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Math Help - Another Mathmatical Problem..

  1. #1
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    Another Mathmatical Problem..

    Problem:

    The following experimental data values of x and y are believed to be related by the law y = mx^2 + c, where m and c are constants. By plotting a suitable graph, verify that this law does indeed relate the values and find approximate values of m and c.

    x 2.3 4.1 6.0 8.4 9.9 11.3

    y 13.9 31.2 60.2 111.8 153.0 197.5
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  2. #2
    Eater of Worlds
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    I used Excel to plot this graph using your data and a quadric regression. I hope I didn't get it too small. Note the coorelation coefficient R^2. It's 1. That means it's as good as it gets as far as regressions go.

    Incase you can't make it out, the equation is 1.4938x^{2}+0.0809x+5.8118
    Last edited by galactus; November 24th 2008 at 05:39 AM.
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  3. #3
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    Could you breifly explain how you solved this problem? I'm a little confused.

    Once i understand this problem, i shall try some similar ones.

    Thanks for your help so far.
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  4. #4
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    Do not beg for answers! You can wait for a response!
    -=USER WARNED=-
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  5. #5
    Eater of Worlds
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    All I done was to use Excel. It did all the work. If you want to perform a quadric regression by hand....good luck. That's what technology is for. Do you have a TI-83?. I believe it'll do regression: linear, quadric, cubic, quartic, sine, logistic, exponential, etc....
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  6. #6
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    Quote Originally Posted by c00ky
    Problem:

    The following experimental data values of x and y are believed to be related by the law y = mx^2 + c, where m and c are constants. By plotting a suitable graph, verify that this law does indeed relate the values and find approximate values of m and c.

    x 2.3 4.1 6.0 8.4 9.9 11.3

    y 13.9 31.2 60.2 111.8 153.0 197.5
    Plot a graph of y against x^2 (x^2 the independent variable and y the
    dependent), it should be a straight line, its slope will be m, and the intercept
    on the x^2=0 axis will be c.

    RonL
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  7. #7
    Eater of Worlds
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    Yes, I am sorry, but I was wrong. A linear regression is more suited, as Cap,N said. I saw the x^2 and got carried away.

    If you want to perform a linear regression 'by hand' you can use the following formulae:

    y=mx+b, n=number of data points.

    m=slope=\frac{n\sum{xy}-(\sum{x})(\sum{y})}{n\sum{x^{2}}-(\sum{x})^{2}}

    b=y-intercept= \frac{\sum{y}}{n}-m\frac{\sum{x}}{n}

    Personally, I would use my calculator to do it, unless, you're forbidden.

    Just thought you'd be interested.
    Last edited by galactus; August 7th 2006 at 02:55 PM.
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by c00ky
    Problem:

    The following experimental data values of x and y are believed to be related by the law y = mx^2 + c, where m and c are constants. By plotting a suitable graph, verify that this law does indeed relate the values and find approximate values of m and c.

    x 2.3 4.1 6.0 8.4 9.9 11.3

    y 13.9 31.2 60.2 111.8 153.0 197.5
    Actually, it's fairly easy to figure out the equations for the coefficients of a least squares (polynomial) regression curve. (The problem for me is the formulae for the error estimates. I don't know how to do those.) If you like I can show you the general method. I should warn you that it involves a little Calculus (not much though). I won't post it unless you ask, since coding it will take a bit of time, but I would be happy to do so.

    -Dan
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  9. #9
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    Quote Originally Posted by topsquark
    I should warn you that it involves a little Calculus (not much though).
    It actually involves quite a lot of calculus,...mutli-variable funtions,....partial diffrenciation,....hessian matrix.
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  10. #10
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    Thanks Guys, I followed captain blacks steps and i think i've cracked it!
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