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Figuring out the equation of a function from a scatter plot

Alright so first of all thanks to anyone who helps me out, ive been stuck on this problem for days and its really irritating. So i have a bunch of points, and im supposed to graph them and then find a function that models it really well algebraically. So basically find an equation that fits the data nicely.

Here are the points:

x: 1932 1936 1948 1952 1956 1960 1964 1968 1972 1976 1980

y: 197 203 198 204 212 216 218 224 223 225 236

And heres the graph:

Attachment 22675

Heres a closeup:

Attachment 22676

So basically, the base function i though that fits it best is f(x)= x^(1/2), and through trial and error the best curve i came up with is f(x)+59*x^(1/2)-2396.5.

So i dont know, i dont get how i can find an equation algebraically, i know that the base formula is f(x)=a(b(x-h)^(1/2))+k, but if i try solving that i came up with a negative square root, or both the variables cancel. So i honestly dont know what to do. Is the base function appropriate? Should i try something else? If not, how do i find the equation by hand?

Thanks so much to anyone whos willing to take the time and help me :D

Re: Figuring out the equation of a function from a scatter plot

Typically, in problems such as this, there is some idea of what kind of function (linear, quadratic, power, logarithmic, exponential, etc.) should fit the data. Do you have any physics behind this problem? Or more context? The data looks to me like a simple linear function would do fairly well. Have you tried a linear function? If so, what is the R squared value?

Re: Figuring out the equation of a function from a scatter plot

Quote:

Originally Posted by

**Ackbeet** Typically, in problems such as this, there is some idea of what kind of function (linear, quadratic, power, logarithmic, exponential, etc.) should fit the data. Do you have any physics behind this problem? Or more context? The data looks to me like a simple linear function would do fairly well. Have you tried a linear function? If so, what is the R squared value?

Thank you so much for replying!

There were no guidelines, we were just told to find the best base function that fits the data, and create an equation algebraically. The problem is about the gold metalist height in high jump in the olympics. All i know from that is y cannot be lower than zero but it can equal or be greater than it. And x theoretically cannot be lower than 1896 since thats when the olympics started but im not sure about that. Yes ive tried a linear function but i consider that to be too simple since this is a grade 12 math course and r^2=0.88 when using a linear regression.

Considering the context, root x seems appropriate, because creating a quadractic or anything with a parabola hard to extrapolate. But with root x, it shows consistency from the start till whenever it ends, correct me if im wrong.

Hopefully that made sense, but a linear function doesnt seem right, i guess a parabola would work if i restricted the domain, but im not sure how to find the equation, whatever it is, by hand :s

Re: Figuring out the equation of a function from a scatter plot

Ah, I see. High jumping. Well, a square root function wouldn't be too bad. But you need to have enough parameters to make it work. Either that, or you can re-zero the x axis by saying that 1932 is t=0. I would just try different functions. Whichever looks the best and has the highest R squared value is what I would go with.

Re: Figuring out the equation of a function from a scatter plot

Quote:

Originally Posted by

**Ackbeet** Ah, I see. High jumping. Well, a square root function wouldn't be too bad. But you need to have enough parameters to make it work. Either that, or you can re-zero the x axis by saying that 1932 is t=0. I would just try different functions. Whichever looks the best and has the highest R squared value is what I would go with.

ahaha yupp, and yea i think i figured it out, all i plan on including is y=a(x^1/2)+b, it seems to work pretty well, i also tried cubic, so y=ax^3+k. Thing is i have to do it by hand so i cant find the rsquare value and it takes a while to try different functions. Any other suggestions?

Re: Figuring out the equation of a function from a scatter plot

Quote:

Originally Posted by

**puregamer** ahaha yupp, and yea i think i figured it out, all i plan on including is y=a(x^1/2)+b, it seems to work pretty well, i also tried cubic, so y=ax^3+k. Thing is i have to do it by hand so i cant find the rsquare value and it takes a while to try different functions. Any other suggestions?

Use Excel.

Re: Figuring out the equation of a function from a scatter plot

im pretty sure i made it clear that i have to do it algebraically