The Analysis of Meteor Data

A problem commonly encountered in meteor studies is the need for a realistic interpretation of statistical data which contains uncertainties in two variables. A simple solution is provided and for illustration applied to diffusion-height data. 1. LINEAR REGRESSION The statistical analysis of data consisting of two variables,each subject to error,in order to determine the existence of any linear relationship between the variables often occurs in observational meteor studies. For a scatter diagram in Cartesian coordinates two regression lines can be recognized: the regression of y on x minimizes the residuals in y whereas the regression of x on y minimizes the residuals in x. The former line of slope mi is the best estimate of the data trend if un­ certainties in x for each data point are negligible while the latter regression line of slope ni2 represents the best estimate if the x uncertainties are dominant. In many situations significant uncertainties are present in both coordinate values and since no convenient procedure appears to be readily available for estimating the best linear fit in this case, the simple but unrealistic approach is often adopted of taking the gradient to be equal to the arithmetic mean of mi and m2. In a recent work Ross (1979) shows how a solution may be obtained in a straightforward way: if the coordinate uncertainties Ax and Ay are the same for all data points and defining $ as (Ax/Ay) then the gradient, m, of the best fit line is given by a solution of the quadratic equation m262 m(6m2 1/mi) 1 = 0 For the special case 6=0 m=mi while for B=°° m=rri2 as expected.