Regression

Regression Type	Regression Equation
Polynomial
Exponential
Hyperbola
Logarithmic
Inverse
Inverse Power
Polyexp
Power

Fourier, Filter and Track Order

Any set of periodic data (ie. a paired (x,y) data set where the dependent variable y repeats itself periodically with respect to the independent variable x) can be approximated by a superposition of sine and cosine curves with varying time period. The Fourier, Filter and Track Order Process Modules are based on the decomposition of a periodic data set into components corresponding to different orders of periodicity by performing a fit to the following Fourier series equation:
 

 
where n is the selected order for the Fourier fit.

The Fourier module calculates the best approximation to the data that can be obtained by fitting it to a Fourier series of the selected order.

The Filter module allows the user to select which orders they wish to retain within the Fourier fit. This could be done to eliminate noise from a signal for instance.

The track order module allows the user to see which orders exist in the data and the corresponding magnitudes.

The plot shown below displays a set of data along with a Fourier fit of order 5 performed on it.
 

 
Track order analysis of the same data (shown below) reveals that the two dominant orders in the above Fourier fit are 2 and 1 with approximate magnitudes of 1 and 0.5 respectively.
 

 
In the following plot, a high pass filter of the same data with first cut-off order set to 2 retains only the 2nd order component of the Fourier series and results in the green line. A low pass filter of the data with second cut-off order set to 1 retains only the 1st order component of the Fourier series and results in the red line.
 

 

Univariate Metrics

The formulae used to calculate univariate metrics for a data set Y of length N is given in the table below.

Metric	Equation
Mean or average
Median	The median is the value of the point which has half the data smaller than that point and half the data larger than that point.
Variance
Standard deviation
Standard error of mean
Skewness
Kurtosis