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Unformatted text preview: STATISTICS 500 Fall 2009 Homework 9, handed out Saturday, 31 Oct 2009 on campus Friday, 6 Nov 2009, in lecture (11 am) or by e-mailto Chuanlong, firstname.lastname@example.org, no later than noon. off campus Monday, 9 Nov 2009, by 4 pm to Nicole Rembert, email: email@example.com or FAX: 515-294-4040 (please include cover page with Stat 500 / Nicole Rembert). 1. Lack of fit, Correlated errors Global temperature Global warming is a contentious environmental issue. The data in temperature.txt on the web site are measurements of the worldwide average annual temperature for 108 years from 1880 to 1987. The response variable is expressed as a temperature anomaly. This is the deviation of that years temperature from the average over all 108 years. The trend in the temperature anomaly is the same as the trend in the temperature. What do these data tell us about the temperature trend? Assessment of the uncertainty in the trend is as important as assessment of the trend. (a) Fit a usual linear regression and estimate the slope (temperature change per year). Estimate the s.e. of the slope assuming that errors are independent. (b) Is the assumption of a linear trend reasonable? Explain why or why not. You are free to choose your favorite lack of fit method, but I strongly suggest you consider more than just a residual plot. If want to use a polynomial, please consider whether that polynomial is appropriate for the apparent trend. All subsequent parts will use the linear model Temp = + 1 Y ear + even though that isnt really appropriate. (c) Estimate the lag-1 correlation in the residuals from the linear model, i.e. the correlation between e t and e t- 1 . (d) Test for a significant lag-1 correlation using the Durbin-Watson test. (e) If you have access to SAS: Use PROC MIXED to estimate the slope, allowing for a non-zero correlation between errors. Assume an AR(1) error structure. Estimate the s.e. of the slope....
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- Fall '08