We have learned how to do simple regressions, and found formulas for the intercept and slope...

 

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We have learned how to do simple regressions, and found formulas for the intercept and slope coefficients in Week 1. This week, we have learned how to do this with multiple regressors using linear algebra. Let us confirm that our methods for the multivariate model reproduces the simple model. Suppose you have the following model: Yi Bo + Bixi + Ei (a) Write down (you don't need to derive) the OLS estimators for 50 and 3₁. (b) Set the model up in matrix form. (c) Show that the multivariate OLS formula, 3OLS = (X'X)-1X'y produces a 2-by-1 column vector, whose first row is BOLS and whose second row is BOLS from part (a) of this question. We have learned how to do simple regressions, and found formulas for the intercept and slope coefficients in Week 1. This week, we have learned how to do this with multiple regressors using linear algebra. Let us confirm that our methods for the multivariate model reproduces the simple model. Suppose you have the following model: Yi Bo + Bixi + Ei (a) Write down (you don't need to derive) the OLS estimators for 50 and 3₁. (b) Set the model up in matrix form. (c) Show that the multivariate OLS formula, 3OLS = (X'X)-1X'y produces a 2-by-1 column vector, whose first row is BOLS and whose second row is BOLS from part (a) of this question.