IA Type II -- Gold Medal Heights

[gamergirl]

I think the graph is of polynomial degree 8 and as we cannot directly plot a degree 8 polynomial graph on excel or anywhere... so matrix are the only solution.

Please give me your suggestions.

[shannonb1896]

Does the task want you to use your algebraically derived function or your technologically derived function (or either or) to test future years? Also, at the end when it asks what modifications can be made, If I used regression again with the additional information, but that will change my entire function. Is that considered a modification and therefore allowed?

[M.C.RAM]

I made a split function out of these points very well on my calculator but i dont know how to write it out can someone help me!!!!!!!!!!

Also does this count as my use of technology if I use the calculator.

And a friend of mine mentioned rmse (root mean square error)?

[mwaddmeplz]

Does the task want you to use your algebraically derived function or your technologically derived function (or either or) to test future years? Also, at the end when it asks what modifications can be made, If I used regression again with the additional information, but that will change my entire function. Is that considered a modification and therefore allowed?

I used both of them and compared the results

[mwaddmeplz]

Thanks for the reply, however i have two new questions:

1. How do i come along choosing the points. My teacher mentioned through mean or median or quartile but the problem is i don't know how. How can i chosen two points so that i can have line of best fit.

2. My teacher mentioned about having two functions together. So lets say i have a quadratic function with a linear function or log function which gives me an asymptote so how can i have these kind of functions where there are two functions within a function for best fit curve.

It would be in the 1st quartile as all of the points given to you are positive but you may extend it to extrapolate.

I have one 11th function now that is working for me but I would just submit the function that most accurately reflects the data.

[M.C.RAM]

how do you find the constant when using the matrices method?

HELP ME PLEASE!!!!!!!!!!!!!!!!

[Callum Rudig]

Is this part of the math portfolio for those graduating Nov 2013?

[garimaib]

can someone please help me? this project is due tomorrow for me and im having lots of problems.

first of all, in the graphs; how do i use the years? 1932,1936,1948 or 4,8,12? it seems like if i use 1932 for x-axis and 197 for y-axis, the linear equation is very hard to fit since 197 is too far away from 0 on y-axis and 1932 is too far away on x-axis so the y-intercept doesn't really make a difference. also, what type of functions fits the best? i know its not sine and cos, do you think its logarithmic or logistic? we have never done logarithmic or logistic graphs in class so i have no clue how to do them. PLEASE HELP SOMEONE!!

[garimaib]

Is this part of the math portfolio for those graduating Nov 2013?

yes it is

[parth861]

Hey i decided to go with a cubic equation but i do not know how to get a cubic equation analytically..... i know that it can be done by using matrices but i dont know how to do .... can some show me with an example???

[xdeeee]

Hey i decided to go with a cubic equation but i do not know how to get a cubic equation analytically..... i know that it can be done by using matrices but i dont know how to do .... can some show me with an example???

I think Desy Glau did an example but with quartic, not sure if it's much help to you though.

on the other hand, currently working on this right now and shout out to Desy Glau .. literally helped me so much with my first IA and now my second

[lacloud]

I'm currently working on this task but due to time limits it's coming out a bit iffy... I have two main problems:

1)The last sentence of the task "What modifications, if any, need to be made to your model to fit the new data?" - implies that your model would function well (or okay) with the new data? The thing is, I was planning on completely scrapping the model I have the in the beginning (which fits the values of that part of the task though) and go for a different one for all the values. Do you think this could be an okay way to go about it, or will the examiner punish me for changing it too much?

2) Is it possible to analytically create a logarithmic function with the values given in this task? If so, how do one go about doing this? (Not asking for specific answer for just this task, but a general way to create one)

if your model is already awesome, you don't need to make any modification. if it's just okay, you may want to make some changes. if it's VERY horrible, restart modelling the whole thing.

yes you can. start with the general formula:

y=a*ln(x)+b

then, pick two points you want to use.

then, substitute the values of x and y, then solve for a and b simultaneously.

however, I'm not sure how well a logarithmic function could fit. it depends on which points you're choosing!

How would I find both a and b if there are two variables? I'm just unclear as to how to solve them simultaneously

[Fermat]

Well you know that y=a+bln(x) and now you can pick any two points, say you pick (p,q) and (r,t)

Now you just substitute the values for x and y like following:

t=a+bln®

q=a+bln(p)

Now you can use your preferred choice of solving the simultaneous equation (for example matrices (rref, Cramer's rule, Gaussian elimination etc) or you can use simple elimination of variables)

[713u]

Hey guys!

What do they mean with the third question/statement? "On a new set of axes, draw your model function and the original graph. Comment on any differences. Discuss the limitations of your model. Refine your model if necessary."

• The original graph is of data points only? How in the world can I comment any differences when there isnt even a function I can compare mine with (found algebraically)!
  

• And what are the limitations of a linear function?
  

• How do I refine my model? Just change the values??
  

Thanks for helping me!!!!

[ibhelpme_]

Just recently started this project and I'm still very confused as to how to find a type of function that models the graph? thanks

[Rahul]

You can use a regression. Put the values into your stat-plot lists on your TI calculator and calculate a regression. In terms of manual work, set up a system of equations. Choose a degree of polynomial. And then do as follows with your table.

Sample table: (calculating cubic regression)

x-f(x)

(-1)-1

0-5

1-11

2-37

Then, set up your cubic equation.

f(x)=ax³+bx²+cx+d

Substitute in your values from your table and solve the system to get the coefficients.

Eg:

f(x)=ax³+bx²+cx+d

f(0)=a(0)³+b(0)²+c(0)+d

5=d

f(-1)=a(-1)³+b(-1)²+c(-1)+5

1=-a+b-c+5

a=b-c+4

f(1)=a(1)³+b(1)²+c(1)+5

11=a+b+c+5

a=6-b-c

Equate:

6-b-c=b-c+4

2=2b

1=b

a=6-1-c

a=5-c

f(2)=a(2)³+(2)²+c(2)+5

37=8a+4+2c+5

28=8a+2c

14=4a+c

14-4a=c

c=5-a

Equate:

14-4a=5-a

3a=9

a=3

c=5-a

c=2

Thus, the function is:

f(x)=3x³+x²+2x+5

I would recommend choosing a degree n of polynomial function if your graph looks polynomial and spreading your n+1 required data points across the entire test interval- you need n+1 points due to the property that there is exactly one polynomial of degree u that passes through any given u+1 points.

Good luck!

Edited February 24, 2013 by RahulArora

[supitselwin]

Hey guys, I'm kind of confused as to how to go about this. Say I want to use a linear best fit line. I've been reading online and this has been linked to the term regression? What exactly is regression? Working backwards using technology am I correct? So using medians to find a best fit line would then be an acceptable analytical approach and not regression?

The notes my portfolio came with stated that we should initially use an analytical approach and use regression to support the findings.

Any insight as to what methods are acceptable for an analytical approach would be appreciated.

[Rahul]

Not necessarily working backwards using technology - as you can see from my post above it can be done by hand, although this is tedious and difficult for non-polynomial regressions. A line of best fit may not work because the gradient may be variant and not constant - in other words, dy/dx may have a degree over one. Analytically, you could analyze the polynomial and its turning and inflection points to determine degree and work out a basic equation from sight; however, I'm not certain that that is the type of approach desired.

[supitselwin]

Thanks Rahul, so what do you suggest is the desirable approach for this situation?

[ibhelpme_]

I'm sorry for sounding so stupid, but I really do not understand this at all. I do not understand how to find what function models the graph, or why. I also am having trouble understanding how I would draw this on a new set of axes.