In reality, we never observe the data generating process of the phenomenon we are investigating. But...

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In reality, we never observe the data generating process of the phenomenon we are investigating. But we can simulate our "own world". Consider a true regression model Y = Bo + B121 + B2x2 + u. Generate data in R, so that you have 300 observations. Make it so that a1 - N(-2, 2), r2 ~ N(1,5), u~ N(0,1) and so that the correlation between r1 and x2 is approximately 0.33. Choose the true value of the beta parameters yourselves, thus creating "own world" in which we want to determine the effect of r1 and r2 on y (think of a general econometrics task). 1. Plot the data and calculate the correlation between r1 and r2 to check whether you simulated the data according to the requirements. Also, estimate the standard deviations of xi and r2. 2. Estimate the model Y = Bo + Bir1 + e. Will you get an unbiased estimate for 31? Why or why not? 3. If there is a bias, on what does it depend? Is it downward or upward? 4. Estimate the full model. Did you estimate the set true values? If not, why? What is the insight for working with real life ? Hint: Make sure you do not confuse variance and standard deviation when going from Normal distribution parameters to the simulating. In reality, we never observe the data generating process of the phenomenon we are investigating. But we can simulate our "own world". Consider a true regression model Y = Bo + B121 + B2x2 + u. Generate data in R, so that you have 300 observations. Make it so that a1 - N(-2, 2), r2 ~ N(1,5), u~ N(0,1) and so that the correlation between r1 and x2 is approximately 0.33. Choose the true value of the beta parameters yourselves, thus creating "own world" in which we want to determine the effect of r1 and r2 on y (think of a general econometrics task). 1. Plot the data and calculate the correlation between r1 and r2 to check whether you simulated the data according to the requirements. Also, estimate the standard deviations of xi and r2. 2. Estimate the model Y = Bo + Bir1 + e. Will you get an unbiased estimate for 31? Why or why not? 3. If there is a bias, on what does it depend? Is it downward or upward? 4. Estimate the full model. Did you estimate the set true values? If not, why? What is the insight for working with real life ? Hint: Make sure you do not confuse variance and standard deviation when going from Normal distribution parameters to the simulating.

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