Question

I have a chart in excel that represents some value over a one day period. So I add the reference function and I get something like this:

y = 1E-13x6 - 2E-10x5 + 8E-08x4 - 1E-05x3 + 0,0004x2 + 0,0275x + 8,414

A mesure in my data set is:

09:36:21 => 5,27

The firts thing I need to know is how to transform the timestamp into a value to give to the function. After some cell value transforming I’ve found out that excel gives timestamps a representation between 0.00000 and 0.99999, so for example 09:36:21 is 0.400243055555556. Then I’ve coded a little java test script:

double x = 0.400243055555556;
double x6 = (1*Math.pow(10, -13))*Math.pow(x, 6);
double x5 = (2*Math.pow(10, -10))*Math.pow(x, 5);
double x4 = (8*Math.pow(10, -8))*Math.pow(x, 4);
double x3 = (1*Math.pow(10, -5))*Math.pow(x, 3);
double x2 = (4*Math.pow(10, -4))*Math.pow(x, 2);
double y = x6 - x5 + x4 - x3 + x2 + 0.0275*x + 8.414;

But after executing this script I get y = 8.425070122712738. So this is obviously not working. I must say that all the values in the chart range from 5 to 12.

I’m obviously doing something wrong, but I don’t know what. Maybe I’ve coded the function badly, or maybe the x I’m choosing is not a right value, but something is wrong. Can anyone help?

Update: My code wasn’t that good, what duffymo suggested worked better. But the problem was that Excel was giving my the wrong tendendy line. I’ve managed to get the good one using a scatter graph.

Answer 1

I would not recommend coding it this way – roundoff could be an issue.

I would recommend Horner scheme:

I coded it this way and got the same answer that you did:

public class Horner
{
   public static final NumberFormat DEFAULT_FORMAT = new DecimalFormat("0.000");

   public static void main(String[] args)
   {
      double [] a = { 8.414, 0.0275, 0.0004, -1.0e-5, 8.0e-8, -2.0e-10, 1.0e-13 };
      for (double x = 0.0; x < 1.0;  x += 0.05)
      {
         double y = a[0] + x*(a[1] + x*(a[2] + x*(a[3] + x*(a[4] + x*(a[5])))));
         System.out.println("x = " + DEFAULT_FORMAT.format(x) + " y = " + DEFAULT_FORMAT.format(y));
      }
   }
}

Here’s the result I get. The higher order terms aren’t doing much good; the coefficients are small, and when you raise a fraction to a power it diminishes the effect even more.

x = 0.000 y = 8.414
x = 0.050 y = 8.415
x = 0.100 y = 8.417
x = 0.150 y = 8.418
x = 0.200 y = 8.420
x = 0.250 y = 8.421
x = 0.300 y = 8.422
x = 0.350 y = 8.424
x = 0.400 y = 8.425
x = 0.450 y = 8.426
x = 0.500 y = 8.428
x = 0.550 y = 8.429
x = 0.600 y = 8.431
x = 0.650 y = 8.432
x = 0.700 y = 8.433
x = 0.750 y = 8.435
x = 0.800 y = 8.436
x = 0.850 y = 8.438
x = 0.900 y = 8.439
x = 0.950 y = 8.440

Still not what you want, but I think the coding is far simpler.