Outlier Detection Method in Linear Regression Based on Sum of Arithmetic Progression

Table 1

Sample calculations for illustrating the relation between 2/n and (𝑎₁+𝑎_𝑛)/𝑆_𝑛.

𝑎𝑛	Data set 1	Data set 2	Data set 3	Data set 4	Data set 5
𝑎1	100	100	100	99.99	1
𝑎2	101	101	101	101	101
𝑎3	102	102	102	102	102
𝑎4	103	103	103	103	103
𝑎5	104	104.01	204	104	104
(𝑎1 + 𝑎5)/𝑆5	0.4	0.40001	0.498	0.399	0.255
2/𝑛	0.4	0.4	0.4	0.4	0.4
Outlier?	—	Yes-𝑎5	Yes-𝑎5	Yes-𝑎1	Yes-𝑎1