Intro
I was a little surprised that no one had written a linear regression function and posted it on the web (perhaps I didn't look hard enough). I spent a little time researching and wrote the code displayed below.
A few comments:
Because the Arduino language cannot pass arrays to sub-functions, the code passes pointers instead. That's why the lrCoef variable is passed to the function but isn't passed back.
Also, it is apparently difficult to find the length of an array in the Arduino language. It's not impossible, but it appears to be easier to handle if the length is provided up front.
The Linear Regression Code
// example
float y[4]={3, 4, 5, 6};
float x[4]={2.9875,3.9937,4.9925,5.9925};
float lrCoef[2]={0,0};
void setup(){
Serial.begin(9600);
delay(1000);
// call simple linear regression algorithm
simpLinReg(x, y, lrCoef, 4);
Serial.print(lrCoef[0],8);
Serial.print(" ");
Serial.println(lrCoef[1],8);
}
void loop(){
}
void simpLinReg(float* x, float* y, float* lrCoef, int n){
// pass x and y arrays (pointers), lrCoef pointer, and n. The lrCoef array is comprised of the slope=lrCoef[0] and intercept=lrCoef[1]. n is length of the x and y arrays.
// http://en.wikipedia.org/wiki/Simple_linear_regression
// initialize variables
float xbar=0;
float ybar=0;
float xybar=0;
float xsqbar=0;
// calculations required for linear regression
for (int i=0; i<n; i++){
xbar=xbar+x[i];
ybar=ybar+y[i];
xybar=xybar+x[i]*y[i];
xsqbar=xsqbar+x[i]*x[i];
}
xbar=xbar/n;
ybar=ybar/n;
xybar=xybar/n;
xsqbar=xsqbar/n;
// simple linear regression algorithm
lrCoef[0]=(xybar-xbar*ybar)/(xsqbar-xbar*xbar);
lrCoef[1]=ybar-lrCoef[0]*xbar;
}
