MathGroup Archive 2008

[Date Index] [Thread Index] [Author Index]

Search the Archive

Estimating slope from noisy data


I have difficulties to estimate the correct slope from noisy data.
This is the code to generate the noisy data:

slope = 1.0;
sigma = 0.5;
xrange = 1.0;

SeedRandom[123]; (* initialize random generator *)
rnd = {#, #*slope + RandomReal[NormalDistribution[0, sigma]]} &;

(* generate 2000 data points *)
data = Table[
   rnd[RandomReal[NormalDistribution[0, xrange/3.0]]], {2000}];

subset = Take[data, 8];
ListPlot[subset, PlotRange -> {{-3, 3}, {-3, 3}},
 PlotStyle -> PointSize[.025]]
fit = Regress[subset, x, x, IncludeConstant -> False,
  RegressionReport -> {SummaryReport, ParameterCITable}]

The correct slope is exactly 1. As the data is quite noisy, the CI of
the slope is very big. The estimated slope is far to big (1.947). If I
use more data points, the estimation gets better; I could also use a
wider x-range, to get a better estimate for the slope. However, I'm
quite limited in the x-range, so using a wider x-range is no option
for me.

I could check the RSquared for significance (If[Abs[r*Sqrt[n - 2]/
Sqrt[1 - r^2]] >=
  Quantile[StudentTDistribution[n - 2], 1 - 0.05], r, 0] (*
significance of 95% *)). I this case, it is significant.

Is there any other way to get a good estimate for the slope, without
using too many data points?

(Keywords: fit, regression, slope, noisy, rsquared, limited data)

  • Prev by Date: Re: export pdf font question
  • Next by Date: Re: Manipulate: Positioning of controls within panel
  • Previous by thread: Re: Gradient fill as Background for Plot
  • Next by thread: Re: Estimating slope from noisy data