ISYE 6414 OFFICIAL MIDTERM 1
CERTIFICATION SCRIPT 2026 QUESTIONS
WITH SOLUTIONS GRADED A+
◍ The pooled variance estimator is:A) The sample variance estimator
assuming equal variances.B) The variance estimator assuming equal means
and equal variances.C) The sample variance estimator assuming equal
means.D) None of the above.
Answer: A) The sample variance estimator assuming equal variances.
◍ What is a coefficient that can efficiently summarize how well the X's can be
used to predict Y?.
Answer: R**21 - SSE / SST
◍ independence assumption.
Answer: response variables are independently drawnresponses are not
related to each other (unlike in time series)
◍ The larger the coefficient of determination or R-squared, the higher the
variability explained by the simple linear regression model.A) TrueB) False.
Answer: A) True
◍ In simple linear regression, the confidence interval of the response increases
as the distance between the predictor value and the mean value of the
predictors decreases.A) TrueB) False.
Answer: B) False
◍ What is the overarching objective of ANOVA?.
Answer: To compare the means of multiple samples.
◍ A negative value of β 1 is consistent with an inverse relationship between x
and y.A) TrueB) False.
, Answer: A) True
◍ The prediction interval will never be smaller than the confidence interval for
data points with identical predictor values.A) TrueB) False.
Answer: A) True
◍ β₁_hat.
Answer: estimated expected change in response variable w/ one unit change
in predicting variable
◍ What is the p-value?.
Answer: The p-value is a measure of how reject-able the null hypothesis is.
The smaller the p-value, the more reject-able the null hypothesis is for the
observed data.
◍ random variable.
Answer: varies with change in predictors along with other random changes
◍ reject the null hypothesis.
Answer: β₁ is significant
◍ estimated regression line.
Answer: average estimated mean response for all settings of the predicting
variable
◍ In terms of model parameter interpretation, how would you interpret a
positive value for B1, negative value, and value close to 0?.
Answer: A positive value of B1 is consistent with a direct relationship
between x and yA negative value of B1 is consistent with an inverse
relationship between x and yA close to zero value of B1 means that there is
not a significant association between x and y
◍ (multiple linear regression) The objective of multiple linear regression is:a)
To predict future new responsesB) To model the association of explanatory
variables to a response variable accounting for controlling factors.C) To test
hypothesis using statistical inference on the model.D) All of the above.
Answer: D) all of the above
, ◍ assumptions of simple linear regression.
Answer: -linearity/mean zero assumption-constant variance
assumption-independence assumption-normal distribution of error
◍ how do we diagnose the assumptions?.
Answer: evaluate the residuals (differences between observed and fitted
responses -- this is NOT error term because we don't actually know β₀ and
β₁) by plotting them against both fitted and predictive values and checking if
the scatter plot is random around the zero line (it should be!)
◍ confidence interval.
Answer: provides an interval estimate for the true average value of y for all
instances of a particular x
◍ We do not need to assume independence between data points for making
inference on the regression coefficients.A) TrueB) False.
Answer: B) False
◍ What does ANOVA stand for?.
Answer: Analysis of variance
◍ correlation coefficient.
Answer: a statistic that efficiently summarizes how well the Xs are linearly
related to ythe square of the correlation coefficient is R-squared: p² = R²
◍ λ = 1.
Answer: const (don't transform)
◍ What are the primary objectives of ANOVA?.
Answer: 1. Analysis of the variance in the data 2. Testing for equal means3.
Estimation of simultaneous confidence intervals for the mean differenceThe
2nd and 3rd objective are statistical inference problems
◍ What are influential points?.
Answer: A data point that is far from the mean of both the y's and the x's are
influential points and can change the values of the estimated parameters
significantly.
CERTIFICATION SCRIPT 2026 QUESTIONS
WITH SOLUTIONS GRADED A+
◍ The pooled variance estimator is:A) The sample variance estimator
assuming equal variances.B) The variance estimator assuming equal means
and equal variances.C) The sample variance estimator assuming equal
means.D) None of the above.
Answer: A) The sample variance estimator assuming equal variances.
◍ What is a coefficient that can efficiently summarize how well the X's can be
used to predict Y?.
Answer: R**21 - SSE / SST
◍ independence assumption.
Answer: response variables are independently drawnresponses are not
related to each other (unlike in time series)
◍ The larger the coefficient of determination or R-squared, the higher the
variability explained by the simple linear regression model.A) TrueB) False.
Answer: A) True
◍ In simple linear regression, the confidence interval of the response increases
as the distance between the predictor value and the mean value of the
predictors decreases.A) TrueB) False.
Answer: B) False
◍ What is the overarching objective of ANOVA?.
Answer: To compare the means of multiple samples.
◍ A negative value of β 1 is consistent with an inverse relationship between x
and y.A) TrueB) False.
, Answer: A) True
◍ The prediction interval will never be smaller than the confidence interval for
data points with identical predictor values.A) TrueB) False.
Answer: A) True
◍ β₁_hat.
Answer: estimated expected change in response variable w/ one unit change
in predicting variable
◍ What is the p-value?.
Answer: The p-value is a measure of how reject-able the null hypothesis is.
The smaller the p-value, the more reject-able the null hypothesis is for the
observed data.
◍ random variable.
Answer: varies with change in predictors along with other random changes
◍ reject the null hypothesis.
Answer: β₁ is significant
◍ estimated regression line.
Answer: average estimated mean response for all settings of the predicting
variable
◍ In terms of model parameter interpretation, how would you interpret a
positive value for B1, negative value, and value close to 0?.
Answer: A positive value of B1 is consistent with a direct relationship
between x and yA negative value of B1 is consistent with an inverse
relationship between x and yA close to zero value of B1 means that there is
not a significant association between x and y
◍ (multiple linear regression) The objective of multiple linear regression is:a)
To predict future new responsesB) To model the association of explanatory
variables to a response variable accounting for controlling factors.C) To test
hypothesis using statistical inference on the model.D) All of the above.
Answer: D) all of the above
, ◍ assumptions of simple linear regression.
Answer: -linearity/mean zero assumption-constant variance
assumption-independence assumption-normal distribution of error
◍ how do we diagnose the assumptions?.
Answer: evaluate the residuals (differences between observed and fitted
responses -- this is NOT error term because we don't actually know β₀ and
β₁) by plotting them against both fitted and predictive values and checking if
the scatter plot is random around the zero line (it should be!)
◍ confidence interval.
Answer: provides an interval estimate for the true average value of y for all
instances of a particular x
◍ We do not need to assume independence between data points for making
inference on the regression coefficients.A) TrueB) False.
Answer: B) False
◍ What does ANOVA stand for?.
Answer: Analysis of variance
◍ correlation coefficient.
Answer: a statistic that efficiently summarizes how well the Xs are linearly
related to ythe square of the correlation coefficient is R-squared: p² = R²
◍ λ = 1.
Answer: const (don't transform)
◍ What are the primary objectives of ANOVA?.
Answer: 1. Analysis of the variance in the data 2. Testing for equal means3.
Estimation of simultaneous confidence intervals for the mean differenceThe
2nd and 3rd objective are statistical inference problems
◍ What are influential points?.
Answer: A data point that is far from the mean of both the y's and the x's are
influential points and can change the values of the estimated parameters
significantly.
