Introduction to Regression Flashcards
What is the summation operator?
Σ signifying the addition of all the values in a given range
What is the range of the summation operator?
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
What is the constant rule?
nΣi=1(c) = nc
How do you calculate a random variable’s deviation from its own mean?
The sum of the deviations from the mean is always zero
nΣi=1(x_i - x̅) = 0
What are the 4 main differences between correlation and regression?
- 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
What are the steps to deriving the Ordinary Least Squares (OLS) estimates for the Bivariate Regression Model?
- 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
What is the sum of squared residuals (SSR)?
SSR = Σε^2 = Σ(y_i - β0 - x_iβ_i)^2
What are the 3 main types of variables used in econometrics?
- Continuous variables
- Natural log of continuous variables
- Dummy variables (take values zero or one)
What does R^2 measure?
The fraction of the variation in y is explained by the regression model
What is the equation for R^2?
R^2 = SSM/SST = 1 - SSR/SST
What is the Sum of Squared Model (SSM)?
A measure of the variation in the predicted value in Y
What is the formula for SSM?
SSM = Σ(y_i - ȳ)^2
What is the Sum of Squared Total (SST)?
A statement about how much movement there is in y in the sample
What is the formula for SST?
SST = Σ(y_i - ȳ)^2
What are differences-in-differences?
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
What is the treatment group?
Those who were affected by the policy
What is the control group?
Those who were not affected by the policy
