Data Analysis and Statistics (Mathematics)

Mathematics

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
Fit
Residuals

p1 = polyfit(sdate,pop,1);
pop1 = polyval(p1,sdate);
plot(cdate,pop1,'b-',cdate,pop,'g+')

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

p = polyfit(sdate,pop,2);
pop2 = polyval(p,sdate);
plot(cdate,pop2,'b-',cdate,pop,'g+')

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

p = polyfit(sdate,pop,4);
pop4 = polyval(p,sdate);
plot(cdate,pop4,'b-',cdate,pop,'g+')

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

**Comparison Plots of Fit and Residual**
Fit	Residuals
`p1 = polyfit(sdate,pop,1);` `pop1 = polyval(p1,sdate);` `plot(cdate,pop1,'b-',cdate,pop,'g+')`	`res1 = pop - pop1;` `figure, plot(cdate,res1,'g+')`
`p = polyfit(sdate,pop,2);` `pop2 = polyval(p,sdate);` `plot(cdate,pop2,'b-',cdate,pop,'g+')`	`res2 = pop - pop2;` `figure, plot(cdate,res2,'g+')`
`p = polyfit(sdate,pop,4);` `pop4 = polyval(p,sdate);` `plot(cdate,pop4,'b-',cdate,pop,'g+')`	`res4 = pop - pop4;` `figure, plot(cdate,res4,'g+')`

Polynomial Fit Exponential Fit