# polyplot documentation

This function plots a polynomial fit to scattered x,y data. This function can be used to easily add a linear trend line or other polynomial fit to a data plot.

## Syntax

polyplot(x,y)
polyplot(x,y,n)
polyplot(...,'LineProperty',LineValue,...)
polyplot(...,'error')
polyplot(...,'error','ErrorLineProperty',ErrorLineValue)
[h,p,delta] = polyplot(...)

## Description

polyplot(x,y) places a least-squares linear trend line through scattered x,y data.

polyplot(x,y,n) specifies the degree n of the polynomial fit to the x,y data. Default n is 1.

polyplot(...,'LineProperty',LineValue,...) formats linestyle using LineSpec property name-value pairs (e.g., 'linewidth',3).

polyplot(...,'error') includes lines corresponding to approximately +/- 1 standard deviation of errors delta. At least 50% of data should lie within the bounds of error lines.

polyplot(...,'error','ErrorLineProperty',ErrorLineValue) formats error lines with line property name-value pairs. All arguments occurring after 'error' are assumed to be error line property specifications.

[h,p,delta] = polyplot(...) returns handle(s) h of plotted line(s), coefficients p of polynomial fit p(x), and error estimate delta, which is the standard deviation of error in predicting a future observation at x by p(x). Assuming independent, normal, constant-variance errors, y +/- delta contains at least 50% of the predictions of future observations at x.

## Examples

Given some data:

x = 1:100;
y = 12 - 0.01*x.^2 + 3*x + sind(x) + 30*rand(size(x));


Plot the data and add a simple linear trend line:

plot(x,y,'bo')
hold on
polyplot(x,y);

legend('data','linear fit','location','southeast') Instead of a linear trend, make it a cubic fit:

figure
plot(x,y,'bo')
hold on

polyplot(x,y,3);
legend('data','cubic fit','location','southeast') A fat, red 7th-order polynomial fit:

figure
plot(x,y,'bo')
hold on
polyplot(x,y,7,'r','linewidth',4);
legend('data','7^{th} order fit','location','southeast') Same as above, but with +/- 1 standard deviation of error lines:

figure
plot(x,y,'bo')
hold on
polyplot(x,y,7,'r','linewidth',4,'error');
legend('data','7^{th} order fit','\pm1\sigma','location','southeast') Heavy black dotted quadratic fit with thin dashed magenta error lines:

figure
plot(x,y,'bo')
hold on
polyplot(x,y,2,'k:','linewidth',5,'error','m--','linewidth',.3) 