A Property of Symmetric (Interchangeable) Random Variables
Solomon Kullback, H. Y. Yasaimaibodi · The American Statistician · 1967
sum of the weights is equal to the number of observations (N). Then multiply -x by X and subtract the product from Line 2, Col. 2 which is X2. We have 170.0 [ (30.0 1 6.0) (30.0) 1. This is Line 4, Col. 2 orEx2. To obtain Line 4, Col. 3 we repeat the operation i.e., 212.0 [ (x) (36.0) 1 = 32.0. The same operation is performed for the check. Thus in Line 4 we have 20.0 + 32.0 = 52.0, our arithmetic checks. Line 5, Col. 3 is obtained as follows: 276.0- [ (y) (36.0) ] = 60.0. The same operation is performed for the check. 524.0-[ (y) (72.0) ] = 92.0. To check our work we sum 32.0 + 60.0 = 92.0. The final reduction or obtaining the SS of the Residuals is performed in the same manner: 60.0 - [ (32.0 1 20.0) (32.0) ] = 8.8 Line 6, Col. 3. We perform the same operation to the check: 92.0 - [(32.0 1 20.0) (52.0) ] =