Question

Write a JavaScript program to implement the Least-Squares Linear Regression algorithm shown below, for an arbitrary set of ( x, y ) data points entered by the user.

The Algorithm: 1. Read in a series of ( x, y ) data pairs. While doing so, calculate the following sums: • N = number of data pairs. • Sx = ∑ x = Summation ( total ) of all X values. • Sy = ∑ y = Summation ( total ) of all Y values. • Sxx = ∑ x2 = Summation ( total ) of all X2 values. • Syy = ∑ y2 = Summation ( total ) of all Y2 values. • Sxy = ∑ xy = Summation ( total ) of all X∙Y values. 2. Then calculate: • Slope, m = ( N ∙ Sxy – Sx ∙ Sy ) / ( N ∙ Sxx – Sx ∙ Sx )

Answer 1

The above problem can be solved by following the steps mentioned below-

STEP 1- We will define the js function that calculates the slope using least square linear regression method.

STEP 2- The function prompts the user to enter value of x data point or enter E to leave entering the data points. And if the user enters the value x, prompt him to enter the value y.

STEP 3- Check if the user has entered E, if yes then do not prompt user to enter any value again.

STEP 4- Steps 2 and 3 are coded in an infinite loop which breaks when user enters E.

STEP 5- After each iteration, value of summation of x, summation of y, summation of x², summation of y², summation of x.y is updated and stored in a variable. Also, count N keeps on getting incremented by 1.

STEP 6 - Using the formula to calculate the value of slope m, ( N ∙ Sxy – Sx ∙ Sy ) / ( N ∙ Sxx – Sx ∙ Sx ), calculate the value and display it to the user.

The code has been run on Google Chrome developer tools console and user input is taken by prompt.

JavaScript Code-

//define the javascript function
function LeastSquareLR(){
   //define and initialize the variables whereever needed
   var x; //to store x value of data point
   var y ;   //to store y value of data point
   var Sx = 0, Sy = 0, Sxx = 0, Syy = 0, Sxy = 0,N = 0,i;
   //infinite loop to keep on entering data points until user wants to end input
   while(true){
       //prompt the user to enter
       x = prompt("Enter the value of x or E to exit");
       //if input is E, break the loop
       if(x == 'E')
           break;
       x = parseInt(x);
       //user enters y value
       y = parseInt(prompt("Enter the value of y"));
      
       Sx = Sx + x;   //summation of x
       Sy = Sy + y;   //summation of y
       Sxx = Sxx + (x*x);   //summation of x^2
       Syy = Syy + (y*y);   //summation of y^2
       Sxy = Sxy + (x*y);   //summation of x*y
      
       //increment N
       N++;
   }
   //user formula to calculate slope m
   var m = ((N*Sxy -(Sx*Sy))/(N*Sxx - (Sx*Sx)));
   //display the result upto 3 decimal places
   console.log(m.toFixed(3));
}
//call the above function
LeastSquareLR();

Image of Code-

Output-

User inputs-

Console Output-

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