[Type here]
MIDTERM – SOLUTION KEY
THEORY QNS
*Q1) Consider a linear regression model with 2 independent variables (assume both are
correlated with the response variable). If we add an interaction term between the independent
variables to the model, how will the model be affected:
A) The R2 will increase (or remain the same) with certainty while the adjusted R2 can
increase or decrease
B) Both the R2 and adjusted R2 will increase with certainty.
C) The R2 will decrease (or remain the same) with certainty while the adjusted R2 can
increase or decrease
D) Both the R2 and adjusted R2 will decrease with certainty.
Solution A: The R2 is bound to increase with the addition of new variables or stay the same if the
interaction variable doesn’t improve model. The adjusted R 2 adds a penalty term on the number
of variables in the model, hence it may go down or up (if the new interaction variable offers
significant predictive performance). (Week 1 Lesson 4)
*Q2) Consider the correlation matrix of independent variables below. What pair of variables
would be least valuable to use in a linear regression model?
A) Education and Income
B) CompPrice and Price
C) Population and CompPrice
D) Income and Price
, [Type here]
Solution B: An assumption of linear regression is the lack of multicollinearity in the independent
variables. As a result, it is natural to reject the most highly correlated pair of variables, which
from the correlation matrix above is clearly Price and CompPrice. (Week 1 Lesson 8)
*Q3) Which of the following is NOT a binary dependent variable?
(a). Whether a customer will default on his debt.
(b). Would a student pass a course.
(c). Change in value of an investment.
(d). If a firm would go bankrupt in the next year.
Answer – Option C (Week 4 Lesson 2)
Change in value of an investment can have more than two values. Rest all only take two
values. Hence Option C is not a binary dependent variable
Q4)In the model log(Y) = b0 + b1*log(X), the elasticity of Y is the percentage change in Y (the
dependent variable), when X (the independent variable) increases by one unit.
A. False
B. True
Answer: False (A) (Week 3 Lesson 4)
Explanation: Elasticity is the percent change in Y when X increases by 1%
*Q5) The odds for your team winning is 0.6 in the next game. What is the probability of your
team losing in the next game?
(A) 0.4
(B) 0.375
(C) 0.6
(D) 0.625
Ans) (D) (Week 4 Lesson 1)
odds = 0.6 = p/(1-p)
This means that p = 0.6/1.6 = 0.375
Hence probability of team losing = 1-0.375 = 0.625
*Q6)While calculating a difference in difference, we run a regression which is as follows:
lm( y ~ d1 +d2 + d3)where d1 and d2 are dummy variables and d3 is their interaction term. We
thus get its coefficients according to the below equation: Y = a + b*d1 + c*d2 + d*d3
What is the difference in difference estimator?
(A) a
(B) (d-c)-(b-a)
(C) a+b+c+d
(D) d
Answer: (D) d - Difference in difference estimator is given by coefficient of interaction term
(Week 5 Lesson 5)
MIDTERM – SOLUTION KEY
THEORY QNS
*Q1) Consider a linear regression model with 2 independent variables (assume both are
correlated with the response variable). If we add an interaction term between the independent
variables to the model, how will the model be affected:
A) The R2 will increase (or remain the same) with certainty while the adjusted R2 can
increase or decrease
B) Both the R2 and adjusted R2 will increase with certainty.
C) The R2 will decrease (or remain the same) with certainty while the adjusted R2 can
increase or decrease
D) Both the R2 and adjusted R2 will decrease with certainty.
Solution A: The R2 is bound to increase with the addition of new variables or stay the same if the
interaction variable doesn’t improve model. The adjusted R 2 adds a penalty term on the number
of variables in the model, hence it may go down or up (if the new interaction variable offers
significant predictive performance). (Week 1 Lesson 4)
*Q2) Consider the correlation matrix of independent variables below. What pair of variables
would be least valuable to use in a linear regression model?
A) Education and Income
B) CompPrice and Price
C) Population and CompPrice
D) Income and Price
, [Type here]
Solution B: An assumption of linear regression is the lack of multicollinearity in the independent
variables. As a result, it is natural to reject the most highly correlated pair of variables, which
from the correlation matrix above is clearly Price and CompPrice. (Week 1 Lesson 8)
*Q3) Which of the following is NOT a binary dependent variable?
(a). Whether a customer will default on his debt.
(b). Would a student pass a course.
(c). Change in value of an investment.
(d). If a firm would go bankrupt in the next year.
Answer – Option C (Week 4 Lesson 2)
Change in value of an investment can have more than two values. Rest all only take two
values. Hence Option C is not a binary dependent variable
Q4)In the model log(Y) = b0 + b1*log(X), the elasticity of Y is the percentage change in Y (the
dependent variable), when X (the independent variable) increases by one unit.
A. False
B. True
Answer: False (A) (Week 3 Lesson 4)
Explanation: Elasticity is the percent change in Y when X increases by 1%
*Q5) The odds for your team winning is 0.6 in the next game. What is the probability of your
team losing in the next game?
(A) 0.4
(B) 0.375
(C) 0.6
(D) 0.625
Ans) (D) (Week 4 Lesson 1)
odds = 0.6 = p/(1-p)
This means that p = 0.6/1.6 = 0.375
Hence probability of team losing = 1-0.375 = 0.625
*Q6)While calculating a difference in difference, we run a regression which is as follows:
lm( y ~ d1 +d2 + d3)where d1 and d2 are dummy variables and d3 is their interaction term. We
thus get its coefficients according to the below equation: Y = a + b*d1 + c*d2 + d*d3
What is the difference in difference estimator?
(A) a
(B) (d-c)-(b-a)
(C) a+b+c+d
(D) d
Answer: (D) d - Difference in difference estimator is given by coefficient of interaction term
(Week 5 Lesson 5)
