Beyond Aggregation - Real-Time Analytics - page 465

double n = ( double )y.length;
b = (sumXY - (sumX*sumY)/n)/(sumX2 - (sumX*sumX)/n);
a = sumY/n - (b*sumX)/n;
}
Notice that the preceding function only requires a single pass over the data.
This means that it is also amenable to a simple streaming formulation,
useful for real-time analysis:
public class StreamingSimpleLinearModel {
double sumX = 0.0, sumY = 0.0;
double sumXY = 0.0, sumX2 = 0.0;
double n = 0.0;
boolean dirty = true ;
double a = 0.0,b = 0.0;
private void update() {
if (!dirty) return ;
b = (sumXY - (sumX*sumY)/n)/(sumX2 - (sumX*sumX)/
n);
a = sumY/n - b*sumX/n;
dirty = false ;
}
public void observe( double y, double x) {
sumX += x;sumY += y;
sumXY += x*y;sumX2 += x*x;
n += 1.0;
dirty = true ;
}
public double b() { update(); return b; }
public double a() { update(); return a; }
}
Multivariate Linear Regression
Computing the best estimates for B when there is more than one x variable,
excluding the intercept term, is a bit more complicated, but it's still
straightforward. Using a technique called ordinary least squares , which is
sometimes used as a synonym for multivariate linear regression, the values
of B have a closed form so long as certain requirements are met.