The profit earned (in lakh rupee) by a company making computers is as follows. Find the linear equation for th

Question 40 of 41

The profit earned (in lakh $\text{\text{₹}}$ ) by a company making computers is as follows. Find the linear equation for the trend from these data by least square method and estimate the profit for the year 2017:

Year	2011	2012	2013	2014	2015
Profit (lakh $\text{\text{₹}}$ )	31	35	39	41	44

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2026Subjective· 5mImportance★★★★★

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With $x=$ year $-2013$ : $\Sigma x=0,\Sigma y=190,\Sigma xy=32,\Sigma x^2=10$ ; $a=\bar y=38,\ b=\tfrac{32}{10}=3.2$ ; $\hat y=38+3.2x$ ; for 2017 ( $x=4$ ), $\hat y=50.8$ .

Let $x=\text{year}-2013$ so that $\Sigma x=0$ .

Year	$y$	$x$	$xy$	$x^2$
2011	31	$-2$	$-62$	4
2012	35	$-1$	$-35$	1
2013	39	0	0	0
2014	41	1	41	1
2015	44	2	88	4
Sum	190	0	32	10

Since $\Sigma x=0$ , the least-squares constants are …

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