Aspire Faculty ID #17265 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

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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