All questions pertain to the simple (two-variable) linear regression model for which the population regression equation...

 

Transcribed Image Text:

All questions pertain to the simple (two-variable) linear regression model for which the population regression equation can be written in conventional notation as: Y B1+ B2X1+ uz Equation 1 where Y, and X, are observable variables, B, and Bz are unknown (constant) regression coefficients, and u, is an unobservable random error term. The Ordinary Least Squares (OLS) sample regression equation corresponding to regression Equation (1) is Y = B+ B2X+ Q Equation 2 where B, is the OLS estimator of the intercept coefficient B, B2 is the OLS estimator of the slope coefficientß2, u is the OLS residual for the i-th sample observation, and N is sample size (the number of observations in the sample). a) State the Ordinary Least Squares (OLS) estimation criterion. State the OLS normal [5 marks] equations. [5 marks] b) Derive the OLS normal equations from the OLS estimation criterion. All questions pertain to the simple (two-variable) linear regression model for which the population regression equation can be written in conventional notation as: Y B1+ B2X1+ uz Equation 1 where Y, and X, are observable variables, B, and Bz are unknown (constant) regression coefficients, and u, is an unobservable random error term. The Ordinary Least Squares (OLS) sample regression equation corresponding to regression Equation (1) is Y = B+ B2X+ Q Equation 2 where B, is the OLS estimator of the intercept coefficient B, B2 is the OLS estimator of the slope coefficientß2, u is the OLS residual for the i-th sample observation, and N is sample size (the number of observations in the sample). a) State the Ordinary Least Squares (OLS) estimation criterion. State the OLS normal [5 marks] equations. [5 marks] b) Derive the OLS normal equations from the OLS estimation criterion.