Multivariate Regression Analysis Estimation. Why Multiple Regression? Suppose you want to estimate the effect of x1 on y, but you know the following:

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Multiple Regression Analysis

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Multivariate Regression Analysis Estimation

Why Multiple Regression? Suppose you want to estimate the effect of x1 on y, but you know the following: 1.Y=f(x1,x2) and 2.X1 and x2 are correlated. The correct model is Suppose you choose to estimate a Simple Linear Regression What problems do you encounter? SLR estimator is biased!

The MLR Model Interpreting OLS estimates Deriving OLS estimates: Minimize SSR means one must solve the Normal Equations for the OLS estimators.

For the k=2, MLR model, the OLS solution is Interpreting OLS estimators (see the interpreting OLS estimators word file)interpreting OLS estimators Goodness-of-Fit

Regression through the Origin: Usually not a good idea OLS Estimator population characteristics Expected Value MLR Assumptions MLR.1Linear in the Parameters MLR.2Random sample of size n MLR.3No Perfect Multicollinearity. MLR.4Zero conditional mean of the stochastic term. E(u|x)=0 Given these assumptions, OLS estimators are Unbiased. We now have the tools to consider the reason we proposed estimating a MLR in the first place The case of Omitted Variables (See the omitted variables word file)omitted variables

Variance MLR5Homoskedasticity Assumption. Var(u|x)=  2 Wooldridge writes: Where What are some implicationsWhat are some implications? Click the link.

Standard Errors The Gauss-Markov Theorem