Stata 1    Over the next couple of weeks we will use the data file hprice1 (hprice1.dta) to build a   do file and start using and programming in Stata. The data file hprice1 contains a small sample of house prices.

a)   Set up a do file which you use to open the data file, save a log file and explore your data set. You will continue to build on this do file next week.

b)   Reporting  the  average,  the  standard  deviation,  and  the   minimum,  median  and maximum values, for the house price (in $000s), the number of bedrooms and the lot size (in square feet (sqrft)).

c)   Create and save a histogram of the house price.

Q1 (Wooldridge Appendix A Q. 10)

Suppose that in a particular state a standardized test is given to all graduating high school students. Let score denote a student’s score on the test. Someone discovers that performance on the test is related to the size of the student’s graduating high school class.  The relationship is quadratic:

ScoTe = 46.5 + 0.082 ∗ claSS − 0.000147 claSS2

a.   How do you literally interpret the value 46.5 in the equation?  By itself, is it of much interest? Explain.

b.   From the equation, what is the optimal size of the graduating class (i.e. the class size      that maximizes the test score)? (Round your answer to the nearest integer.) What is the highest achievable test score?

c.   Sketch a graph that illustrates your solutions in part b.

d.   Does it seem likely that score and class have a deterministic relationship? That is, is it realistic to think that once you know the size of a student’s graduating class you know, with certainty, his or her test score?  Explain.

Q2  (Wooldridge Appendix C Question 1)

Let Y1, Y2, Y3 and Y4 be independent, identically distributed random variables from a population   with a mean u and variance G 2 . Let  =  (Y1  + Y2  + Y3  + Y4)  denote the average of these four random variables.

a.   What is the expected value and variance of  in terms of u and variance 2 ?

b.   Now consider a different estimator of u.

 =  Y1  +  Y2  +  Y3  +  Y4

This is an example of a weighted average of the Yi . Show that  W is also a weighted average of u.  Find the variance of W.

c.    Based on the above, which estimator of u do you prefer,  or W?

Q3

The following table gives the joint probability density function P(X = x,Y = y) = f (x, y)  of two random variables X and Y :

a.   Evaluate the marginal distributions of X and Y, fX(x) and fY(y).

b.   Evaluate E(X) and E(Y).

c.   Find the conditional distribution f (X = x| Y = 10) and its mean.

d.   Compare E(X) and E(X|Y=10). Are the conditional and  unconditional expectations the same? If no, why are they different?

e.   Explain whether or not X and Y are statistically independent.

Q4 (Wooldridge Appendix B Question 4)

For a randomly selected local labour market area in Australia, let X represent the proportion of adults over age 65 who are employed, i.e. the mature age employment rate. The X is restricted to a value between zero and one.  Suppose the cumulative distribution function for X is given   by: F(x) = 3x2  − 2x3 for all 0 ≤ x ≤ 1. Find the probability that the mature-age employment rate is at least 0.6 (60%).