Question

Following table shows that all India Infant Mortality Rates (per '000) for years 1980 to 1986:

Years	1980	1981	1982	1983	1984	1985	1986
IMR	10	6	5	3	3	1	0

Fit a trend line to the above data by the method of least squares.

Answer 1

Year (t)	IMR (y)	u = t – 1983	u2	y.u
1980	10	–3	9	–30
1981	6	–2	4	–12
1982	5	–1	1	–5
1983	3	0	0	0
1984	3	1	1	3
1985	1	2	4	2
1986	0	3	9	0
Total	28	0	28	–42

The equation of trend line is y = a + bu

where

u = `("t"-"middle year")/1`

= `("t"-1983)/1`

∴ = t – 1983

∴ The normal equations are

∑y = na + b∑u and ∑y.u = a∑u + b∑u²

28 = 7a +b.0

∴ a = `28/7`

= 4

∑y.u = a∑u + b∑u²

–42 = a(0) + b(28)

∴ b = `-42/28`

= `-3/2` 

= 1.5

∴ The equation of trend line is 

y = a + b.u

y = 4 + (–1.5).u

y = 4 – 1.5u