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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
If $y=a+b(x-2005)$ fits the time series data
$x$ (year): $2003,; 2004,; 2005,; 2006,; 2007$
$y$ (yield in tons): $6,; 13,; 17,; 20,; 24$
Then the value of $a+b$ is:
Solution
Let
$u=x-2005$
Then values of $u$:
$-2,; -1,; 0,; 1,; 2$
Corresponding $y$:
$6,; 13,; 17,; 20,; 24$
Now,
$\sum y=6+13+17+20+24=80$
$\sum u=0$
Since $\sum u=0$
$a=\frac{\sum y}{n}$
$=\frac{80}{5}$
$=16$
Now,
$\sum uy=(-2)(6)+(-1)(13)+0(17)+1(20)+2(24)$
$=-12-13+0+20+48$
$=43$
$\sum u^2=4+1+0+1+4=10$
$b=\frac{\sum uy}{\sum u^2}$
$=\frac{43}{10}$
$=4.3$
Now,
$a+b=16+4.3$
$=20.3$
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