Linear_regression_One_Regressor

Linear_regression_One_Regressor - Simple linear regression...

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Unformatted text preview: Simple linear regression model i i i u x y + + = 1 β β i=1,2,…,n i denotes the i-th observation n is the number of observation x is the independent variable (regressor) y is the dependent variable (regressand) u is the error term (captures variables other than x that are omitted from the model) Model assumes direction of causality runs from x to y. β is the intercept parameter (i.e. the value of the dependent variable y when the independent variable x is equal to zero) 1 β is the slope parameter (indicates the effect of increasing x by one unit on the dependent variable); 1 = β indicates no relationship between x and y; 1 β is positive indicates a positive relationship; and 1 β is negative indicates a negative relationship The method of ordinary least squares (OLS) Minimizes the sum of squared residuals For the model i i i u x y + + = 1 β β ( 29 ( 29 ( 29 ∑ ∑ = =--- = n i i i n i i x x y y x x 1 2 1 1 ˆ β is the OLS estimator for 1 β (the slope) x y 1 ˆ β β- = is the OLS estimator of β (the intercept) Predicted values i i x y 1 ˆ ˆ ˆ β β + = One property of predicted values 1. Mean of predicted values of dependent variable is always equal to mean of actual values of the dependent variable when an intercept β is included in the model i.e....
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This note was uploaded on 04/28/2011 for the course ECON 2P91 taught by Professor Ogwang during the Winter '09 term at Brock University.

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Linear_regression_One_Regressor - Simple linear regression...

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