Thread: 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

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

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.

Do not beg for answers! You can wait for a response!
-=USER WARNED=-

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....

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

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.



b=y-intercept=

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

Just thought you'd be interested.

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

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.

Thanks Guys, I followed captain blacks steps and i think i've cracked it!