566 Prof. K. Pearson on Lines and Planes cj 



The geometry of these results is indicated in the accompanying 

 diagram : — 



EE' is found by making $(y f — yf a minimum, 



FF' „ „ ' SO'-*) 2 



AA' 



S(p 2 ) 



The equation to EE' referred to C is y= Txy J y $, 



FF' 



O-y 



The angle 6 which AA' makes with Ox is determined by 



tan 20 



2fxy <Tx o~y 

 <J 2 x — G l y 



Further : 



(Mean sq. residual) 2 = a 2 x o-'^/cot 2 6 



/Wat gy ^T - VA ft /ABLE 











"Z.\ 





V • 



v\ 



Physically the axes of the correlation type-ellipse are the 

 directions of independent or uncorrelated variation. Hence 

 the line of best fit is a direction of uncorrelated variation, 



