625.661 Statistical Models and Regression Module 1 Assignment solution

Description

1. In a linear regression model,
𝑦 = 𝛽ଵ𝑥 + 𝜀
where x is the only independent variable (or so-called regressor).
With n independent paired data (y1, x1), …., (yn, xn) satisfying this model,
a) derive the ordinary least squares (OLS) estimator of  ଵ
.
b) derive an estimator for the variance of OLS estimator of  ଵ
.
2. In Problem 1, add the intercept term 𝛽଴
to the model and change x to (x
– c), where c is a known constant. Then do a) and b).
3. In Problem 1, add the intercept term 𝛽଴
to the model and change x to
(𝑥 − 𝑥̅) , where , is the sample mean of x x n x . Then do a) and b).
n
i
i
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