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Fit a straight line for the following data:
X 1 2 3 4 5 6
Y 49 54 60 73 80 86
straight line • 4.0k  views
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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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