Question

Determine the SSE and the s_e for the following data. Use the residuals and determine how many of them are within ±1s_e and ±2s_e. How do these numbers compare with what the empirical rule says should occur if the error terms are normally distributed?

x	y	Residuals (y-y?)
141	25	6.5898
119	29	-9.1209
103	46	-6.4560
91	70	6.7926
68	88	4.1859
29	112	-6.7558
24	128	4.7644

Answer 1

from above:

x	y	error e =(y ? y?)	e2
141	25	6.5898	43.4255
119	29	-9.1209	83.1908
103	46	-6.456	41.6799
91	70	6.7926	46.1394
68	88	4.1859	17.5218
29	112	-6.7558	45.6408
24	128	4.7644	22.6995
		total	300.2977

SSE =300.2977

se =sqrt(SSE/(n-2))=sqrt(300.2977/(7-2))=7.7498

here only one value -9.1209 is out side of -/+ 1se interval therefore (6/7)*100=85.71 % values fall within -/+ 1se interval against 68% wich is predicted from empirical rule

here all values arewithin -/+ 2se interval therefore 100 % values fall within -/+ 1se interval against 95% wich is predicted from empirical rule