Calculate slope and intercept value for logarithmic trendline as excel

Question

I'm creating logarithmic trendlines with the help of an Excel algorithm. However, I am unable to calculate the slope and intercept values as done in Excel. I believe my formula contained several errors.

This is my code

 var X= [10, 25, 30, 40]; Y= [5, 4, 7, 12];

 var Slope, Intercept, SX = 0, SY = 0,
            SXX = 0, SXY = 0, SYY = 0,
            SumProduct = 0, N = X.length;

            for (var i = 0; i < N; i++) {
                SX = SX + X[i];
                SY = SY + Y[i];
                SXY = SXY + X[i] * Y[i];
                SXX = SXX + X[i] * X[i];
                SYY = SYY + Y[i] * Y[i];
            }

            Slope = ((N * SXY) - (SX * SY)) / ((N * SXX) - (SX * SX));

            Intercept = (SY - (Slope * SX)) / N;

Fiddle link

Excel Formula:

Logarithmic Equation: y=(c*LN(x))+b

where:

c = INDEX(LINEST(y,LN(x)),1)
b = INDEX(LINEST(y,LN(x)),1,2)

Screenshot for Excel output

Please suggest how to derive the Excel formula in JavaScript.

Answer 1

You missed Math.log() for ln() in Excel. Edit for parts like this.

for (var i = 0; i < N; i++) {
    SX = SX + Math.log(X[i]);
    SY = SY + Y[i];
    SXY = SXY + Math.log(X[i]) * Y[i];
    SXX = SXX + Math.log(X[i]) * Math.log(X[i]);
    SYY = SYY + Y[i] * Y[i];
}

I've verified the output is the same as Excel.

> Slope

3.8860409979365333

> Intercept

-5.252238189415747