Fit a straight line for the following data:

X	1	2	3	4	5	6
Y	49	54	60	73	80	86

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written 9.3 years ago by

teamques10 ★ 70k

X	$x_i=X-3.5$	$y_i$	$x_iy_i$	$x_i^2$
1	-2.5	49	-122.5	1
2	-1.5	54	-81	4
3	-0.5	60	-30	9
4	0.5	73	36.5	16
5	1.5	80	120	25
6	2.5	86	215	36
$\sum x=0$	$ \sum y_i = 402$	$\sum x_iy_i=138$	$ \sum x_i^2=91$

$ \\ \; \\ \; \\ \; \\ \sum_{i=1}^{n} y_i \;=\; Na + b \sum_{i=1}^{n} x_i \; \; \; \; \; \; \therefore 402=6a+0b \; \; \; \therefore a \;=\; \dfrac{402}{6} \;=\; 67 \\ \; \\ \; \\ \sum_{i=1}^{n} x_i y_i \;=\; a \sum_{i=1}^{n} x_i + b \sum_{i=1}^{n} x_i^2 \; \; \; \; \; \; \therefore 138=0a+91b \; \; \; \; \therefore b \;=\; \dfrac{138}{91} \;=\; 1.5165 $

∴The equation of line becomes y = 67+1.5165x = 67+1.5165(X-3.5)

∴ y=67+1.5165X-5.3076

∴ y=61.692+1.5165X

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