Time Scale in Least Square Method

Table 1

Values for results obtained.

For 𝑛=10
Simple linear regression equation		Sum of vertical deviations	Observation 𝑌𝑖	Estimation 𝑌𝑖
Normal	3.27 + 1.01x	0	62	62
Fwd	7.42 − 0.59x	5	62	57
Bckwd	−0.89+2.62𝑥	−5	62	67
For 𝑛=20
Simple linear regression equation		Sum of vertical deviations	Observation 𝑌𝑖	Estimation 𝑌𝑖
Normal	2.90+1.09𝑥	0	155	155
Fwd	11.26−0.90𝑥	10	155	145
Bckwd	−5.46+3.08𝑥	−10	155	165
For 𝑛=30
Simple linear regression equation		Sum of vertical deviations	Observation 𝑌𝑖	Estimation 𝑌𝑖
Normal	3.45+0.97𝑥	0	291	291
Fwd	14.17−0.77𝑥	15	291	276
Bckwd	−7.27+2.70𝑥	−15	291	306
For 𝑛=40
Simple linear regression equation		Sum of vertical deviations	Observation 𝑌𝑖	Estimation 𝑌𝑖
Normal	3.38+0.96𝑥	0	448	448
Fwd	17.94−0.89𝑥	20	448	428
Bckwd	−11.17+2.81𝑥	−20	448	468
For 𝑛=50
Simple linear regression equation		Sum of vertical deviations	Observation 𝑌𝑖	Estimation 𝑌𝑖
Normal	3.54+0.93𝑥	0	638	638
Fwd	22.07−0.99𝑥	25	638	613
Bckwd	−15.00+2.86𝑥	−25	638	663