ISYE6414 (Regression) Midterm 2
(multiple linear regression) The estimators for the regression coefficients are:
A) Biased but with small variance
B) Unbiased under normality assumptions but biased otherwise.
C) Biased regardless of the distribution of the data.
D) Unbiased regardless of the distribution of the data. - questions and answers-D) Unbiased
regardless of the distribution of the data.
(multiple linear regression) The objective of multiple linear regression is:
a) To predict future new responses
B) 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 - questions and answers-D) all of the above
(multiple linear regression) The sampling distribution of the estimated regression coefficients is
A) Centered at the true regression parameters.
B) The t-distribution assuming that the variance of the error term is unknown an replaced by its
estimate.
C) Dependent on the design matrix
D) All of the above - questions and answers-D) All of the above
(multiple linear regression) We can test for a subset of regression coefficients
A) Using the F statistic test of the overall regression.
B) Only if we are interested whether additional explanatory variables should be considered in
addition to the controlling variables.
C) To evaluate whether all regression coefficients corresponding to the predicting variables
excluded from the reduced model are statistically significant.
D) None of the above - questions and answers-D) None of the above
(multiple linear regression) What are the different roles of predicting variables? - questions and
answers-Controlling - to control for bias selection in the sampleExplanatory - to explain
variability in the response variablePredictive - to best predict variability in the response
regardless of their explanatory power.
(multiple linear regression) What are the sources of prediction uncertainty when using a
regression line to predict future responses? - questions and answers-1. Due to the new
observations2. Due to parameter estimates of betas
, (multiple linear regression) What is the model interpretation for Beta i (B hat i) - questions and
answers-Beta hat i is the estimated expected change in the response variable associated with
one unit of change in the i-th predicting variable holding fixed all other predictors in the model
for all i = 1, ..., p
(multiple linear regression) What is the process for testing subsets of coefficients? - questions
and answers-basically you first measure the sum of squares explained by using only X1 to
predict Y, then you calculate the extra sum of squares explained by adding X2, then X3, etc.
until you get to the last predictor.
(multiple linear regression) Which one correctly characterizes the sampling distribution of the
estimated variance?
A) The estimated variance of the error term has a 𝜒2distribution regardless of the distribution
assumption of the error terms.
B) The number of degrees of freedom for the 𝜒2 distribution of the estimated variance is n-p-1
for a model without intercept.
C) The sampling distribution of the mean squared error is different of that of the estimated
variance.
D) None of the above - questions and answers-none of the above
(multiple linear regression) Which one is correct?
A) The regression coefficients can be estimated only if the predicting variables are not linearly
dependent.
B) The estimated regression coefficient 𝛽∧𝑖 is interpreted as the change in the response variable
associated with one unit of change in the i-th predicting variable .
C) The estimated regression coefficients will be the same under marginal and conditional model,
only their interpretation is not.
D) Causality is the same as association in interpreting the relationship between the response
and the predicting variables. - questions and answers-A) The regression coefficients can be
estimated only if the predicting variables are not linearly dependent.
(multiple linear regression) Which one is correct?
A) A multiple linear regression model with p predicting variables but no intercept has p model
parameters.
B) The interpretation of the regression coefficients is the same whether or not interaction terms
are included in the model.
C) Multiple linear regression is a general model encompassing both ANOVA and simple linear
regression.
D) None of the above - questions and answers-C) Multiple linear regression is a general model
encompassing both ANOVA and simple linear regression.
(multiple linear regression) The estimators for the regression coefficients are:
A) Biased but with small variance
B) Unbiased under normality assumptions but biased otherwise.
C) Biased regardless of the distribution of the data.
D) Unbiased regardless of the distribution of the data. - questions and answers-D) Unbiased
regardless of the distribution of the data.
(multiple linear regression) The objective of multiple linear regression is:
a) To predict future new responses
B) 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 - questions and answers-D) all of the above
(multiple linear regression) The sampling distribution of the estimated regression coefficients is
A) Centered at the true regression parameters.
B) The t-distribution assuming that the variance of the error term is unknown an replaced by its
estimate.
C) Dependent on the design matrix
D) All of the above - questions and answers-D) All of the above
(multiple linear regression) We can test for a subset of regression coefficients
A) Using the F statistic test of the overall regression.
B) Only if we are interested whether additional explanatory variables should be considered in
addition to the controlling variables.
C) To evaluate whether all regression coefficients corresponding to the predicting variables
excluded from the reduced model are statistically significant.
D) None of the above - questions and answers-D) None of the above
(multiple linear regression) What are the different roles of predicting variables? - questions and
answers-Controlling - to control for bias selection in the sampleExplanatory - to explain
variability in the response variablePredictive - to best predict variability in the response
regardless of their explanatory power.
(multiple linear regression) What are the sources of prediction uncertainty when using a
regression line to predict future responses? - questions and answers-1. Due to the new
observations2. Due to parameter estimates of betas
, (multiple linear regression) What is the model interpretation for Beta i (B hat i) - questions and
answers-Beta hat i is the estimated expected change in the response variable associated with
one unit of change in the i-th predicting variable holding fixed all other predictors in the model
for all i = 1, ..., p
(multiple linear regression) What is the process for testing subsets of coefficients? - questions
and answers-basically you first measure the sum of squares explained by using only X1 to
predict Y, then you calculate the extra sum of squares explained by adding X2, then X3, etc.
until you get to the last predictor.
(multiple linear regression) Which one correctly characterizes the sampling distribution of the
estimated variance?
A) The estimated variance of the error term has a 𝜒2distribution regardless of the distribution
assumption of the error terms.
B) The number of degrees of freedom for the 𝜒2 distribution of the estimated variance is n-p-1
for a model without intercept.
C) The sampling distribution of the mean squared error is different of that of the estimated
variance.
D) None of the above - questions and answers-none of the above
(multiple linear regression) Which one is correct?
A) The regression coefficients can be estimated only if the predicting variables are not linearly
dependent.
B) The estimated regression coefficient 𝛽∧𝑖 is interpreted as the change in the response variable
associated with one unit of change in the i-th predicting variable .
C) The estimated regression coefficients will be the same under marginal and conditional model,
only their interpretation is not.
D) Causality is the same as association in interpreting the relationship between the response
and the predicting variables. - questions and answers-A) The regression coefficients can be
estimated only if the predicting variables are not linearly dependent.
(multiple linear regression) Which one is correct?
A) A multiple linear regression model with p predicting variables but no intercept has p model
parameters.
B) The interpretation of the regression coefficients is the same whether or not interaction terms
are included in the model.
C) Multiple linear regression is a general model encompassing both ANOVA and simple linear
regression.
D) None of the above - questions and answers-C) Multiple linear regression is a general model
encompassing both ANOVA and simple linear regression.
