# Matrix Algebra

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Consider the linear regression model

Yi = BXi+ Ui

where

B= Beta

i = 1,2 .....5

Xi = 2i

Yi = [1 2 3 3 4 ] ' (i.e a 5x1 vector)

and Sigma ^2 = 1

Compute the OLS Estimate of B .

Can you work it out slowly, step by step, as I am having a hard time doing the problems in the book, and need a sample to look back at.

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#### Solution Preview

Please see the attached file.

Solution

The given model can be written in matrix form as

where Y= [1 2 3 3 4]' and X= [2 4 6 8 10]' and is a 1x1 vector (scalar), since it is given that YÂ¬Â¬i = ith element of the vector Y and Xi = 2*i , i = 1,2,3,4,5

Now Y and X are 5x1 vectors and , ui is ...

#### Solution Summary

The solution explains how ordinary least square estimator is found.

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