Curve Fitting

**Apprentice123** · September 14th 2010, 04:00 PM

Determine the equation of a straight that best fit the points:

Code:

X|  0  |   2 |   4 |  6  |  8  |  10  |
Y|1.12 |5.06 |9.09 |13.12 |17.14 |21.11 |

**mr fantastic** · September 14th 2010, 04:12 PM

Originally Posted by Apprentice123

Determine the equation of a straight that best fit the points:

Code:

X|  0  |   2 |   4 |  6  |  8  |  10  |
Y|1.12 |5.06 |9.09 |13.12 |17.14 |21.11 |

What method are you expected to use? Linear regression by hand? Technology? etc. Please be more specific about what method you're expected to use.

**Apprentice123** · September 14th 2010, 04:39 PM

Originally Posted by mr fantastic

What method are you expected to use? Linear regression by hand? Technology? etc. Please be more specific about what method you're expected to use.

Least Squares method
I do not understand is how to find the equation of the line. What would be the polynomial

**mr fantastic** · September 14th 2010, 07:32 PM

Originally Posted by Apprentice123

Least Squares method
I do not understand is how to find the equation of the line. What would be the polynomial

Please answer the question I asked in my first reply: Are you expected to do it using technology (eg. calculator that has a linear regression program) or by hand?

**Apprentice123** · September 14th 2010, 07:45 PM

Originally Posted by mr fantastic

Please answer the question I asked in my first reply: Are you expected to do it using technology (eg. calculator that has a linear regression program) or by hand?

Ohh, sorry. Is by hand

**HallsofIvy** · September 15th 2010, 03:23 AM

Then what formulas do you know? I doubt that you are expected to derive the "least squares" solution by from scratch.

**Apprentice123** · September 15th 2010, 05:37 AM

Originally Posted by HallsofIvy

Then what formulas do you know? I doubt that you are expected to derive the "least squares" solution by from scratch.

I know the method of least squares, where I have several meeting points and a polinimio.
What polynomial I need to find in this case?

**HallsofIvy** · September 15th 2010, 07:50 AM

There are several different formulas to compute "least squares". What formula are you using?

**Apprentice123** · September 15th 2010, 02:09 PM

Originally Posted by HallsofIvy

There are several different formulas to compute "least squares". What formula are you using?

Is this:

$\sum_{k=1}^{m} (d_k)^2 = \sum_{k=1}^{m} [f(x_k) - \phi (x_k)]^2$

$\phi (x) = \alpha_1 g_1(x) + ... + \alpha_n g_n(x)$

$F(\alpha_1 , \alpha_2 , ..., \alpha_n ) = \sum_{k=1}^{m} (d_k)^2 = \sum_{k=1}^{m} [f(x_k) - \phi (x_k)]^2$

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