Introduction to Regression

Question 1

What is the summation operator?

Answer 1

Σ signifying the addition of all the values in a given range

Question 2

What is the range of the summation operator?

Answer 2

The number on top gives the upper limit (if n it means all values). The number on the bottom is the lower limit from where the summation begins

Question 3

What is the constant rule?

Answer 3

nΣi=1(c) = nc

Question 4

How do you calculate a random variable’s deviation from its own mean?

Answer 4

The sum of the deviations from the mean is always zero

nΣi=1(x_i - x̅) = 0

Question 5

What are the 4 main differences between correlation and regression?

Answer 5

• Regression can investigate the relationship between 2 or more variables
• The direction of causality is asserted
• The influence of each variable upon the dependent variable is measured
• The statistical significance of each variable can be ascertained

Question 6

What are the steps to deriving the Ordinary Least Squares (OLS) estimates for the Bivariate Regression Model?

Answer 6

• Differentiate y with respect to x to obtain β1
• Obtain the estimated residual ε = y_i - β0 - x_iβ1
• Differentiate the SSR with respect to β0 and β1, equate each to zero and solve for β0 and β1

Question 7

What is the sum of squared residuals (SSR)?

Answer 7

SSR = Σε^2 = Σ(y_i - β0 - x_iβ_i)^2

Question 8

What are the 3 main types of variables used in econometrics?

Answer 8

• Continuous variables
• Natural log of continuous variables
• Dummy variables (take values zero or one)

Question 9

What does R^2 measure?

Answer 9

The fraction of the variation in y is explained by the regression model

Question 10

What is the equation for R^2?

Answer 10

R^2 = SSM/SST = 1 - SSR/SST

Question 11

What is the Sum of Squared Model (SSM)?

Answer 11

A measure of the variation in the predicted value in Y

Question 12

What is the formula for SSM?

Answer 12

SSM = Σ(y_i - ȳ)^2

Question 13

What is the Sum of Squared Total (SST)?

Answer 13

A statement about how much movement there is in y in the sample

Question 14

What is the formula for SST?

Answer 14

SST = Σ(y_i - ȳ)^2

Question 15

What are differences-in-differences?

Answer 15

A method that applies on experimental research design to outcomes in a natural experiment. It involves comparing the difference in the average outcomes of two groups, a treatment and control group, both before and after the treatment took place

Question 16

What is the treatment group?

Answer 16

Those who were affected by the policy

Question 17

What is the control group?

Answer 17

Those who were not affected by the policy