ISYE 6414 OFFICIAL MIDTERM 1 FINAL
TEST 2026 QUESTIONS WITH CORRECT
ANSWERS GRADED A+
◍ Can a distribution not be memoryless and still be exponential.
Answer: no
◍ In simple linear regression, we aim to create a non-deterministic, linear
model between the explanatory variable and the response variable. (T/F).
Answer: True. The 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.
◍ In simple linear regression, while performing a t-test for statistical
significance, we fail to reject the null hypothesis if |t-value| < t-critical
value. (T/F).
Answer: True, with a t-test, the null hypothesis is rejected if |t-value| <
t-critical value
◍ In a general sense, a fitted model is simply the output of minimizing the
errors as measured by a particular criterion. (T/F).
Answer: True. The fitted line is the line that makes the errors as small as
possible given a criterion (like OLS), as shown in the graph on the slide. In
this graph we have two lines, one in red and one in blue. The criterion would
be a function of the deviances of the data from the line, also called error
terms; this function of the error terms will make up the criterion used to
obtain the line.
◍ What are the variables in logistic regreession.
Answer: the coefficients
,◍ in soft and hard classification SVMs what are the variables.
Answer: the coefficients
◍ In simple linear regression, the correlation coefficient between the predictor
variable and the response variable is equal to the slope of the regression line.
(T/F).
Answer: False. Correlation Coefficient is a statistic that efficiently
summarizes how well the X's are linearly related to Y is the correlation
coefficient.
◍ What are data points called that are far from the mean of the x's?.
Answer: Leverage pointsNote, 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.
◍ When t-value for a beta value is smaller than our p-threshold, we reject the
null hypothesis which is by default is that the beta value is equal to zero (0).
(T/F).
Answer: False. If a t-value is large, we reject the null hypothesis that beta is
equal to zero. if the null hypothesis is rejected, we interpret this that beta is
statistically significant. Statistical significance means that beta is statistically
different from zero. The statement about a t-value being smaller than a
p-threshold is a nonsensical statement (they don't get compared directly)
◍ The linearity assumption is not required for ANOV
A. (T/F).
Answer: True
◍ if x* is one of the observations for the predicting variable, then we use
estimation. (T/F).
Answer: True
◍ What is a bi-modal distribution?.
Answer: Here are key characteristics of a bi-modal distribution:Two Peaks:
The distribution has two prominent peaks or modes.Valley Between Peaks:
There is typically a dip or valley between the two modes.Separation: The
, modes are separated by a range of values with lower frequency or
probability.
◍ Under what conditions should you run A/B tests.
Answer: When you can collect data quickly. When the data is representative
and the amount of data is small compared to the whole population
◍ what is the memoryless property.
Answer: it doesn't matter what's happened in the past, all that matters is
where we are now
◍ order linear regression, ridge regession, elastic net and lasso regression in
order of variable selected ascending.
Answer: lasso, elastic net, ridge and linear (tied)
◍ In Box-Cox transformation, if the value of lambda is 1, we:.
Answer: Do not need to transform
◍ Given a simple linear regression model, for a future y (at x) the prediction
interval is narrower than the confidence interval for the mean response.
(T/F).
Answer: False, the line estimate is the same, but the interval is wider than
the confidence interval for the mean response. (Module 1 Topic 1.2 Lesson
6)
◍ what is the difference between Weibull and geometric distribution.
Answer: weibull - time between failures; geometric - number of tries
between failures
◍ What are the assumptions does a geometric distribution make?.
Answer: Each Bernoulli trial is independent and identically distributed
◍ If we have independent chi-squared random variables, their sum is also a
chi-square distribution. (T/F).
Answer: True
◍ Do optimization implicitly assume that we know all of the values of the
input data exactly?.
TEST 2026 QUESTIONS WITH CORRECT
ANSWERS GRADED A+
◍ Can a distribution not be memoryless and still be exponential.
Answer: no
◍ In simple linear regression, we aim to create a non-deterministic, linear
model between the explanatory variable and the response variable. (T/F).
Answer: True. The 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.
◍ In simple linear regression, while performing a t-test for statistical
significance, we fail to reject the null hypothesis if |t-value| < t-critical
value. (T/F).
Answer: True, with a t-test, the null hypothesis is rejected if |t-value| <
t-critical value
◍ In a general sense, a fitted model is simply the output of minimizing the
errors as measured by a particular criterion. (T/F).
Answer: True. The fitted line is the line that makes the errors as small as
possible given a criterion (like OLS), as shown in the graph on the slide. In
this graph we have two lines, one in red and one in blue. The criterion would
be a function of the deviances of the data from the line, also called error
terms; this function of the error terms will make up the criterion used to
obtain the line.
◍ What are the variables in logistic regreession.
Answer: the coefficients
,◍ in soft and hard classification SVMs what are the variables.
Answer: the coefficients
◍ In simple linear regression, the correlation coefficient between the predictor
variable and the response variable is equal to the slope of the regression line.
(T/F).
Answer: False. Correlation Coefficient is a statistic that efficiently
summarizes how well the X's are linearly related to Y is the correlation
coefficient.
◍ What are data points called that are far from the mean of the x's?.
Answer: Leverage pointsNote, 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.
◍ When t-value for a beta value is smaller than our p-threshold, we reject the
null hypothesis which is by default is that the beta value is equal to zero (0).
(T/F).
Answer: False. If a t-value is large, we reject the null hypothesis that beta is
equal to zero. if the null hypothesis is rejected, we interpret this that beta is
statistically significant. Statistical significance means that beta is statistically
different from zero. The statement about a t-value being smaller than a
p-threshold is a nonsensical statement (they don't get compared directly)
◍ The linearity assumption is not required for ANOV
A. (T/F).
Answer: True
◍ if x* is one of the observations for the predicting variable, then we use
estimation. (T/F).
Answer: True
◍ What is a bi-modal distribution?.
Answer: Here are key characteristics of a bi-modal distribution:Two Peaks:
The distribution has two prominent peaks or modes.Valley Between Peaks:
There is typically a dip or valley between the two modes.Separation: The
, modes are separated by a range of values with lower frequency or
probability.
◍ Under what conditions should you run A/B tests.
Answer: When you can collect data quickly. When the data is representative
and the amount of data is small compared to the whole population
◍ what is the memoryless property.
Answer: it doesn't matter what's happened in the past, all that matters is
where we are now
◍ order linear regression, ridge regession, elastic net and lasso regression in
order of variable selected ascending.
Answer: lasso, elastic net, ridge and linear (tied)
◍ In Box-Cox transformation, if the value of lambda is 1, we:.
Answer: Do not need to transform
◍ Given a simple linear regression model, for a future y (at x) the prediction
interval is narrower than the confidence interval for the mean response.
(T/F).
Answer: False, the line estimate is the same, but the interval is wider than
the confidence interval for the mean response. (Module 1 Topic 1.2 Lesson
6)
◍ what is the difference between Weibull and geometric distribution.
Answer: weibull - time between failures; geometric - number of tries
between failures
◍ What are the assumptions does a geometric distribution make?.
Answer: Each Bernoulli trial is independent and identically distributed
◍ If we have independent chi-squared random variables, their sum is also a
chi-square distribution. (T/F).
Answer: True
◍ Do optimization implicitly assume that we know all of the values of the
input data exactly?.
