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Concept visual
Start from A
A Regression is a method to determine the relationship between one variable ( y ) and other variables ( x ). In statistics, a Linear Regression is an approach to modeling a linear relationship between y and x. In Machine Learning, a Linear Regression is a supervised machine learning algorithm.
(from the previous chapter):
const xArray = [50,60,70,80,90,100,110,120,130,140,150];
const yArray = [7,8,8,9,9,9,10,11,14,14,15];
// Define Data const data = [{
x:xArray, y:yArray, mode: "markers"
}];
// Define Layout const layout = {
xaxis: {range: [40, 160], title: "Square Meters"}, yaxis: {range: [5, 16], title: "Price in Millions"}, title: "House Prices vs. Size"
};
Plotly.newPlot("myPlot", data, layout);Try it Yourself »
From the scattered data above, how can we predict future prices?
This is a linear graph predicting prices based on the lowest and the highest price:
const xArray = [50,60,70,80,90,100,110,120,130,140,150];
const yArray = [7,8,8,9,9,9,9,10,11,14,14,15];
const data = [
{x:xArray, y:yArray, mode:"markers"},
{x:[50,150], y:[7,15], mode:"line"}
];
const layout = {
xaxis: {range: [40, 160], title: "Square Meters"}, yaxis: {range: [5, 16], title: "Price in Millions"}, title: "House Prices vs. Size"
};
Plotly.newPlot("myPlot", data, layout);Try it Yourself »
Formula
A linear graph can be written as y = ax + by is the price we want to predict a is the slope of the line x are the input values b is the intercept
Model predicts prices using a linear relationship between price and size:
const xArray = [50,60,70,80,90,100,110,120,130,140,150];
const yArray = [7,8,8,9,9,9,10,11,14,14,15];
// Calculate Slope let xSum = xArray.reduce(function(a, b){return a + b;}, 0);
let ySum = yArray.reduce(function(a, b){return a + b;}, 0);
let slope = ySum / xSum;
// Generate values const xValues = [];
const yValues = [];
for (let x = 50; x <= 150; x += 1) {
xValues.push(x);
yValues.push(x * slope);
}Formula
In the example above, the slope is a calculated average and the intercept = 0.Model predicts prices using a linear regression function:
const xArray = [50,60,70,80,90,100,110,120,130,140,150];
const yArray = [7,8,8,9,9,9,10,11,14,14,15];
// Calculate Sums let xSum=0, ySum=0 , xxSum=0, xySum=0;
let count = xArray.length;
for (let i = 0, len = count; i < count; i++) {
xSum += xArray[i];
ySum += yArray[i];
xxSum += xArray[i] * xArray[i];
xySum += xArray[i] * yArray[i];
}
// Calculate slope and intercept let slope = (count * xySum - xSum * ySum) / (count * xxSum - xSum * xSum);
let intercept = (ySum / count) - (slope * xSum) / count;
// Generate values const xValues = [];
const yValues = [];
for (let x = 50; x <= 150; x += 1) {
xValues.push(x);
yValues.push(x * slope + intercept);
}If scattered data points do not fit a linear regression (a straight line through the points), the data may fit an polynomial regression. A Polynomial Regression, like linear regression, uses the relationship between the variables x and y to find the best way to draw a line through the data points.