ISYE 6414 ACTUAL EXAM PAPER 2026
QUESTIONS WITH ANSWERS GRADED A+
◍ [1.5 Assumptions and Diagnostics] Which statement about leverage points
is true?They should always be removed from the dataset.They can
significantly influence regression results but should not always be
removed.They are the same as outliers.They have no effect on regression
models..
Answer: They can significantly influence regression results but should not
always be removed.(See 1.5 Assumptions and DiagnosticsAn important
aspect in regression is the presence of outliers, which are data points far
from the majority of the data in x and/or y. Data points that are far from the
mean of the x's are called leverage points. A data point that is far from the
mean of the x's and/or the y's is called influential point if it influences the
regression model fit significantly. They can change the value of the
estimated parameters, the statistical significance, the magnitude the
estimated parameters, or even the sign. It is important to note that an outlier,
including a leverage point, may or may not impact the regression fit
significantly, thus it may or may not be an influential point.It is tempting to
just discard outliers. But sometimes the outliers belong to the data. Other
times, there are good reasons for excluding subset of points when there are
errors in a data entry or in the experiment. When outliers belong in the data,
you will have to perform the statistical analysis with and without the outliers
and inform the reader about how an outlier influences the regression fit.)
◍ The estimators for the regression coefficients are:A) Biased but with small
varianceB) Unbiased under normality assumptions but biased otherwiseC)
Biased regardless of the distribution of the data.D) Unbiased regardless of
the distribution of the data..
Answer: D
,◍ [1.5 Assumptions and Diagnostics] What does a histogram of residuals help
evaluate in regression?Linearity.Constant variance.Normality of
residuals.Independence of errors..
Answer: Normality of residuals.("The histogram is often used to evaluate
the shape of the distribution of the residuals." (Section 1.5 Assumptions and
Diagnostics))
◍ [1.8 ANOVA: Estimation Method] In ANOVA, how is the pooled variance
estimator’s degrees of freedom calculated?Total number of samples minus
1.Total number of samples minus the number of groups.Number of groups
minus 1.Number of groups minus total samples..
Answer: Total number of samples minus the number of groups.([1.8
ANOVA: Estimation Method]We use n−k to calculate the degrees of
freedom, where k is the number of groups and n is the total number of
samples. We replace μi with Yi for i=1,...,k, number of groups.)
◍ [1.1 Basics] In regression, which statement is true about predicting and
response variables? Both are random variables.Predicting variables are
fixed, and response variables are random.Predicting variables are random,
and response variables are fixed.Both are fixed variables..
Answer: Predicting variables are fixed, and response variables are
random.(The response variable is a random variable because it varies with
changes in the predicting variable. This is particularly important in the
context of statistical inference on the regression. I will add here that in
experimental or observational studies from which we derive the data for the
regression analysis, we observe the response variable and hence we have
observations of the response random variable. The predicting variable or
variables are assumed fixed. Specifically, we set the predicting variables
fixed, before the response is measured.)
◍ [1.7 ANOVA: Basic Concepts] Which statement is true about the use of
boxplots in ANOVA?Boxplots are not useful in visualizing group mean
differences.Boxplots can help identify outliers within groups but do not test
statistical significance.Boxplots directly test statistical significance of group
, means.Boxplots are irrelevant in the context of ANOV
A. .
Answer: Boxplots can help identify outliers within groups but do not test
statistical significance.("Boxplots are often used in ANOVA to visualize
group differences and identify outliers." (Section 1.7 ANOVA: Basic
Concepts))
◍ T/F: The coefficient of variation is used to evaluate goodness-of-fit..
Answer: F
◍ [1.11 Model Fit Assessment] Which assumption is not required for ANOVA
but is required for simple linear regression?Constant
variance.Linearity.Normality.Independence..
Answer: Linearity.("Linearity is not an assumption of ANOVA — a key
difference from Simple Linear Regression." (Section 1.11 Model Fit
Assessment))
◍ [1.9 Test for Equal Means] What is the null hypothesis in an F-test for equal
means in ANOVA?All group means are equal.All group means are
different.At least one group mean differs from the others.The largest group
mean is significantly higher..
Answer: All group means are equal.("The null hypothesis of the F-test is
that all group means are equal." (Section 1.9 Test for Equal Means))
◍ SST = ?.
Answer: SSE + SSTR
◍ T/F: The prediction of the response variable and the estimation of the mean
response have the same interpretation..
Answer: F
◍ 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.
◍ [1.2 Estimation Method] What is the objective of simple linear
regression?To create a deterministic linear model.To fit a non-deterministic
, linear model.To minimize absolute deviations.To maximize the sum of
squared residuals..
Answer: To fit a non-deterministic linear model.(See 1.2 Estimation
MethodThe linear model is non-deterministic. The model's fundamental
shape (a line) is determined in one sense, but the confidence intervals for
fitting (or prediction intervals for prediction) are an attempt to account for
the inherently non-deterministic nature of the relationship.)
◍ Cross validation.
Answer: Split the data into two parts, first part called the training data and
testing/validation data. The training data will be used to fit the model and
thus get the estimated regression coefficients. The testing or validation data
will be used to predict or classify the responses for this portion of the data,
then compare to the observed response to estimate the classification error,
one can repeat the process several times.
◍ [1.5 Assumptions and Diagnostics] What does goodness of fit describe?How
well a model minimizes residuals.The independence of the residuals.The
significance of regression coefficients.How much variability is explained by
the predictors..
Answer: How much variability is explained by the predictors.
◍ [1.5 Assumptions and Diagnostics] What is true about R-squared in simple
linear regression?It equals the square of the correlation coefficient.It
measures the variability in the predictors.It reflects the statistical
significance of coefficients.It is independent of the correlation coefficient..
Answer: It equals the square of the correlation coefficient.(See 1.5
Assumptions and Diagnostics"the square of the correlation coefficients is
actually the R squared.")
◍ Where does uncertainty from prediction come from?.
Answer: from the estimation of regression parameters and from the newness
of the observation itself
◍ [Various] Select all of the the statements that are True.Note: for the multiple
answer questions, an incorrect answer cancels out a correct answer.the F-test
QUESTIONS WITH ANSWERS GRADED A+
◍ [1.5 Assumptions and Diagnostics] Which statement about leverage points
is true?They should always be removed from the dataset.They can
significantly influence regression results but should not always be
removed.They are the same as outliers.They have no effect on regression
models..
Answer: They can significantly influence regression results but should not
always be removed.(See 1.5 Assumptions and DiagnosticsAn important
aspect in regression is the presence of outliers, which are data points far
from the majority of the data in x and/or y. Data points that are far from the
mean of the x's are called leverage points. A data point that is far from the
mean of the x's and/or the y's is called influential point if it influences the
regression model fit significantly. They can change the value of the
estimated parameters, the statistical significance, the magnitude the
estimated parameters, or even the sign. It is important to note that an outlier,
including a leverage point, may or may not impact the regression fit
significantly, thus it may or may not be an influential point.It is tempting to
just discard outliers. But sometimes the outliers belong to the data. Other
times, there are good reasons for excluding subset of points when there are
errors in a data entry or in the experiment. When outliers belong in the data,
you will have to perform the statistical analysis with and without the outliers
and inform the reader about how an outlier influences the regression fit.)
◍ The estimators for the regression coefficients are:A) Biased but with small
varianceB) Unbiased under normality assumptions but biased otherwiseC)
Biased regardless of the distribution of the data.D) Unbiased regardless of
the distribution of the data..
Answer: D
,◍ [1.5 Assumptions and Diagnostics] What does a histogram of residuals help
evaluate in regression?Linearity.Constant variance.Normality of
residuals.Independence of errors..
Answer: Normality of residuals.("The histogram is often used to evaluate
the shape of the distribution of the residuals." (Section 1.5 Assumptions and
Diagnostics))
◍ [1.8 ANOVA: Estimation Method] In ANOVA, how is the pooled variance
estimator’s degrees of freedom calculated?Total number of samples minus
1.Total number of samples minus the number of groups.Number of groups
minus 1.Number of groups minus total samples..
Answer: Total number of samples minus the number of groups.([1.8
ANOVA: Estimation Method]We use n−k to calculate the degrees of
freedom, where k is the number of groups and n is the total number of
samples. We replace μi with Yi for i=1,...,k, number of groups.)
◍ [1.1 Basics] In regression, which statement is true about predicting and
response variables? Both are random variables.Predicting variables are
fixed, and response variables are random.Predicting variables are random,
and response variables are fixed.Both are fixed variables..
Answer: Predicting variables are fixed, and response variables are
random.(The response variable is a random variable because it varies with
changes in the predicting variable. This is particularly important in the
context of statistical inference on the regression. I will add here that in
experimental or observational studies from which we derive the data for the
regression analysis, we observe the response variable and hence we have
observations of the response random variable. The predicting variable or
variables are assumed fixed. Specifically, we set the predicting variables
fixed, before the response is measured.)
◍ [1.7 ANOVA: Basic Concepts] Which statement is true about the use of
boxplots in ANOVA?Boxplots are not useful in visualizing group mean
differences.Boxplots can help identify outliers within groups but do not test
statistical significance.Boxplots directly test statistical significance of group
, means.Boxplots are irrelevant in the context of ANOV
A. .
Answer: Boxplots can help identify outliers within groups but do not test
statistical significance.("Boxplots are often used in ANOVA to visualize
group differences and identify outliers." (Section 1.7 ANOVA: Basic
Concepts))
◍ T/F: The coefficient of variation is used to evaluate goodness-of-fit..
Answer: F
◍ [1.11 Model Fit Assessment] Which assumption is not required for ANOVA
but is required for simple linear regression?Constant
variance.Linearity.Normality.Independence..
Answer: Linearity.("Linearity is not an assumption of ANOVA — a key
difference from Simple Linear Regression." (Section 1.11 Model Fit
Assessment))
◍ [1.9 Test for Equal Means] What is the null hypothesis in an F-test for equal
means in ANOVA?All group means are equal.All group means are
different.At least one group mean differs from the others.The largest group
mean is significantly higher..
Answer: All group means are equal.("The null hypothesis of the F-test is
that all group means are equal." (Section 1.9 Test for Equal Means))
◍ SST = ?.
Answer: SSE + SSTR
◍ T/F: The prediction of the response variable and the estimation of the mean
response have the same interpretation..
Answer: F
◍ 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.
◍ [1.2 Estimation Method] What is the objective of simple linear
regression?To create a deterministic linear model.To fit a non-deterministic
, linear model.To minimize absolute deviations.To maximize the sum of
squared residuals..
Answer: To fit a non-deterministic linear model.(See 1.2 Estimation
MethodThe linear model is non-deterministic. The model's fundamental
shape (a line) is determined in one sense, but the confidence intervals for
fitting (or prediction intervals for prediction) are an attempt to account for
the inherently non-deterministic nature of the relationship.)
◍ Cross validation.
Answer: Split the data into two parts, first part called the training data and
testing/validation data. The training data will be used to fit the model and
thus get the estimated regression coefficients. The testing or validation data
will be used to predict or classify the responses for this portion of the data,
then compare to the observed response to estimate the classification error,
one can repeat the process several times.
◍ [1.5 Assumptions and Diagnostics] What does goodness of fit describe?How
well a model minimizes residuals.The independence of the residuals.The
significance of regression coefficients.How much variability is explained by
the predictors..
Answer: How much variability is explained by the predictors.
◍ [1.5 Assumptions and Diagnostics] What is true about R-squared in simple
linear regression?It equals the square of the correlation coefficient.It
measures the variability in the predictors.It reflects the statistical
significance of coefficients.It is independent of the correlation coefficient..
Answer: It equals the square of the correlation coefficient.(See 1.5
Assumptions and Diagnostics"the square of the correlation coefficients is
actually the R squared.")
◍ Where does uncertainty from prediction come from?.
Answer: from the estimation of regression parameters and from the newness
of the observation itself
◍ [Various] Select all of the the statements that are True.Note: for the multiple
answer questions, an incorrect answer cancels out a correct answer.the F-test
