Probstat/week14 practice 1

Least square estimators

1. You should work in pairs. Try the following for $n=3,5,20,100$

• First, you pick a parameter $\alpha$ and $\beta$ and generate a sample of size $n$ using the formula:

$Y=\alpha +\beta x+e$

Use random values for $x$ in the range that you like. For the error $e$, you can generate a random error based on a normal distributions.

• Give the data to your partner.

• After you get the data from your friend, find the least square estimators for $\alpha$ and $\beta$.

• Ask for the correct parameters and see how close you get to those parameters as we increase the size of the samples $n$.

Multiple linear regression

Follow the same procedure as in the previous section, but try with 2 variables $x_{1}$ and $x_{2}$. I.e., you pick parameter $\alpha ,\beta _{1},\beta _{2}$ and generate samples from the following formula

$Y=\alpha +\beta _{1}x_{1}+\beta _{2}x_{2}+e$.