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Fit a curve $y=ax+bx_2$ for the data:
written 7.8 years ago by | • modified 4.0 years ago |
x | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
y | 2.51 | 5.82 | 9.93 | 14.84 | 20.55 | 27.06 |
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written 7.8 years ago by | • modified 4.0 years ago |
x | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|
y | 2.51 | 5.82 | 9.93 | 14.84 | 20.55 | 27.06 |
written 7.8 years ago by | • modified 7.8 years ago |
x | $x^2$ | $x^3$ | $x^4$ | y | $xy$ | $x^2y$ |
---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 2.51 | 2.51 | 2.51 |
2 | 4 | 8 | 16 | 5.82 | 11.64 | 23.28 |
3 | 9 | 27 | 81 | 9.93 | 29.79 | 89.37 |
4 | 16 | 64 | 256 | 14.84 | 59.36 | 237.44 |
5 | 25 | 125 | 625 | 20.55 | 102.75 | 513.75 |
6 | 36 | 216 | 1296 | 27.06 | 62.36 | 974.16 |
$\sum x=21$ | $ \sum x^2=91$ | $\sum x^3=441$ | $\sum x^4=2275$ | $ \sum y=80.71$ | $\sum xy=368.41$ | $\sum x^2y=1840.51$ |
$ \\ \; \\ \; \\ \sum y \;=\; a\sum x + b \sum x^2 + c \sum x^2 + cN \; \; \; \therefore 80.71=21a+91b+6c \; \; \; \; \ldots (i) \\ \; \\ \; \\ \sum xy \;=\; a \sum x^2 + b \sum x^3 + c \sum x \; \; \; \therefore 91a+441b+21c \; \; \; \; \ldots (ii) \\ \; \\ \; \\ \sum x^2y \;=\; a \sum x^3 + b \sum x^4 + c \sum x^2 \; \; \; \therefore 1840.51 = 441a+2275b+91c \; \; \; \; \ldots (iii) $
Solving equations (i), (ii), (iii) simultaneously, we get
a=2.11 , b=0.4 , c=0
$ \therefore y=2.11x+0.4x^2 $ This is an equation of parabola.
Note: This is another method where we didn’t convert into X=x-3.5 (in this case). We can solve by previous method also.