Basic OLS and hypothesis testing Flashcards
What are the four OLS assumptions?
1) Xi,…Xn are independent and identically distributed draws from an underlying distribution, X
2) E[ui | X] = 0. Error terms have mean zero
3) V[ui] = σ2. Variance of the error terms is constant across observations
4) Corr [ui, uj] = 0 . Error terms are uncorrelated across observations
What is the formula for the OLS coefficient estimator?
What are two key weaknesses of the OLS model?
1) Basic OLS is very sensitive to outliers, so you should check you results and data graphically
2) If you have only 1 independent variable, the likelihood of omitted variable bias is very high
What is the efficiency of OLS?
Under Gauss-Markov assumptions, the OLS estimator beta is the best linear unbiased estimator (BLUE).
When do you use weighted least squares?
When you want to weight different observations in your sample differently either because of known gheteroskedasticity of use of a complex survey with different sampling problems.
1) Xi…Xn are iid draws from an underlying distribution x
2) E[u | Xi,…Xki] = ??? error terms may vary with x
3) X1i,…Xki and Yi have finite fourth moments. No huge outlier
4) the regression of any Xk on all the other covariates has R2<1. No perfect multicollinearity
What is the formula for weighted least squares?
Put a weight on the numerator and denominator of Beta one.
Hypothesis testing: what is the formula for a one-sample Z-test for the population mean, when σ is known?
Z = (xbar-miu)/σ/sqrt(n) where n >30
Population σ is known
Hypothesis testing: What is the formula for a one-sample t-test for a population mean when the population is normally distributed and σ is not known?
t = (Xbar-miu)/[s/srqt(n)]
What is the formula for a two-sample Z-test for difference of population means?
– Two samples must be independnent, normally distributed, σx and σy are known
Z = (xbar-ybar)-D/{sqrt(σx2/n + σy2/m)
What is the definition of “best” estimator?
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