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# PS2--Answers - Econ 141 Problem Set 2 Answers Fall 2007 Due...

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Econ 141: Problem Set 2: Answers Fall 2007 Due Wednesday, September 26th in Class Example SAS code appended at the end. The intention of this exercise is to get you to interpret the regression coefficient estimates and standard errors in a context where you know the underlying population model. When you move to real world data, you will not know the underlying population model, and you will need to be able to use economic and statistical intuition to predict whether the coefficient estimates are biased and to generate precise estiamtes. This entire problem set is to be done in SAS (or an equivalent data analysis software). The first section sets up the data that you will adapt for later questions. You will likely want to have four distinct sections to your SAS code, one for each section of the problem set. These problems draw from the SAS code presented in section 3, which is posted on bspace. The Model Setup You will generate the data for this anaylsis yourself, so there is no data to upload. Start by generating 100 observations of a random variable, x, that is distributed uniformly between 0 and 1 and a random variable, u, that has the standard normal distribution. Also generate a variable, y = 10 * x + u . Then answer the following questions: 1. What is the mean of the variable x in your sample? What is it’s variance in your sample? What should the mean of x be in the population? The mean of x in the sample is 0.53 and the variance is 0.084. The mean of x in the population should be 0.50 . 2. What is the mean of the variable u in your sample? What is it’s variance in your sample? What should the mean and variance of u be in the population? The mean of u in the sample is 0.004 and the variance is 0.755. The mean of u in the population should be 0 and the variance should be 1. 3. What is the covariance between the variables x and y in your sample? The covariance between x and y in the sample is 0.833. 1

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4. If you were to run a regression of y on x with no intercept, y = βx + u , what should the true value of β be? What should σ 2 (the variance of u i ) be?
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