Economics 421Homework #1
Due June 3
1) In what follows a and b are parameters and µ has mean zero and variance s². Find the expected value (mean) and variance of the following random variables being sure to define any other terms which might arise.
a) Y = a + bX + µ where X is a fixed number.
b) Y = exp(X) + µ where X is a fixed number.
c) Y = a + bX + µ where X is a random variable.
d) Y = exp(X) + µ where X is a random variable.
e) XY where Y = a + bX where X is a random variable. Assume E(X)=0.
2) In 1 e above, what is implied if b=0?
3) Write down and explain the assumptions on the regression model and on the error term.
4) Spend some time becoming familiar with your econometric software. Download the homework 1 data set from my homepage and read it into ET.
a)Compute descriptive statistics on the two variables.
b)Plot them against each other. Does the plot suggest correlation? How so?
c)Estimate the model Y = a + bX1 + u. What are the estimates of a and b?
d)Compute Yfit*resid, x1*resid. Find the descriptive statistics for these two variables, for yfit, and for resid. Relate these values to what we have learned about the least squares regression model.
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