Fit a straight line to the following data: (x,y)=(-1,-5),(1,1),(2,4),(3,7),(4,10). Estimate y when x=7.

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written 7.8 years ago by

X	$y_i$	$X_iy_i$	$X_i^2$
-1	-5	5	1
1	1	1	1
2	4	8	4
3	7	21	9
4	10	40	16
$\sum X=9$	$ \sum y_i = 17$	$\sum X_iy_i=75$	$ \sum X_i^2=31$

$ \\ \; \\ \; \\ \; \\ \sum_{i=1}^{n} y_i \;=\; Na + b \sum_{i=1}^{n} x_i \; \; \; \; \; \; \therefore 17=5a+9b \; \; \; …(i) \\ \; \\ \; \\ \sum_{i=1}^{n} x_i y_i \;=\; a \sum_{i=1}^{n} x_i + b \sum_{i=1}^{n} x_i^2 \; \; \; \; \; \; \therefore 75=9a+31b \; \; \; \; …(ii) $

Solving equations (i) and (ii) simultaneously,

$ \\ \; \\ ∴a=-2 \; \; and \; \; b=3 $

∴ The equation of line becomes y=-2+3X

$\\ \; \\ $

∴ For x=7, y=-2+3*7 = 21-2 = 19

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