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Maths for biz
- Thread starter hello
- Start date
In general it is not possible to take a bunch of data points and pass a known curve through them. You should plot the points and draw a curve by hand and see if it looks like something you have seen. It is obvious that the curve is not a straight line just from looking at the points, but maybe it's a parabola. If this is a textbook problem, a parabola is not unlikely. If the curve is a parabola, you can determine an equation using three of the data points
There are an infinite number of curves that will fit the given points exactly. In the case above, there are for example an infinite number of polynomials of degree higher than 5 that will fit exactly. There is also a unique quintic that will fit exactly. There is, however, no reason whatsoever to believe that a demand curve is a polynomial of degree 5 or greater. Moreover, such a model has zero degrees of freedom, which means that it has zero probability of being correct.Unit Price (P) in $ Quantity Demanded (Q) in units
0 500
5 450
8 372
10 300
12 212
15 50
What is the eqn for the curve from the above data? Do you have any suggestions on any free math software to be downloaded from the net?
There is reason to believe that a demand curve can be modeled by part of a parabola or hyperbola because those curves have features that fit well with the assumptions behind a demand curve. (A cubic with no local extremum also makes sense, but you really do not have enough data points to model that.) Understand (as gitodd has already explained) that it is extremely unlikely that you will get a perfect fit.
If you know how to do linear regressions, I assume you have already tried a linear regression and got a poor r squared. So build the square and square root of y and try regressing them against x separately. If you do not get good r squares from either approach, try regressing the square of y and y against x and also the square root of y and y against x. If none of that looks good. Show us your results and we can dream up some other things to try
By the way, excel has a feature that allows you to do multiple regressions, but it may require an add-on.
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If you have excel with a data analysis add-on, you can find the best fit for a quadratic equation by regressing quantity demanded against unit price and the square of unit price. What you are doing is treating a non-linear function in one variable as a linear function in multiple variables. The multiple regression process will give an approximation that minimizes errors.the equation is a quadratic equation which I need to form it myself. but i have no idea how to come up with the equation? Please help me with it. Thanks.
If you do not have software to do multiple regressions, you can do a trial and error method to get an approximation that is not as good but may be good enough for pratical use.
Take any three data points, \(\displaystyle (c_1, q_1), (c_2, q_2), and (c_3, q_3)\).
Solve the following system for x, y, and z
\(\displaystyle q_1 = x + y * c_1 + z * (c_1)^2.\)
\(\displaystyle q_2 = x + y * c_2 + z * (c_2)^2.\)
\(\displaystyle q_3 = x + y * c_3 + z * (c_3)^2.\)
This gives you an approximation in quadratic form, namely: \(\displaystyle q = x + yc + zc^2.\)
Now test the approximation against the remaining data points. If the approximation is not good when tested, try the process over with different data points. Stop when you have an approximation that is good enough.