Page 1 of 58
ISYE 6414 REGRESSION ANALYSIS MIDTERM EXAM 1 & 2
COMPLETE ACTUAL Questions and Verified Solutions
Latest Update This Year
ISYE 6414 REGRESSION ANALYSIS MIDTERM EXAM 1
QUESTION: The estimators for the regression coefficients are:
A) Biased but with small variance
B) Unbiased under normality assumptions but biased otherwise
C) Unbiased under normality assumptions but biased otherwise.
D) Unbiased regardless of the distribution of the data. - ANSWER-D) Unbiased regardless of the
distribution of the data.
QUESTION: The assumption of normality:
A) It is needed for deriving the estimators of the regression coefficients.
B) It is not needed for linear regression modeling and inference.
C) It is needed for the sampling distribution of the estimators of the regression coefficients and
hence for inference.
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D) It is needed for deriving the expectation and variance of the estimators of the regression
coefficients. - ANSWER-C) It is needed for the sampling distribution of the estimators of the
regression coefficients and hence for inference.
QUESTION: What is the difference between estimation and prediction? - ANSWER-If X* is one of
the observations for the predicting variable, then we use estimation. Estimated regression line
for the value X* is interpreted as the average estimated mean response for all settings under
which the predicting variable is equal to X*
If X* is a new observation of the predicting variables, then we use prediction. Predicted
regression line for the value X* is interpreted as the estimated mean response for one setting
under which the predicting variable is equal to X*
QUESTION: What is the primary motivation for using regression? - ANSWER-TO use the
regression equation to predict future responses.
QUESTION: When using regression for prediction, what are the two sources for uncertainty? -
ANSWER-1. Due to the new (n+t1)th observation
2. Due to parameter estimates (of B0 and B1)
QUESTION: The estimated versus predicted regression line for a given x*:
, Page 3 of 58
A) Have the same variance
B) Have the same expectation
C) Have the same variance and expectation
D) None of the above - ANSWER-B) Have the same expectation
QUESTION: The variability in the prediction comes from:
A) The variability due to a new measurement
B) The variability due to estimation
C) The variability due to a new measurement and due to estimation
D) None of the above - ANSWER-C) The variability due to a new measurement and due to
estimation
What are the variables in regression? - ANSWER-1. Response (dependent) variable - one
particular variable that we are interested in understanding or modelling, such as sales of a
particular product.
2. Predicting or Explanatory (independent) variable - set of other variables that we think might
be useful in predicting or modelling the response variable (like the price of a product)
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QUESTION: Which regression variable is a Random variable? - ANSWER-Response Variable - It
varies with changes in the predictor along with other random changes
QUESTION: Which regression variable is a Fixed variable? - ANSWER-Predicting Variable - It
does not change with the response but it is set fixed before the response is measured.
QUESTION: What are the objectives in regression analysis? - ANSWER-1. Prediction - of the
response variable
2. Modelling - the relationship between the response variable and the explanatory variables
3. Testing - hypotheses of association relationships.
QUESTION: What are the given assumptions when building a linear regression model? -
ANSWER-1. Linearity/Mean Zero Assumption - it cannot be true that for certain subgroups in
the population, the model is consistently too low, while for others, it's consistently too high.
2. Constant Variance Assumption - means that it cannot be true that the model is more
accurate for some parts of the population, and less accurate for other parts of the populations.
3. Independence Assumption are independent random variables - it cannot be true knowing
that the model under-predicts y for one particular case tells you anything or all about what it
does for any other case. (her language)
ISYE 6414 REGRESSION ANALYSIS MIDTERM EXAM 1 & 2
COMPLETE ACTUAL Questions and Verified Solutions
Latest Update This Year
ISYE 6414 REGRESSION ANALYSIS MIDTERM EXAM 1
QUESTION: The estimators for the regression coefficients are:
A) Biased but with small variance
B) Unbiased under normality assumptions but biased otherwise
C) Unbiased under normality assumptions but biased otherwise.
D) Unbiased regardless of the distribution of the data. - ANSWER-D) Unbiased regardless of the
distribution of the data.
QUESTION: The assumption of normality:
A) It is needed for deriving the estimators of the regression coefficients.
B) It is not needed for linear regression modeling and inference.
C) It is needed for the sampling distribution of the estimators of the regression coefficients and
hence for inference.
, Page 2 of 58
D) It is needed for deriving the expectation and variance of the estimators of the regression
coefficients. - ANSWER-C) It is needed for the sampling distribution of the estimators of the
regression coefficients and hence for inference.
QUESTION: What is the difference between estimation and prediction? - ANSWER-If X* is one of
the observations for the predicting variable, then we use estimation. Estimated regression line
for the value X* is interpreted as the average estimated mean response for all settings under
which the predicting variable is equal to X*
If X* is a new observation of the predicting variables, then we use prediction. Predicted
regression line for the value X* is interpreted as the estimated mean response for one setting
under which the predicting variable is equal to X*
QUESTION: What is the primary motivation for using regression? - ANSWER-TO use the
regression equation to predict future responses.
QUESTION: When using regression for prediction, what are the two sources for uncertainty? -
ANSWER-1. Due to the new (n+t1)th observation
2. Due to parameter estimates (of B0 and B1)
QUESTION: The estimated versus predicted regression line for a given x*:
, Page 3 of 58
A) Have the same variance
B) Have the same expectation
C) Have the same variance and expectation
D) None of the above - ANSWER-B) Have the same expectation
QUESTION: The variability in the prediction comes from:
A) The variability due to a new measurement
B) The variability due to estimation
C) The variability due to a new measurement and due to estimation
D) None of the above - ANSWER-C) The variability due to a new measurement and due to
estimation
What are the variables in regression? - ANSWER-1. Response (dependent) variable - one
particular variable that we are interested in understanding or modelling, such as sales of a
particular product.
2. Predicting or Explanatory (independent) variable - set of other variables that we think might
be useful in predicting or modelling the response variable (like the price of a product)
, Page 4 of 58
QUESTION: Which regression variable is a Random variable? - ANSWER-Response Variable - It
varies with changes in the predictor along with other random changes
QUESTION: Which regression variable is a Fixed variable? - ANSWER-Predicting Variable - It
does not change with the response but it is set fixed before the response is measured.
QUESTION: What are the objectives in regression analysis? - ANSWER-1. Prediction - of the
response variable
2. Modelling - the relationship between the response variable and the explanatory variables
3. Testing - hypotheses of association relationships.
QUESTION: What are the given assumptions when building a linear regression model? -
ANSWER-1. Linearity/Mean Zero Assumption - it cannot be true that for certain subgroups in
the population, the model is consistently too low, while for others, it's consistently too high.
2. Constant Variance Assumption - means that it cannot be true that the model is more
accurate for some parts of the population, and less accurate for other parts of the populations.
3. Independence Assumption are independent random variables - it cannot be true knowing
that the model under-predicts y for one particular case tells you anything or all about what it
does for any other case. (her language)
