ISYE 6414 MAIN EXAMINATION 2026 SET QUESTIONS AND
SOLUTIONS RATED A+
✔✔A multiple linear regression model contains 6 quantitative predicting variables and
an intercept. The number of parameters to estimate in this model is 7. - ✔✔false
See Lesson 3.2: Basic Concepts
The number of parameters to estimate in a multiple linear regression model containing 6
quantitative predicting variables and an intercept is 8: 7 regression coefficients
(β0,β1,...,β6) and the variance of the error terms (σ2).
✔✔In multiple linear regression, the estimated regression coefficient corresponding to a
quantitative predicting variable is interpreted as the estimated expected change in the
response variable when there is a change of one unit in the corresponding predicting
variable holding all other predictors fixed. - ✔✔true
See Lesson 3.4: Model Interpretation
"The estimated value for one of the regression coefficient βi represents the estimated
expected change in y associated with one unit of change in the corresponding
predicting variable, Xi, holding all else in the model fixed."
✔✔A partial F-Test can be used to test whether the regression coefficients associated
with a subset of the predicting variables in a multiple linear regression model are all
equal to zero. - ✔✔true
See Lesson 3.7: Testing for Subsets of Regression Parameters
We use the Partial F-test to test the null hypothesis that the regression coefficients
associated to a subset of the predicting variables are all equal to zero. The alternative
hypothesis is that at least one of these regression coefficients is not zero.
✔✔The estimated variance of the error terms of a multiple linear regression model with
intercept can be obtained by summing up the squared residuals and dividing the sum by
n - p , where n is the sample size and p is the number of predictors. - ✔✔false
See Lesson 3.3: Regression Parameter Estimation
The estimated variance of the error terms of a multiple linear regression model with
intercept should be obtained by summing up the squared residuals and dividing that by
n-p-1, where n is the sample size and p is the number of predictors as we lose p+1
degrees of freedom when we estimate the p coefficients and 1 intercept.
✔✔For a given predicting variable, the corresponding estimated regression coefficient
will likely be different in a conditional model versus a marginal model. - ✔✔true
See Lesson 3.4: Model Interpretation
, "Importantly, the estimated regression coefficients for the conditional and marginal
relationships can be different, not only in magnitude but also in sign or direction of the
relationship."
✔✔In the case of multiple linear regression, controlling variables are used to control for
sample bias. - ✔✔true
See Lesson 3.4: Model Interpretation
"Controlling variables can be used to control for bias selection in a sample."
✔✔Conducting t-tests on each β parameter in a multiple linear regression model is the
preferable to an F-test when testing the overall significance of the model. - ✔✔false
See Lesson 3.7: Testing for Subsets of Coefficients
"We cannot and should not select the combination of predicting variables that most
explains the variability in the response based on the t-tests for statistical significance
because the statistical significance depends on what other variables are in the model."
✔✔An example of a multiple linear regression model is Analysis of Variance (ANOVA). -
✔✔true
See Lesson 3.2 Basic Concepts
"Earlier, we contrasted the simple linear regression model with the ANOVA model...
Multiple linear regression is a generalization of both models."
✔✔Given a quantitative predicting variable and a qualitative predicting variable with 7
categories in a linear regression model with intercept, 7 dummy variables need to be
included in the model. - ✔✔False
See Lesson 3.2: Basic Concepts
We only need 7 dummy variables. "When we have qualitative variables with k levels, we
only include k-1 dummy variables if the regression model has an intercept."
✔✔It is good practice to create a multiple linear regression model using a linearly
dependent set of predictor variables. - ✔✔false
See Lesson 3.13: Model Evaluation and Multicollinearity
It is good practice to create a multiple linear regression model using a linearly
independent set of predicting variables. "XTX is not invertible if the columns of X are
linearly dependent, i.e. one predicting variable, corresponding to one column, is a linear
combination of the others."
✔✔The causation of a predicting variable to the response variable can be captured
using multiple linear regression on observational data, conditional of other predicting
variables in the model. - ✔✔false
SOLUTIONS RATED A+
✔✔A multiple linear regression model contains 6 quantitative predicting variables and
an intercept. The number of parameters to estimate in this model is 7. - ✔✔false
See Lesson 3.2: Basic Concepts
The number of parameters to estimate in a multiple linear regression model containing 6
quantitative predicting variables and an intercept is 8: 7 regression coefficients
(β0,β1,...,β6) and the variance of the error terms (σ2).
✔✔In multiple linear regression, the estimated regression coefficient corresponding to a
quantitative predicting variable is interpreted as the estimated expected change in the
response variable when there is a change of one unit in the corresponding predicting
variable holding all other predictors fixed. - ✔✔true
See Lesson 3.4: Model Interpretation
"The estimated value for one of the regression coefficient βi represents the estimated
expected change in y associated with one unit of change in the corresponding
predicting variable, Xi, holding all else in the model fixed."
✔✔A partial F-Test can be used to test whether the regression coefficients associated
with a subset of the predicting variables in a multiple linear regression model are all
equal to zero. - ✔✔true
See Lesson 3.7: Testing for Subsets of Regression Parameters
We use the Partial F-test to test the null hypothesis that the regression coefficients
associated to a subset of the predicting variables are all equal to zero. The alternative
hypothesis is that at least one of these regression coefficients is not zero.
✔✔The estimated variance of the error terms of a multiple linear regression model with
intercept can be obtained by summing up the squared residuals and dividing the sum by
n - p , where n is the sample size and p is the number of predictors. - ✔✔false
See Lesson 3.3: Regression Parameter Estimation
The estimated variance of the error terms of a multiple linear regression model with
intercept should be obtained by summing up the squared residuals and dividing that by
n-p-1, where n is the sample size and p is the number of predictors as we lose p+1
degrees of freedom when we estimate the p coefficients and 1 intercept.
✔✔For a given predicting variable, the corresponding estimated regression coefficient
will likely be different in a conditional model versus a marginal model. - ✔✔true
See Lesson 3.4: Model Interpretation
, "Importantly, the estimated regression coefficients for the conditional and marginal
relationships can be different, not only in magnitude but also in sign or direction of the
relationship."
✔✔In the case of multiple linear regression, controlling variables are used to control for
sample bias. - ✔✔true
See Lesson 3.4: Model Interpretation
"Controlling variables can be used to control for bias selection in a sample."
✔✔Conducting t-tests on each β parameter in a multiple linear regression model is the
preferable to an F-test when testing the overall significance of the model. - ✔✔false
See Lesson 3.7: Testing for Subsets of Coefficients
"We cannot and should not select the combination of predicting variables that most
explains the variability in the response based on the t-tests for statistical significance
because the statistical significance depends on what other variables are in the model."
✔✔An example of a multiple linear regression model is Analysis of Variance (ANOVA). -
✔✔true
See Lesson 3.2 Basic Concepts
"Earlier, we contrasted the simple linear regression model with the ANOVA model...
Multiple linear regression is a generalization of both models."
✔✔Given a quantitative predicting variable and a qualitative predicting variable with 7
categories in a linear regression model with intercept, 7 dummy variables need to be
included in the model. - ✔✔False
See Lesson 3.2: Basic Concepts
We only need 7 dummy variables. "When we have qualitative variables with k levels, we
only include k-1 dummy variables if the regression model has an intercept."
✔✔It is good practice to create a multiple linear regression model using a linearly
dependent set of predictor variables. - ✔✔false
See Lesson 3.13: Model Evaluation and Multicollinearity
It is good practice to create a multiple linear regression model using a linearly
independent set of predicting variables. "XTX is not invertible if the columns of X are
linearly dependent, i.e. one predicting variable, corresponding to one column, is a linear
combination of the others."
✔✔The causation of a predicting variable to the response variable can be captured
using multiple linear regression on observational data, conditional of other predicting
variables in the model. - ✔✔false
