ISYE 6414 - UNIT 2 FLASHCARDS
EXAM QUESTIONS WITH 100%
CORRECT ANSWERS
What is the hypothesis testing procedure for overall regression and what is it testing? -
Answer-Analysis of Variance for multiple regression. We will use analysis of variance
(ANOVA) to test the hypothesis that the regression coefficients are zero.
What are the null and alternative hypotheses for ANOVA for MLR? - Answer-H0: the
regression coefficients all equal zero.
HA: At least one of the regression coefficients is not equal to zero.
If there is a coefficient that does NOT equal zero, what does that mean? - Answer-that
at least one of these predictors included in the model has predictive power.
What is the f-statistic? - Answer-The f statistic is going to be the ratio between the mean
sum of square regression and mean sum of square of error.
When do we reject the f-statistic? and what does this mean? - Answer-If it's larger than
the critical point, with alpha being the significance level of the test. This means, again,
that at least one of the coefficients is different from 0 at the alpha significance level.
What is the partial F-test? - Answer-The hypothesis test for whether a subset of
regression coefficients are all equal to zero.
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 and
replaced by its estimate.
C) Dependent on the design matrix.
D) All of the above. - Answer-D
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. - Answer-D
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 in 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. - Answer-D
The expectation of the mean response is: - Answer-UNBIASED
If we replace the unknown variance with its estimator, sigma^2=MSE, for PREDICTION,
the sampling distribution becomes... - Answer-t distribution with n-p-1 DF
Is the predicted regression line is the same as the estimated regression line at x*? How
does it affect confidence intervals? - Answer-Yes, but the prediction confidence interval
is wider than the estimation confidence interval because of the higher variability in the
prediction.
The estimated versus predicted regression line for a given x*:
A) Have the same variance
B) Have the same expectation
C) Have the same variance and expectation
D) None of the above - Answer-B
Which one is correct?
A) The prediction intervals need to be corrected for simultaneous inference when
multiple predictions are made jointly.
B) The prediction intervals are centered at the predicted value.
C) The sampling distribution of the prediction of a new response is a t-distribution.
D) All of the above. - Answer-D
T/F: In a multiple linear regression model with 6 predicting variables but without
intercept, there are 7 parameters to estimate. - Answer-True
T/F: The only objective of multiple linear regression is prediction. - Answer-False
T/F: We can make causal inference in observational studies. - Answer-False
T/F: In order to make statistical inference on the regression coefficients, we need to
estimate the variance of the error terms. - Answer-True
T/F: We cannot estimate a multiple linear regression model if the predicting variables
are linearly dependent. - Answer-True
T/F: The estimated regression coefficients are unbiased estimators. - Answer-True
EXAM QUESTIONS WITH 100%
CORRECT ANSWERS
What is the hypothesis testing procedure for overall regression and what is it testing? -
Answer-Analysis of Variance for multiple regression. We will use analysis of variance
(ANOVA) to test the hypothesis that the regression coefficients are zero.
What are the null and alternative hypotheses for ANOVA for MLR? - Answer-H0: the
regression coefficients all equal zero.
HA: At least one of the regression coefficients is not equal to zero.
If there is a coefficient that does NOT equal zero, what does that mean? - Answer-that
at least one of these predictors included in the model has predictive power.
What is the f-statistic? - Answer-The f statistic is going to be the ratio between the mean
sum of square regression and mean sum of square of error.
When do we reject the f-statistic? and what does this mean? - Answer-If it's larger than
the critical point, with alpha being the significance level of the test. This means, again,
that at least one of the coefficients is different from 0 at the alpha significance level.
What is the partial F-test? - Answer-The hypothesis test for whether a subset of
regression coefficients are all equal to zero.
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 and
replaced by its estimate.
C) Dependent on the design matrix.
D) All of the above. - Answer-D
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. - Answer-D
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 in 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. - Answer-D
The expectation of the mean response is: - Answer-UNBIASED
If we replace the unknown variance with its estimator, sigma^2=MSE, for PREDICTION,
the sampling distribution becomes... - Answer-t distribution with n-p-1 DF
Is the predicted regression line is the same as the estimated regression line at x*? How
does it affect confidence intervals? - Answer-Yes, but the prediction confidence interval
is wider than the estimation confidence interval because of the higher variability in the
prediction.
The estimated versus predicted regression line for a given x*:
A) Have the same variance
B) Have the same expectation
C) Have the same variance and expectation
D) None of the above - Answer-B
Which one is correct?
A) The prediction intervals need to be corrected for simultaneous inference when
multiple predictions are made jointly.
B) The prediction intervals are centered at the predicted value.
C) The sampling distribution of the prediction of a new response is a t-distribution.
D) All of the above. - Answer-D
T/F: In a multiple linear regression model with 6 predicting variables but without
intercept, there are 7 parameters to estimate. - Answer-True
T/F: The only objective of multiple linear regression is prediction. - Answer-False
T/F: We can make causal inference in observational studies. - Answer-False
T/F: In order to make statistical inference on the regression coefficients, we need to
estimate the variance of the error terms. - Answer-True
T/F: We cannot estimate a multiple linear regression model if the predicting variables
are linearly dependent. - Answer-True
T/F: The estimated regression coefficients are unbiased estimators. - Answer-True
