ISYE 6414-REGRESSION ANALYSIS
PROJECT REPORT FINAL TEST 2026
QUESTIONS WITH CORRECT ANSWERS
GRADED A+
◍ what is convex quadratic program.
Answer: f(x) is a convex quadratic function. Minimize f(x) or Maximize
-f(x). constraint set X is defined by linear equations and inequalites
◍ What are some downsides of surveys?.
Answer: Even if you what appears to be a representative sample in simple
ways, maybe it isn't in more complex ways.
◍ The test statistic used in ANOVA for pairwise comparison follows an
F-distribution. (T/F).
Answer: False(The test statistic for equal means follows an F-statistic.)
◍ what is constraint set X in a convex optimization progrem.
Answer: a convex set
◍ what are the variables in k-means clustering.
Answer: coordinate of cluster centers and if a point is part of certain cluster
◍ What does k < 1 mean in a weibull distribution.
Answer: modeling when failure rate decreases with time; worst things fail
first (mechancial parts), the parts that are left are the better ones and take
longer to fail
◍ ANOVA can be used to compare medians across more than two groups.
(T/F).
Answer: True(True, ANOVA can compare means across two or more
groups, allowing for the identification of significant differences.)
,◍ If the interarrival time is exponential what type of distribution is the arrival.
Answer: poisson
◍ In testing for statistically positive significance of the regression coefficients
in multiple linear regression, failing to reject the null hypothesis proves
statistical positivity for all the predicting coefficients. (T/F).
Answer: False(False, rejecting the null hypothesis would mean that at least
one predictor coefficient is positive.)
◍ what is imperfect information.
Answer: Neither one really knows the others profit margins exactly. And in
still other situation, some people have more information than others, so it's
not symmetric
◍ what are the variables and constants in optimization model for linear
regression.
Answer: the data is the constant and the coefficients are the variables
◍ what are deterministic simulations.
Answer: same inputs give the same outputs
◍ What is the process of neural networks?.
Answer: * Each input neuron accepts a single piece of information * for
example, if we are trying to solve the CAPTCHA problem we might divide
the picture of a digit into pixels and every pixel's status between fully white
and fully black goes to its own input neuron* As inputs come in, they're
passed to the first level of hidden neurons. Each simulated neuron calculates
a weighted value of those inputs and sends the result to neurons at the next
level. Those next level neurons do the same thing. There may be several
layers of hidden neurons one after another.* Eventually the output layer
neurons get their inputs and each one uses those inputs to find their results. *
Example: In CAPTCHA have one output neuron for each possible number
of letters and each output neuron's result is like a level of certainty that the
input image is that number or letter * In the end, the models predicted output
is whoever output neuron has the highest result
, ◍ What should you do if your problem is too hard.
Answer: Use a heuristic: rule of thumb process. It is ually gives good
solutions
◍ what is a general non-convex program.
Answer: Optimization problem is not convex
◍ In ANOVA with k population samples, the sampling distribution of the
pooled variance is a chi-square distribution with N - 2 degrees of freedom.
(T/F).
Answer: False (False, the sampling distribution of the pooled variance is a
chi-square distribution with N - k degrees of freedom.)
◍ A multiple linear regression model was used to estimate the response
variable Y using the predictors X1, X2, X3 (see picture)What is the total
number of observations used for building this MLR model?17941797
17991800.
Answer: 1800 Explanation (from Module 3 Topic 3.2 Lesson 6):The
residual degrees of freedom n−p−1=1794Number of predictors,
p=5Solving:n = 1794+ 5 + 1 =1800
◍ A dataset contains 696 data points and 10 categories with:SSTR = 1250SSE
= 3750Select the correct value of F₀. (Make sure to check the last two
decimal places)27.722.8625.40 None of the above.
Answer: 25.40
◍ In simple linear regression, the correlation coefficient between the predictor
variable and the response variable is equal to the slope of the regression line
(β₁). (T/F).
Answer: False (False. Correlation coefficient is a statistic that efficiently
summarizes how well the X's are linearly related to Y. It is not the same as
the slope.)
◍ The following situation is a sign of multicollinearity: The F-test for overall
model adequacy is significant, whereas the t-tests result in almost all the β
parameters not being statistically significant. (T/F).
PROJECT REPORT FINAL TEST 2026
QUESTIONS WITH CORRECT ANSWERS
GRADED A+
◍ what is convex quadratic program.
Answer: f(x) is a convex quadratic function. Minimize f(x) or Maximize
-f(x). constraint set X is defined by linear equations and inequalites
◍ What are some downsides of surveys?.
Answer: Even if you what appears to be a representative sample in simple
ways, maybe it isn't in more complex ways.
◍ The test statistic used in ANOVA for pairwise comparison follows an
F-distribution. (T/F).
Answer: False(The test statistic for equal means follows an F-statistic.)
◍ what is constraint set X in a convex optimization progrem.
Answer: a convex set
◍ what are the variables in k-means clustering.
Answer: coordinate of cluster centers and if a point is part of certain cluster
◍ What does k < 1 mean in a weibull distribution.
Answer: modeling when failure rate decreases with time; worst things fail
first (mechancial parts), the parts that are left are the better ones and take
longer to fail
◍ ANOVA can be used to compare medians across more than two groups.
(T/F).
Answer: True(True, ANOVA can compare means across two or more
groups, allowing for the identification of significant differences.)
,◍ If the interarrival time is exponential what type of distribution is the arrival.
Answer: poisson
◍ In testing for statistically positive significance of the regression coefficients
in multiple linear regression, failing to reject the null hypothesis proves
statistical positivity for all the predicting coefficients. (T/F).
Answer: False(False, rejecting the null hypothesis would mean that at least
one predictor coefficient is positive.)
◍ what is imperfect information.
Answer: Neither one really knows the others profit margins exactly. And in
still other situation, some people have more information than others, so it's
not symmetric
◍ what are the variables and constants in optimization model for linear
regression.
Answer: the data is the constant and the coefficients are the variables
◍ what are deterministic simulations.
Answer: same inputs give the same outputs
◍ What is the process of neural networks?.
Answer: * Each input neuron accepts a single piece of information * for
example, if we are trying to solve the CAPTCHA problem we might divide
the picture of a digit into pixels and every pixel's status between fully white
and fully black goes to its own input neuron* As inputs come in, they're
passed to the first level of hidden neurons. Each simulated neuron calculates
a weighted value of those inputs and sends the result to neurons at the next
level. Those next level neurons do the same thing. There may be several
layers of hidden neurons one after another.* Eventually the output layer
neurons get their inputs and each one uses those inputs to find their results. *
Example: In CAPTCHA have one output neuron for each possible number
of letters and each output neuron's result is like a level of certainty that the
input image is that number or letter * In the end, the models predicted output
is whoever output neuron has the highest result
, ◍ What should you do if your problem is too hard.
Answer: Use a heuristic: rule of thumb process. It is ually gives good
solutions
◍ what is a general non-convex program.
Answer: Optimization problem is not convex
◍ In ANOVA with k population samples, the sampling distribution of the
pooled variance is a chi-square distribution with N - 2 degrees of freedom.
(T/F).
Answer: False (False, the sampling distribution of the pooled variance is a
chi-square distribution with N - k degrees of freedom.)
◍ A multiple linear regression model was used to estimate the response
variable Y using the predictors X1, X2, X3 (see picture)What is the total
number of observations used for building this MLR model?17941797
17991800.
Answer: 1800 Explanation (from Module 3 Topic 3.2 Lesson 6):The
residual degrees of freedom n−p−1=1794Number of predictors,
p=5Solving:n = 1794+ 5 + 1 =1800
◍ A dataset contains 696 data points and 10 categories with:SSTR = 1250SSE
= 3750Select the correct value of F₀. (Make sure to check the last two
decimal places)27.722.8625.40 None of the above.
Answer: 25.40
◍ In simple linear regression, the correlation coefficient between the predictor
variable and the response variable is equal to the slope of the regression line
(β₁). (T/F).
Answer: False (False. Correlation coefficient is a statistic that efficiently
summarizes how well the X's are linearly related to Y. It is not the same as
the slope.)
◍ The following situation is a sign of multicollinearity: The F-test for overall
model adequacy is significant, whereas the t-tests result in almost all the β
parameters not being statistically significant. (T/F).
