really hard quadratic equation, someone please help?

Question

jack1 · Answer

if flow from a fire hose varies with water pressure, and can be estimated by the equation:

$$F = a x^2 + b x + c$$

find the least-squares values for the constants a, b, and c with the below data:

FLOW (F)         94    118    147     180     230
Pressure (x)    10     16      25        40      60

jack1 · Answer

@amorfide do you guys have a sec? @dumbcow

jack1 · Answer

i know what to do with linear ones, but this is really hard

anonymous · Answer

I don't know how to do least-squares

anonymous · Answer

but I know you can plug in the numbers for three of the points and solve it as a system of equations

jack1 · Answer

yeah...?

.sam. · Answer

Yeah what Peter said

jack1 · Answer

ok so just like a matrix then?

agent0smith · Answer

Well not exactly, because you have to do it for all points... the least squares method minimizes the errors. Been a while since I've done it, but it's vaguely familiar. http://www.efunda.com/math/leastsquares/leastsquares.cfm

agent0smith · Answer

This is for a parabola http://www.efunda.com/math/leastsquares/lstsqr2dcurve.cfm

jack1 · Answer

@agent0smith that link is brilliant, exactly what i need, thanks man!

amorfide · Answer

Sorry I can not do this

jack1 · Answer

@amorfide all good, thanks for gettin back to us anyway

agent0smith · Answer

No prob. I'd try to work through it but it's too late, GL on it.

jack1 · Answer

does this seem right to you guys...?

$$F = -0.013406x^2 + 3.58357x + 62.1491$$

agent0smith · Answer

Compare the points to the graph... https://www.google.com/search?q=-0.013406x%5E2%2B3.58357x%2B62.1491&aq=f&oq=-0.013406x%5E2%2B3.58357x%2B62.1491&aqs=chrome.0.57.1312j0&sourceid=chrome&ie=UTF-8 The points from the table above, match up with those points on the graph pretty closely.

agent0smith · Answer

Or just plug the x values from this

FLOW (F)         94    118    147     180     230
Pressure (x)    10     16      25        40      60

Into your equation, and check you get reasonably close to the actual F values.

jack1 · Answer

i never knew google could do that, cheers man!
Yep, going off that, they match really closely, i think I'd be more confidant if I had more that 5 points of data to go off, but it matches what I'm supposed to have

agent0smith · Answer

Yeah google is great for graphs, a bit more interaction than wolfram alpha.

And like you said, you can't be much more confident because you only have a few points; your line of best fit can only be a best fit for the data you're given.