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Interactive Polynomial Regression

The Polynomial Regression problem attempts to fit datapoints with a polynomial function by finding optimal coefficients. In the general case, the output $y_i$ is described by the p-th degree polynomial shown in Equation 1. \begin{equation} y_i=\beta_0+\beta_{1}x_{i}+\beta_{2}x_{i}^2+\cdots+\beta_{p}x_{i}^p+\epsilon_i \end{equation} There are $p$ different polynomial terms and each of them is associated to a specific $\beta$ coefficient and then there is also the coefficient $\beta_0$ not associated to any variable because this is the intercept. The $\epsilon$ term takes into account all the factors and noise not included in the inputs. Click the button below for an introduction on polynomial regression.

Click this other button to see how to code polynomial regression from scratch in Python.

This article provides an interactive code for the Polynomial Regression written in Javascript. The code can be modified and it runs by clicking the button "Run Code".

n=300; //Number of samples pol_order=3; //Polynomial order x_min=-5; //Min value for features x_max=5; //Max value for features coeff_range=1 //Max absolute coefficient value sigma_noise=10; //Standard deviation for gaussian noise //Sample Generation x_sample=math.random([n,1],x_min,x_max); x=x_sample; var i; for (i = 2; i <= pol_order; i++) { x=math.concat(x,math.dotPow(x_sample,i)); } //Generate Coefficients coeffs=math.random([pol_order+1,1],-coeff_range,coeff_range) //Features including the bias x=math.concat(math.ones([n,1]),x); //Generate Polynomial Output with Noise noise=ai_lib.generate_normal_sample(n,0,sigma_noise); y=math.add(math.multiply(x,coeffs),noise); //Estimation of coefficients coeff_est=ai_lib.ols(x,y); //Estimated linear function using the estimated coefficients y_est=math.multiply(x,coeff_est) //Settings for the plot var original_sample = { x: math.transpose(x_sample)[0], y: math.transpose(y)[0], mode: 'markers', type: 'scatter', name: 'Samples' }; var estimated_function = { x: math.transpose(x_sample)[0], y: math.transpose(y_est)[0], mode: 'markers', type: 'scatter', name: 'Estimated Function' }; var layout = { xaxis: { range: [math.min(x_sample)-1, math.max(x_sample)+1], autorange: false }, yaxis: { range: [math.min(y)-30, math.max(y)+30], autorange: false }, legend: { x: 1, y: 0.5 }, margin: { t: 0 } } //Print the values of the estimated coefficients document.getElementById("text").innerHTML='The values of the estimated coefficient are:'+math.round(coeff_est,3); //Plot of the original samples and the estimated linear function var data = [original_sample,estimated_function]; PLOT = document.getElementById('plot'); Plotly.newPlot( PLOT, data,layout );

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Interactive Polynomial Regression Code modifiable by the user in Javascript
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