Getting the function from this data?

Question

hey... i've been doing a survey for school. The data i collected goes this way....

x f(x)
0 0
10 0,2
20 1,2
30 4,2
40 7,7
50 11,8
60 18,8
70 31,6
80 46,6
90 69,8
100 100

the question is:... CAN I GET A FUNCTION FROM THIS DATA... OR WOULD IT BE JUST APPROXIMATE...? IF I CAN, WHICH IS THAT FUNCTION?.... PLEASE, SHOW HOW YOU REALIZED... THANKS


PS: THIS FUNCTION WOULD BE DEFINED FOR ALL x VALUES BETWEEN 0 AND 100... thanks!!

im in high school guys... i dont understand the "L1" "L2" or "L_infinity"....

Answer 1

You are talking about curve fitting.
The simplest solution would be an 10th order poly to cover your 11 data points. Exact match to your data, but not very practical in general.

Your data looks more exponential, so a good approximation would be A*[e^(ax) - 1] where x is your independent variable, and A & a are constants that need to be matched with your data.

L2 error cost leads to A=2.269722043, a=0.038186113
L1 error cost gives A=2.03160386, a=0.039164571
L_infinity cost gives A=2.251572631, a=0.038291751

all fairly similar, and all gives a reasonably good approximate match to your data.

For an exact fit, the 10th order poly is as below:

y = sum(i=0 to 10, a_i * x^i)

a_10= -4.2328E-15
a_9 = 2.00617E-12
a_8 = -4.05952E-10
a_7 = 4.59001E-08
a_6 = -3.18794E-06
a_5 = 0.000140749
a_4 = -0.003938751
a_3 = 0.066949244
a_2 = -0.612839048
a_1 = 2.261484127
a_0 = 0.0

Answer 2

there is definitely a function. yet to derive a function from authentic existence records needs arithmetic and information which you will learn in college, presented you % a math-proper degree. it is truthfully not ordinary to do it with severe college math know-how. it is a correlation undertaking. First you should work out if the dating is a linear one. Plot each and all the records on a graph to work out if a linear dating could properly be drawn. The diagram is noted as a scatter diagram. i attempted plotting your factors given, certainly, it is not a linear dating. to make certain non-linear dating, you should apply Pearson's correlation coefficient. return to the scatter diagram, and seem on the form. It sounds like a stepped downward sloping curve. you should desire to aim employing y and a million/x to get carry of a function some thing appear as if this y = a/x + c. although, i've got not got plenty time to hand to assist you with that. to make certain the dating, enter all your records in Excel. there are various statistical applications in Excel for correlation and regression. attempt locate them and stick to to the records and notice what you could arise with. good luck!

Answer 3

i do not think your function will realize