Abstract
This paper presents the hypothesis testing of parameters for ordinary linear circular regression model assuming the circular random error distributed as von Misses distribution. The main interests are in testing of the intercept and slope parameter of the regression line. As an illustration, this hypothesis testing will be used in analyzing the wind and wave direction data recorded by two different techniques which are HF radar system and anchored wave buoy.
Highlights
A circular random variable is a variable which takes values on the circumference of a circle, i.e. the angle is in the range (0, 2π ) radians or (00, 3600)
A continuous linear variable is a random variable with realisations on the straight line which may be analysed by usual techniques
Ordinary linear circular regression model is applied when we wish to determine the relationship between a single circular explanatory variable X and a circular response variable Y
Summary
A circular random variable is a variable which takes values on the circumference of a circle, i.e. the angle is in the range (0, 2π ) radians or (00, 3600). Figure below gives a simple (or even simplistic) scatter plot for each data set In both cases the observations (direction, in radians) has been measured simultaneously by an anchored buoy (Y) and by radar (X). Since 1o is only 2o from 359o, the point (1o, 359o) on the simple scatter plot should not really be far from the ideal model y = x In this respect, the simple scatter plot is misleading but it illustrate that an ordinary linear regression model which ignore the circularity of the data is misleading. The simple scatter plot is misleading but it illustrate that an ordinary linear regression model which ignore the circularity of the data is misleading Perhaps such scatter plots should be drawn on a torus which maintains the “wrapping” of the measurements scales. This shows the chief problem with ordinary linear regression when applied to circular variables and below we will propose an ordinary linear circular regression model which is more suited to this form of data, Hussin (2004)
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