3. Generating artificial data sets. This is an important skill since they can be used to understand the properties of models and investigate the performance of a particular computer algorithm. Since you have chosen the values for parameters, you know roughly what answer you would hope your econometric methods should give.

(a) Generate several artificial data sets from the Normal linear regression model by using the following steps: (i) Choose values for þ; h and N (e.g.

þ D 2, h D 1 and N D 100); (ii) Generate N values for the explanatory variable from a distribution of your choice (e.g. take N D 100 draws from the U.0; 1/ distribution); (iii) Generate N values of the errors by taking N i.i.d. draws from the N.0; h1/; and (iv) Construct data on the dependent variables using your chosen value for þ and the data generated in steps

(ii) and (iii) (i.e. use yi D þxi C "i for i D 1; : : : ; N).

(b) Make XY-plots of each data set to see how your choices of þ; h, and N are reflected in the data.