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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.
straight line • 1.4k  views
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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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