ISYE6414 Final Exam Study Guide Questions And
Answers Verified 100% Correct
To test if a coefficient is less than a critical value, C, we conduct a one-sided
test on the _________ tail of a ___________ distribution.
left, normal
left, t
right, normal
right, t
None of the above -ANSWER-- left, t
See 1.4 Statistical Inference
"For β 1 greater than zero we're interested on the right tail of the distribution of the
β ^ 1."
A multiple linear regression model contains 6 quantitative predicting variables and
an intercept. The number of parameters to estimate in this model is 7. -ANSWER--
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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -
ANSWER-- 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). -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- false
, See Lesson 3.4 Model Interpretation
"This is particularly prevalent in a context of making causal statements when the
setup of the regression does not allow so. Causality statements can only be made in
a controlled environment such as randomized trials or experiments. "
For a multiple linear regression model to be a good fit, we need the linearity
assumption to hold for only one of the predicting variables. -ANSWER-- false
See Lesson 3.11: Assumptions and diagnostics
In multiple linear regression, we need the linearity assumption to hold for all of the
predicting variables, for the model to be a good fit. "For example, if the linearity
does not hold with one or more predicting variables, then we could transform the
predicting variables to improve the linearity assumption."
Multicollinearity among the predicting variables will not impact the standard
errors of the estimated regression coefficients. -ANSWER-- false
See Lesson 3.13: Multicollinearity
Multicollinearity in the predicting variables can impact the standard errors of the
estimated coefficients. "However, the bigger problem is that the standard errors
will be artificially large."
The presence of certain types of outliers, such as influential points, can impact
the statistical significance of some of the regression coefficients. -ANSWER--
true
See Lesson 3.11: Assumptions and diagnostics
Outliers that are influential can impact the statistical significance of the beta
parameters.
Multicollinearity in multiple linear regression means that the rows in the
design matrix are (nearly) linearly dependent. -ANSWER-- false
See Lesson 3.13: Model Evaluation and Multicollinearity
Multicollinearity in multiple linear regression means that the columns in the design
matrix are (nearly) linearly dependent.
Answers Verified 100% Correct
To test if a coefficient is less than a critical value, C, we conduct a one-sided
test on the _________ tail of a ___________ distribution.
left, normal
left, t
right, normal
right, t
None of the above -ANSWER-- left, t
See 1.4 Statistical Inference
"For β 1 greater than zero we're interested on the right tail of the distribution of the
β ^ 1."
A multiple linear regression model contains 6 quantitative predicting variables and
an intercept. The number of parameters to estimate in this model is 7. -ANSWER--
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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -
ANSWER-- 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). -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- 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. -ANSWER-- false
, See Lesson 3.4 Model Interpretation
"This is particularly prevalent in a context of making causal statements when the
setup of the regression does not allow so. Causality statements can only be made in
a controlled environment such as randomized trials or experiments. "
For a multiple linear regression model to be a good fit, we need the linearity
assumption to hold for only one of the predicting variables. -ANSWER-- false
See Lesson 3.11: Assumptions and diagnostics
In multiple linear regression, we need the linearity assumption to hold for all of the
predicting variables, for the model to be a good fit. "For example, if the linearity
does not hold with one or more predicting variables, then we could transform the
predicting variables to improve the linearity assumption."
Multicollinearity among the predicting variables will not impact the standard
errors of the estimated regression coefficients. -ANSWER-- false
See Lesson 3.13: Multicollinearity
Multicollinearity in the predicting variables can impact the standard errors of the
estimated coefficients. "However, the bigger problem is that the standard errors
will be artificially large."
The presence of certain types of outliers, such as influential points, can impact
the statistical significance of some of the regression coefficients. -ANSWER--
true
See Lesson 3.11: Assumptions and diagnostics
Outliers that are influential can impact the statistical significance of the beta
parameters.
Multicollinearity in multiple linear regression means that the rows in the
design matrix are (nearly) linearly dependent. -ANSWER-- false
See Lesson 3.13: Model Evaluation and Multicollinearity
Multicollinearity in multiple linear regression means that the columns in the design
matrix are (nearly) linearly dependent.
