Following table shows the all India infant mortality rates (per '000) for years 1980 to 2010: | Year | 1980 | 1985 | 1990 | 1995 | 2000 | 2005 | 2010 | | --- | --- | --- | --- | --- | --- | --- | --- | | IMR | 10 | 7 | 5 | 4 | 3 | 1 | 0 | Fit the trend line to the above data by the method of least squares.

Following table shows the all India infant mortali – Class 12 Mathematics And Statistics

Question 18 of 25

Following table shows the all India infant mortality rates (per '000) for years 1980 to 2010:

Year	1980	1985	1990	1995	2000	2005	2010
IMR	10	7	5	4	3	1	0
Fit the trend line to the above data by the method of least squares.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2024Subjective· 4mImportance★★★★★

72% · 18/25 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

With $u=\dfrac{\text{year}-1995}{5}$ : $\sum Y=30,\ \sum uY=-44,\ \sum u^2=28$ ; hence $a=\dfrac{30}{7}=4.286$ , $b=\dfrac{-44}{28}=-1.571$ , giving $Y=4.286-1.571u$ .

There are $7$ years (odd count), equally spaced by $5$ . Shift the origin to the middle year 1995 and scale: $u=\dfrac{\text{year}-1995}{5}$ , so $u=-3,-2,-1,0,1,2,3$ .

Year	$Y$	$u$	$uY$	$u^2$
1980	10	-3	-30	9
1985	7	-2	-14	4
1990	5	-1	-5	1
1995	4	0	0	0
2000	3	1	3	1
2005	1	2	2	4
2010	0	3	0	9
Total	30	0	-44	28
…

Start your 14-day free trial to unlock the full solution →

←Previous questionQ6 — Obtain the trend values for the data in using 4-yearly centered moving…→Next questionQ8 — Moving averages are useful in identifying ___. (a) Seasonal component …

🎓Unlock everything free for 14 days

Unlock everything free for 14 days