positive value for B1,.... - ansthen 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,.... - ansis consistent with an inverse relationship between
x and y
When B1 is close to zero... - answe 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? - ansIt is the estimated expected change in the response variable
associated with one unit of change in the predicting variable.
How we interpret ^B0? - ansIt is the estimated expected value of the response variable, when
the predicting variable equals zero.
What is the sampling distribution of ^B1? - anst distribution with N-2 DF
What can we use to test for statistical significance? - anst-test
What would we do if the T value is large? - ansReject the null hypothesis that β1 is equal to
zero. If the null hypothesis is rejected, we interpret this that β1 is statistically significant.
what does 'statistical significance' mean? - ansB1 is statistically different from zero.
what is the distribution of B1? - ansNormal
The estimators for the regression coefficients are:
A) Biased but with small variance
B) Unbiased under normality assumptions but biased otherwise.
C) Unbiased regardless of the distribution of the data. - ansC
The assumption of normality:
A) It is needed for deriving the estimators of the regression coefficients.
B) It is not needed for linear regression modeling and inference.
C) It is needed for the sampling distribution of the estimators of the regression coefficients
and hence for inference.
D) It is needed for deriving the expectation and variance of the estimators of the regression
coefficients. - ansC
What is 'X*'? - anspredictor
Where does uncertainty from estimation come from? - ansfrom estimation alone
Where does uncertainty from prediction come from? - ansfrom the estimation of regression
parameters and from the newness of the observation itself
what is the prediction interval used for? - ansused to provide an interval estimate for a
prediction of y for one member of the population with a particular value of x*
, ISYE 6414 – Georgia Institute of Technology – All Units Exam Guide (2025 Edition) –
Actual Exam Questions with 100% Verified Answers
This comprehensive exam document covers all units of the ISYE 6414 course (Georgia
Tech), providing fully verified questions and answers for the 2025 edition. Topics
include simple and multiple linear regression, ANOVA, logistic regression, Poisson
regression, model assumptions, variable selection, regularization techniques (Ridge,
LASSO, Elastic Net), and statistical inference methods. It is structured for clarity,
with extensive true/false, multiple-choice, and open-answer format, making it a
reliable resource for mastering exam material.
100% Verified Exam Study Guide 2025/2026.
what is the confidence interval used for? - ansto provide an interval estimate for the true
average value of y for all members of the population with a particular value of x*
The estimated versus predicted regression line for a given x*:
A) Have the same variance
B) Have the same expectation
C) Have the same variance and expectation
D) None of the above - ansB
The variability in the prediction comes from:
A) The variability due to a new measurement.
B) The variability due to estimation.
C) The variability due to a new measurement and due to estimation.
D) None of the above. - ansC
residuals - ansthe difference between the observed response and the fitted responses
what does residual analysis NOT check for? (for SLR assumptions) - ansindependence
what can we use to check for normality? - ansQQ plot and histogram
what are two ways to transform data? - anspower and log transformation
outliers - answhich are data points far from the majority of the data in both x and y or just x
leverage points - ansData points that are far from the mean of the x's
influential points - ansA data point that is far from the mean of both the x's and the y's,
because they are influencing the fit of the regression.
R^2 or coefficient of determination - ansa statistic that efficiently summarizes how well the x
can be used to predict the response variable.
How do we interpret R^2? - ansProportion of total variability in Y that can be explained by
the regression (that uses X)
correlation coefficient - ansa statistic that efficiently summarizes how well the X's are
linearly related to Y
what is the objective of ANOVA? - ansto compare the means across the k populations, are
they equal?
3 primary objectives of ANOVA - ansanalyze the variability of data, test whether the means
are equal, estimate confidence intervals
pooled variance estimator (MSE) - answe compare the means, assuming the variances are the
same, and estimate the variance across all samples
Pooled variance estimator - N vs k? - ansN = combined size of samples, k = # of samples
What is the sampling distribution for the pooled variance estimator? - anschi-square
distribution with N - K degrees of freedom
H0 and HA for test of equal means? - ansH0: the means are equal
HA: some means are different
Actual Exam Questions with 100% Verified Answers
This comprehensive exam document covers all units of the ISYE 6414 course (Georgia
Tech), providing fully verified questions and answers for the 2025 edition. Topics
include simple and multiple linear regression, ANOVA, logistic regression, Poisson
regression, model assumptions, variable selection, regularization techniques (Ridge,
LASSO, Elastic Net), and statistical inference methods. It is structured for clarity,
with extensive true/false, multiple-choice, and open-answer format, making it a
reliable resource for mastering exam material.
100% Verified Exam Study Guide 2025/2026.
response (dependent) variables - ansone particular variable that we are interested in
understanding or modeling (y)
predicting or explanatory (independent) variables - ansa 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? - ansrandom, because it varies with
changes in the predictor/s along with other random changes.
What kind of variable is a predicting variable and why? - ansfixed, because it does not
change with the response but it is fixed before the response is measured.
linear relationship - ansa simple deterministic relationship between 2 factors, x and y
what are three things that a regression analysis is used for? - ans1. Prediction of the response
variable, 2. Modeling the relationship between the response and explanatory variables, 3.
Testing hypotheses of association relationships
B0 = ? - ansintercept
B1 = ? - ansslope
for our linear model where: Y = B0 + B1 + EPSILON (E), what does the epsilon represent? -
ansdeviance of the data from the linear model (error term)
what are the 4 assumptions of linear regression? - ansLinearity/Mean Zero, Constant
Variance, Independence, Normality
Linearity/Mean zero assumption - ansMeans 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 - ansMeans 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 - ansMeans 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.
Normality assumption - ansThis 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? - ansB0, B1, sigma squared (variance
of the one pop.)
What do we mean by model parameters in statistics? - ansModel 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? - anschi-square with n-1 DF
Why do we lose 1 DF for s^2? - answe replace mu with zbar
what is the relationship between s^2 and sigma^2? - ansS^2 estimates sigma^2
,ISYE 6414 – Georgia Institute of Technology – All Units Exam Guide (2025 Edition) –
Actual Exam Questions with 100% Verified Answers
This comprehensive exam document covers all units of the ISYE 6414 course (Georgia
Tech), providing fully verified questions and answers for the 2025 edition. Topics
include simple and multiple linear regression, ANOVA, logistic regression, Poisson
regression, model assumptions, variable selection, regularization techniques (Ridge,
LASSO, Elastic Net), and statistical inference methods. It is structured for clarity,
with extensive true/false, multiple-choice, and open-answer format, making it a
reliable resource for mastering exam material.
100% Verified Exam Study Guide 2025/2026.
What is the estimated sampling distribution of sigma^2? - anschi-square with n-2 DF (~
equivalent to MSE)
Why do we lose 2 DF for sigma^2? - answe replaced two parameters, B0 and B1
In SLR, we are interested in the behavior of which parameter? - ansB1
If we have a positive value for B1,.... - ansthen 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,.... - ansis consistent with an inverse relationship between
x and y
When B1 is close to zero... - answe 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? - ansIt is the estimated expected change in the response variable
associated with one unit of change in the predicting variable.
How we interpret ^B0? - ansIt is the estimated expected value of the response variable, when
the predicting variable equals zero.
What is the sampling distribution of ^B1? - anst distribution with N-2 DF
What can we use to test for statistical significance? - anst-test
What would we do if the T value is large? - ansReject the null hypothesis that β1 is equal to
zero. If the null hypothesis is rejected, we interpret this that β1 is statistically significant.
what does 'statistical significance' mean? - ansB1 is statistically different from zero.
what is the distribution of B1? - ansNormal
The estimators for the regression coefficients are:
A) Biased but with small variance
B) Unbiased under normality assumptions but biased otherwise.
C) Unbiased regardless of the distribution of the data. - ansC
The assumption of normality:
A) It is needed for deriving the estimators of the regression coefficients.
B) It is not needed for linear regression modeling and inference.
C) It is needed for the sampling distribution of the estimators of the regression coefficients
and hence for inference.
D) It is needed for deriving the expectation and variance of the estimators of the regression
coefficients. - ansC
What is 'X*'? - anspredictor
Where does uncertainty from estimation come from? - ansfrom estimation alone
Where does uncertainty from prediction come from? - ansfrom the estimation of regression
parameters and from the newness of the observation itself
what is the prediction interval used for? - ansused to provide an interval estimate for a
prediction of y for one member of the population with a particular value of x*
, ISYE 6414 – Georgia Institute of Technology – All Units Exam Guide (2025 Edition) –
Actual Exam Questions with 100% Verified Answers
This comprehensive exam document covers all units of the ISYE 6414 course (Georgia
Tech), providing fully verified questions and answers for the 2025 edition. Topics
include simple and multiple linear regression, ANOVA, logistic regression, Poisson
regression, model assumptions, variable selection, regularization techniques (Ridge,
LASSO, Elastic Net), and statistical inference methods. It is structured for clarity,
with extensive true/false, multiple-choice, and open-answer format, making it a
reliable resource for mastering exam material.
100% Verified Exam Study Guide 2025/2026.
what is the confidence interval used for? - ansto provide an interval estimate for the true
average value of y for all members of the population with a particular value of x*
The estimated versus predicted regression line for a given x*:
A) Have the same variance
B) Have the same expectation
C) Have the same variance and expectation
D) None of the above - ansB
The variability in the prediction comes from:
A) The variability due to a new measurement.
B) The variability due to estimation.
C) The variability due to a new measurement and due to estimation.
D) None of the above. - ansC
residuals - ansthe difference between the observed response and the fitted responses
what does residual analysis NOT check for? (for SLR assumptions) - ansindependence
what can we use to check for normality? - ansQQ plot and histogram
what are two ways to transform data? - anspower and log transformation
outliers - answhich are data points far from the majority of the data in both x and y or just x
leverage points - ansData points that are far from the mean of the x's
influential points - ansA data point that is far from the mean of both the x's and the y's,
because they are influencing the fit of the regression.
R^2 or coefficient of determination - ansa statistic that efficiently summarizes how well the x
can be used to predict the response variable.
How do we interpret R^2? - ansProportion of total variability in Y that can be explained by
the regression (that uses X)
correlation coefficient - ansa statistic that efficiently summarizes how well the X's are
linearly related to Y
what is the objective of ANOVA? - ansto compare the means across the k populations, are
they equal?
3 primary objectives of ANOVA - ansanalyze the variability of data, test whether the means
are equal, estimate confidence intervals
pooled variance estimator (MSE) - answe compare the means, assuming the variances are the
same, and estimate the variance across all samples
Pooled variance estimator - N vs k? - ansN = combined size of samples, k = # of samples
What is the sampling distribution for the pooled variance estimator? - anschi-square
distribution with N - K degrees of freedom
H0 and HA for test of equal means? - ansH0: the means are equal
HA: some means are different
