mctad.simpleLinearRegression = function (data) {
if (!Array.isArray(data) || data.length === 0 ) { return undefined; }
var x = [], y = [], num_acc = 0, x_diff_acc = 0, y_diff_acc = 0, rxy, α, β;
for (var i = 0; i < data.length; i++) {
x.push(data[i][0]);
y.push(data[i][1]);
}
x_bar = mctad.arithmeticMean(x);
y_bar = mctad.arithmeticMean(y);
for (i = 0; i < data.length; i++) {
num_acc += (x[i] - x_bar) * (y[i] - y_bar);
x_diff_acc += Math.pow(x[i] - x_bar, 2);
y_diff_acc += Math.pow(y[i] - y_bar, 2);
}
rxy = num_acc / Math.sqrt(x_diff_acc * y_diff_acc);
β = rxy * (mctad.sampleStandardDeviation(y) / mctad.sampleStandardDeviation(x));
α = y_bar - β * x_bar;
return {
x_bar: x_bar,
y_bar: y_bar,
rxy: rxy,
R2: Math.pow(rxy, 2),
α: α,
β: β
};
};
Simple Linear Regression
Linear Regression is a technique that fits a straight line (or hyperplane in higher dimensions) to a set of observations such that the sum of the square of the distances between the line and the observed values of the dependent variable are minimized.
Simple Linear Regression
mctad.simpleLinearRegression()accepts an Array of Arrays of Numbers, e.g.,[ [1, 2], [3, 4], [5, 6] ]and returns an object of statistical measures related to the simple linear regression it performs, including:
xbar: the arithmetic mean of the x values ybar: the arithmetic mean of the y values rxy: rxy, Pearson's correlation coefficient R2: R2, the coefficient of determination, α: the y-intercept of the simple linear regression line β: the slope of the simple linear regression line