calculateOLP.m File Reference

Function to caluclate the OLP Regression. More...

Functions
function	calculateOLP (in x, in y)
	Function to caluclate the OLP Regression.

Detailed Description

Function to caluclate the OLP Regression.

Author

Marlies Nitschke

Date

December, 2018

Function Documentation

calculateOLP()

function calculateOLP	(	in	x,
		in	y
	)

Function to caluclate the OLP Regression.

The OLP regression analysis exposes systematic differences of two methods instead of similarities. The coefficient considers that both methods can be affected by random errors.

\( \mathbf{x} = \left[x_1,x_2,\ldots,x_N \right]^T \)

\( \mathbf{y} = \left[y_1,y_2,\ldots,y_N \right]^T \)

RMSE = \( \sqrt {\frac{1}{N} \displaystyle\sum_{i=1}^{N}\displaystyle (y_i - (\beta x_i + \alpha))^2 } \)

\( \alpha = \bar{y} - \beta\bar{x} \)

\( \beta = \displaystyle\sqrt {\frac {\beta_y}{\beta_x}} \)

\( \beta_y = \displaystyle\frac {\displaystyle\sum_{i=1}^{N}(x_i - \bar{x})(y_i - \bar{y}) }{\displaystyle\sum_{i=1}^{N}(x_i - \bar{x})^2} \)

\( \beta_x = \displaystyle\frac {\displaystyle\sum_{i=1}^{N}(x_i - \bar{x})(y_i - \bar{y}) }{\displaystyle\sum_{i=1}^{N}(y_i - \bar{y})^2} \)

Relative RMSE = \( \displaystyle\frac{RMSE}{\displaystyle\frac{1}{2} \Bigg\{ [\max_{0<t<T}(x_i(t)) - \min_{0<t<T}(x_i(t)) ] + [\max_{0<t<T}(y_i(t)) - \min_{0<t<T}(y_i(t)) ] \Bigg\} } * 100\% \)

[ out_RMSE, out_beta, out_alpha, out_r,out_DRMSE] = calculateOLP(x, y)

Parameters

x	Double Vector: x signal
y	Double Vector: y signal

Return values

out_RMSE	Double: RMSE : between 0 and 1
out_beta	Double: slope: any real value
out_alpha	Double: y-intercept: any real value
out_r	Double: PPMCC (Pearson's r): between -1 and 1
out_DRMSE	Double: relative RMSE: between -100% and 100%