ISYE 6414 REGRESSION ANALYSIS MIDTERM EXAM 1 AND EXAM 2 ALL 300 QUESTIONS AND CORRECT ANSWERS LATEST UPDATE THIS YEAR

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ISYE 6414 REGRESSION ANALYSIS MIDTERM EXAM
1 AND EXAM 2 ALL 300 QUESTIONS AND CORRECT
ANSWERS LATEST UPDATE THIS YEAR

ISYE 6414 REGRESSION ANALYSIS MIDTERM EXAM 1

QUESTION: Assuming that the data are normally distributed, under the simple linear model, the
estimated variance has the following sample distribution:




A) Chi-square with n-2 degrees of freedom

B) T-distribution with n-2 degrees of freedom

C) Chi-square with n degrees of freedom

D) T-distribution with n degrees of freedom - ANSWER-A) Chi-square with n-2 degrees of
freedom




QUESTION: The fitted values are defined as:



A) The difference between observed and expected responses

B) The regression line with parameters replaced with the estimated regression coefficients

C) The regression line

D) The response values. - ANSWER-B) The regression line with parameters replaced with the
estimated regression coefficients.

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QUESTION: The estimators of the linear regression model are derived by:



A) Minimizing the sum of squared differences between observed and expected values of the
response variable.

B) Maximizing the sum of squared differences between observed and expected values of the
response variable.

C) Minimizing the sum of absolute differences between observed and expected values of the
response variable.

D) Maximizing the sum of absolute differences between observed and expected values of the
response variable. - ANSWER-A) Minimizing the sum of squared differences between observed
and expected values of the response variable.




QUESTION: When using the t-test for statistical significance, when would you interpret B1 as
statistically significant? - ANSWER-We reject the null hypothesis of the absolute value of the t-
value is large. If the null hypothesis is rejected, we interpret this as B1 being statistically
significant.



QUESTION: What is statistical significance? - ANSWER-It means that B1 is statistically different
from zero.



QUESTION: When using the p-value test for statistical significance, when would you interpret
B1 as statistically significant? - ANSWER-If the P-value is small (<.01) then we would reject the
null hypothesis and determine that B1 is statistically significant.



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QUESTION: What is the p-value? - ANSWER-The p-value is a measure of how reject-able the null
hypothesis is. The smaller the p-value, the more reject-able the null hypothesis is for the
observed data.




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.

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.




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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)



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.

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