Answer 1

In the given problem, n = 7 (odd), middle t – value is 1995, h = 5

u = `"t - middle value"/"h" = ("t" - 1995)/(1)` 

We obtain the following table.

Year t	Infant mortality rate  yt	u = `("t" - 1995)/(5)`	u2	uyt	Trend Value
1980	10	–3	9	–30	8.9999
1985	7	–2	4	–14	7.4285
1990	5	–1	1	–5	5.8571
1995	4	0	0	0	4.2857
2000	3	1	1	3	2.7143
2005	1	2	4	2	1.1429
2010	0	3	9	0	–0.4285
Total	30	0	28	–44

From the table, n = 7, `sumy_"t" = 10, sumu = 0, sumu^2 = 28,sumuy_"t" = – 44`

The two normal equations are: `sumy_"t" = "na"' + "b"' sumu  "and" sumuy_"t", = a'sumu + b'sumu^2`

∴ 30 = 7a' + b'(0)               ...(i)   and
– 44 = a'(0) + b'(28)           ...(ii)

From (i), a' = `(30)/(7)` = 4.2857

From (ii), b' = `(-44)/(28)` = 1.5714
∴  The equation of the trend line is y_t = a' + b'u
i.e., y_t = 4.2857 – 1.5714 u, where u = `("t" - 1995)/(5)`.