Database Reference
In-Depth Information
of
B
is usually called
a
, and the second value called
b
and the equation for
reduced to the following simple form:
public class
SimpleLinearModel {
public double
a,b;
public
SimpleLinearModel(
double
a,
double
b) {
this
.a = a;
this
.b = b;
}
public double
y(
double
x) {
return
a + b*x;
}
}
The error to minimize is similarly simplified:
public double error(double[] y,double [] x) {
double error = 0.0;
for(int i=0;i<y.length;i++) error +=
(y[i]-a-b*x[i])*(y[i]-a-b*x[i]);
return error;
}
After a little bit of calculus, it is found that this function is minimized when
b
isequaltothecovarianceof
x
and
y
dividedbythevarianceof
x
.Thevalue
of
a
best minimizes the error when it is equal to the mean of
y
minus the
estimated value of
b
multiplied by the mean of
x
. If all the data are present
in an array, the following function will find the appropriate values of
a
and
b
:
public void fit(double[] y,double[] x) {
double sumX = 0.0, sumY = 0.0;
double sumXY = 0.0, sumX2 = 0.0;
for(int i=0;i<y.length;i++) {
sumX += x[i];
sumY += y[i];
sumXY += x[i]*y[i];
sumX2 += x[i]*x[i];
}
