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Fit a straight line for the following data:
written 7.8 years ago by | • modified 4.0 years ago |
X | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
Y | 49 | 54 | 60 | 73 | 80 | 86 |
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written 7.8 years ago by | • modified 4.0 years ago |
X | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
Y | 49 | 54 | 60 | 73 | 80 | 86 |
written 7.8 years ago by |
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