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Analyzing Residuals

A measure of the "goodness" of fit is the residual, the difference between the observed and predicted data. Compare the residuals for the various fits, using normalized cdate values. It's evident from studying the fit plots and residuals that it should be possible to do better than a simple polynomial fit with this data set.

Comparison Plots of Fit and Residual  
p1 = polyfit(sdate,pop,1);
pop1 = polyval(p1,sdate);

set of three fit plots compared with plots of residuals

res1 = pop - pop1;
figure, plot(cdate,res1,'g+')

p = polyfit(sdate,pop,2);
pop2 = polyval(p,sdate);

res2 = pop - pop2;
figure, plot(cdate,res2,'g+')

p = polyfit(sdate,pop,4);
pop4 = polyval(p,sdate);

res4 = pop - pop4;
figure, plot(cdate,res4,'g+')

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