Wrong regression results

[pablobaezlinero]

Hi everyone,

So I am trying to plot some Time vs Distance data, together with a polynomical regression of degree 3. The data is the following:

Timestamp (ms)	Distance (m)
44156000	0
44954000	826
44991000	863
45501000	1368
45633000	1503
45649000	1531
45667000	1572

Based on Python, I have done this with Python with the following code:

import numpy as np
from sklearn.metrics import r2_score
import matplotlib.pyplot as plt

x = [44156000, 44954000, 44991000, 45501000, 45633000, 45649000, 45667000]
y = [0, 826, 863, 1368, 1503, 1531, 1572]

mymodel = np.poly1d(np.polyfit(x, y, 3))
x_fit = np.linspace(x[0], x[-1], 10000)
plt.scatter(x ,y)
plt.plot(x_fit, mymodel(x_fit), color = 'C1')
plt.title('With direct numbers')
plt.show()

print(f'R^2 = {r2_score(y, mymodel(x))}')
print(f'{mymodel[0]} * x^3 + {mymodel[1]} * x^2 + {mymodel[2]} * x + {mymodel[3]}')

And I get the following plot:

with the following output:

R^2 = 0.9997873136936645
Equation: -18536197.338221278 * x^3 + 1.2356259030900478 * x^2 + -2.7474751118538763e-08 * x + 2.0378899867907668e-16

But, when trying to do the same with HighCharts, I get this plot:

with an R^2 score about 0.5323

The code I have used is the following:

$(function() {
  $('#container').highcharts({
    chart: {
      type: 'scatter',
      zoomType: 'xy'
    },
    title: {
      text: 'Polynomial regression - with extrapolation and different style'
    },
    subtitle: {
      text: 'Source: Heinz  2003'
    },
    xAxis: {
      title: {
        enabled: true,
        text: 'Timestamp (ms)'
      },
      startOnTick: true,
      endOnTick: true,
      showLastLabel: true
    },
    yAxis: {
      title: {
        text: 'Distance (m)'
      }
    },
    legend: {
      layout: 'vertical',
      align: 'left',
      verticalAlign: 'top',
      x: 100,
      y: 70,
      floating: true,
      backgroundColor: '#FFFFFF',
      borderWidth: 1
    },
    plotOptions: {
      scatter: {
        marker: {
          radius: 5,
          states: {
            hover: {
              enabled: true,
              lineColor: 'rgb(100,100,100)'
            }
          }
        },
        states: {
          hover: {
            marker: {
              enabled: false
            }
          }
        },
        tooltip: {
          headerFormat: '<b>{series.name}</b><br>',
          pointFormat: '{point.x} cm, {point.y} kg'
        }
      }
    },
    series: [{
      regression: true,
      regressionSettings: {
        type: 'polynomial',
        color: 'rgba(223, 183, 83, .9)',
        order: 3,
        dashStyle: 'dash'
      },
      name: 'Test input',
      color: 'rgba(223, 83, 83, .5)',
      data: [
      [44156000, 0],
      [44954000, 826],
      [44991000, 863],
      [45501000, 1368],
      [45633000, 1503],
      [45649000, 1531],
      [45667000, 1572]
      ]
    }]
  });
});

Personally, I think that the latter result makes no sense, and the regression fails.

I am doing something wrong? Why does this happen?

Thank you everybody,
Pablo