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2SLS algebraic ANOVA assume assumption autocorrelation autoregression bias biased calculate Chapter confidence interval consistent estimator constant consumption function covariance matrix dependent deviation economist endogenous equal equivalent error term estimating equations exactly example exogenous variables explained fertilizer fitted formula Gauss-Markov theorem geometrically graph hence identified income increase independent instrumental variable likelihood function linear mathematical minimize moving average multicollinearity multiple regression null hypothesis observations obtain OLS estimator parameters partial correlation plane population posterior distribution prediction prediction interval prior distribution prob-value probability problem rainfall random ratio reason reduced form regres regression coefficient regression line regressors relation residual sample mean score Section serial correlation shown in Figure Similarly simple regression slope solution specification standard error statistical statistician substitute Suppose Table technique theorem tion transformation true unbiased estimator uncorrelated variance variation vector yield zero