PUAF 610

Quantitative Methods in Policy Analysis

Fall 2007

Problem Set #9

Referring to problem 2 in problem set #8 using the UMCPsalaries.xls data set, use the natural logarithm of salary as the response variable to try to correct for the heteroscedasticity observed in the residuals produced by a simple linear regression.

Create a new variable, LNsalary, in a new column, and use the Excel command "=LN(salary)" to compute the natural logarithm of each faculty member's salary.

A.

Explain the meaning of the slope and intercept in plain English. Do these values make sense?

Explain the meaning of the standard error in plain English.

HINT: If the logarithm of salary changes by a certain amount, what happens to salary?

C.

Plot the residuals, and compare to last week's plot. Has the heteroscedasticity been corrected?

D.

Compare the two models: last week's linear regression, and this week's nonlinear regression. Compare the values of R², the p-value corresponding to the test of the null hypothesis that the response and explanatory variables are uncorrelated, the standard error of the regression, and the analyses of the residuals. Which model is best overall?

2.

The file Inouye.xls contains data collected by UMCP Prof. David Inouye (and his graduate students) at the Rocky Mountain Biological Lab over the past 30 years. Use this data to answer the following questions:

A.

Is the minimum temperature in April increasing? Is this increase statistically significant? Test the appropriate null hypothesis. (Analysis like this, conducted at thousands of locations around the world, is the basis for claims that climate is changing.)

B.

Do the same for the date of first bare ground. What do you conclude?

C.

One might hypothesize that the date marmots come out of hibernation (as measured by the date of first sighting) is related to climate. Is marmot sighting better explained by the minimum temperature in April, or by the date of bare ground?

3.

The file worldpopulation.xls contains estimates of world population from 1950-2003.

A.

Make a scatterplot of the data. Using the "trendline" tool, fit an exponential curve to the data, displaying the regression equation and r-squared on the plot. Is the equation a good fit to the data? What is the average population growth rate over this period?