3: OLS Regressions

Question 1

Yi

Answer 1

dependent variable/outcome of interest

Question 2

Xi

Answer 2

independent variable/explanatory variable

Question 3

ui

Answer 3

residual/error term

Question 4

ordinary least squares (OLS)

Answer 4

minimising squared residuals and squared prediction errors

OLS estimator chooses regression coefficients by minimising the sum of squared prediction errors

for linear relationship, sample covariance/sample variance

Question 5

multicollinearity

Answer 5

when 2 variables are perfectly collinear (one is a linear function of the other)
- no variation in X1 condition on X2, and vice versa

OLS cannot estimate slope parameters separately

Question 6

goodness of fit

Answer 6

how much of the variation in Y does the regression explain

Question 7

R^2

Answer 7

percentage of total variation in Y explained by estimated regression

ESS/TSS = 1 - SSR/TSS

in univariate regression model, R^2 = sample correlation ^2

Question 8

adjusted R^2

Answer 8

deflating R^2 by some factor so R^2 doesn’t keep increasing when you add more regressors/explanatory variable