hw9ans - Statistics 500 Fall 2009 Solutions to Homework 9 1...

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Statistics 500 – Fall 2009 Solutions to Homework 9 1 1. Trends in temperature. My SAS code: data temp; infile 'c:/philip/stat500/data/temperature.txt' firstobs = 2 ; input year temp; proc reg ; model temp=year / dwprob; run ; proc loess ; model temp = year / smooth = 0.6 dfmethod =exact; run ; proc mixed ; model temp = year / solution ; repeated / subject = intercept type = ar( 1 ); run ; (a) Estimated slope = 0.00449 , s.e. = 0.00035143 (b) The trend seems to be in three linear pieces. From 1880 to 1945 (approx.) we could fit a straight line, then from 1946 to 1987, the slope is close to zero, then the slope is positive again. year temperature anomaly 1880 1900 1920 1940 1960 1980 -0.4 -0.2 0.0 0.2 Your conclusion depends on your choice(s) of diagnostic. Some of the likely choices include: residual plot – does not indicate much problem, but you can see traces of the different slope from the mid 1940’s to mid 1980’s. adding quadratic or higher order terms – if you add year^2 to the model, the quadratic coefficient is not significantly different from zero. chopping year into groups and using an ANOVA lack of fit test. I got p = 0.0021; there is strong evidence that the relationship is more complex than a straight line. The specific result depends on your choice of number of groups and where they start and stop.
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Statistics 500 – Fall 2009 Solutions to Homework 9 2 using loess with a smoothing parameter of 0.6 gives F = (1.374-1.262) / (106-104.13) / (1.262 / 104.13) = 4.94. This would be compared to an F 1.87, 104 distribution. Other versions of SAS may give slightly different numbers. The p-value is 0.01. (c) I got r = 0.45, using proc reg; model … /dwprob;. Other estimators (e.g. using proc mixed or calculating residuals, lagging them, then calculating the correlation) will give slightly different values. If you calculate the correlation between resid and lag(resid), you get 0.458. Fitting an AR(1) model in proc mixed gives r = 0.489. There is no ‘right’ value.
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