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A stochastic error term must be added to all regression equations... 

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to account for variations in the dependent variable that are not explained completely by the independent variables. 


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The components of the error term include: 

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a. omitted variables b. measurement errors in the data c. an underlying theoretical equation that has a different functional form d. purely random and unpredictable events 


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The difference between a particular observation of the dependent variable and the value estimated from the regression equation.
ei = Yi  Yihat 


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Sum(Xi Xbar)(YiYbar)/Sum(XiXbar)^2 


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Variation of dependent variable (TSS) 

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Linear, Correctly Specified, Additive error 


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All X's are uncorrelated with error term If ability got dumped in the error term, it would be correlated with schooling, so there would be bias. Most likely culprit for a change in sign. 


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No serial correlation of error term. Most likely violated in timeseries models. Lingering effects of advertising, etc. 


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Constant Variance/No Heteroskedasticity Violated in crossesectional data, like when comparing Rhode Island and Texas 


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No Perfect Multicollinearity Happens if one variable is a multiple of the other, if they are off by a constant 


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Error Normally Distributed (Not Required) 


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Best Linear Unbiased Estimator Minimum Variance Unbiased E(B) = B Consistent: B goes to B Normally Distributed 


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= E(Var) + B(theta)^2 efficient if minimized 


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= Alpha2 * f(r ability, schooling) 


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Ordinary Least Squares minimizes the sum of the squared residuals 


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Sum(YihatYbar)^2 + Sum(ei)^2 


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Decomposition of Variance 

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Breakdown of TSS into ESS + RSS 


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the excess of the number of observations (N) over the number of coefficients (including the incercept) estimated (K+1). 


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Six Steps of Regression Analysis 

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a. Review Lit b. Specification c. Hypothesize d. Collect Data e. Estimate equation f. Document results 


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Sampling Distribution of Bhat 

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