Introduction to Multiple Regression
(SW Chapter 6&7)
Outline 1. Omitted variable bias 2. Causality and regression analysis 3. Multiple regression and OLS 4. Measures of fit 5. Sampling distribution of the OLS estimator 6. Hypothesis testing
Omitted Variab
Probability distribution
Outcomes: mutually exclusive and collectively exhaustive Probability: relative frequency Cumulative probability distribution The probability that a random variable Y is less than or equal to a particular value y; Y for random vari
Why Use Y To Estimate Y?
Y
Y Y is the least squares estimator of ; Y solves, min (Y m)
is unbiased: E( ) = Y ; consistent:
Y
Y
p
n
2
Y
m
i =1
i
so, Y minimizes the sum of squared residuals optional derivation (also see App. 3.2)
n n d dn 2 (Yi m) = (Yi m
Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals (SW Chapter 5) Object of interest: 1 in, Yi = 0 + 1Xi + ui, i = 1, n
1 = Y/ X, for an autonomous change in X (causal effect)
The Least Squares Assumptions: 1. E(u|X = x) = 0. 2
Introduction to Multiple Regression (SW Chapter 6)
The error u arises because of factors that influence Y but are not included in the regression function; so, there are always omitted variables. Sometimes, the omission of those variables can lead to bias
Candice Ward FIN 5190 Procedure Momentum procedure presupposes that the stocks that perform the best and worst in a given month will continue to move in the same direction in the coming month. Thus, the poorest performer would be shorted in the following
Bernoulli random variable:
Regression with binary dependent variables Example: mortgage loan applications; credit card applications; default risk Continuous random variable Cumulative probability distribution
Probability distribution Normal distribution: