570 Prof. K. Pearson on Lines and Planes of 



We have at once : 



^=3*82 y=3-70 



o>= 2*3748 



<r y = 1-31225 



r xy =--9765 



tan 2e=2rxy(ra : o-yl{o- x ' 2 -(T^) = - 1 5535. 



Hence: tan 0= —'54556, or the best-fitting line passes 

 through the point 3'82, 3'70 at a slope of -'546. This line 

 is shown in the accompanying diagram by AB. The mean 



y 























A> ^ 

















































X 



s> ^ x 



























?entrv 



K 



af. ■ ■ 























^^^ 



X 

























x^X. 

























V 



V B 



square residual is '2484. Had we made S(?/— #') 2 a minimum, 

 the slope of the "best-fitting" line would have been — '5396 

 and the mean square residual '2828 ; had we made S(#— #')* 

 a minimum, the slope of the " best-fitting " line would have 

 been — '5659, and the mean square residual '5118. These 

 lines are of course the regression lines of slopes rxyo-y/ax and 

 cryl(rxyo-x) to the horizontal and mean square vertical and 

 horizontal residuals of <r y \/l—r 2 and car </l — ^respectively. 

 Illustration (2).— The' following system gives four values 

 of a certain function z : 





#=2. 



a?=4. 



2/=16 



2/=26 



219 

 261 



127 

 231 



