IA Type II - Fish Production

[Noxen]

Hey all,

I got the new SL Type II IA for 2012 and 2013 and I found that I need to graph a Sine Regression function against a set of data to test it. For my past IA's I have found some way to use excel to graph by data and regression fits... however I am having some serious trouble figuring out how to plot a sine regression against my data. I ask this because I have already done all the math on my TI-84 Plus. I am trying to figure out how to plot the same graph the TI does when you go to STAT -> CALC -> SinReg L1,L2,Y1. Does anyone have any ideas on how to do this in excel or some other graphing package?

Thanks,

-Noxen

Also, I would prefer and excel solution if anyone knows a way

[El Che]

Does your teacher require you to use Excel for Sine Regression? In my opinion, it is easier to use TI-84 and put the screens on your portfolio. There is a program which enables you to do that. If you want it, I can you send the link of it.

[Noxen]

My teacher tells us to try to avoid using TI screenshots because they lack some quality and he says that they make the paper seem somewhat unprofessional. I have used excel in the past for pretty much all my graphing needs. Is there absolutely no way of graphing a sine function in excel... that's kind of hard to believe.

Thanks though, I may end up having to use TI screenshots :/.

[dessskris]

to my knowledge, Excel cannot generate sine graphs.

if only you had TI-Nspire, I am sure your life would have been much easier. the interface is really nice. it is of a high quality and the graphs look totally professional.

actually I don't recommend using excel, but it's up to you. I don't know any graphing software that can generate a sinusoidal function either. TI-Nspire is the best to use IMO.

PS. do you have a soft copy of the task paper?

[Noxen]

Hey everyone,

I ended up figuring out how do do it. You have to create a table with a whole bunch of x and y values. Basically, make a column with all of your x values. Then next to it you create y values by typing in the equation in the formula box. For example, the equation you would type for a quadratic regression is this " =((0-0.1950435771)*(A79^2))+((777.1864334)*(A79))+(0-773674.6726) ". A79 is the cell of the x-value you are putting into the equation. You only have to do this for one cell, then you can just drag the cell down and it will apply the equation to whatever cells you drag it through. Then you select all the points and create a smooth scatter plot, copy the actual graph part of the plot and paste it into a graph with all of your original data points you are applying the regression to. It seems kind of complex but it is not that hard to figure out.

Now, I do have another problem that is pretty perplexing. I have ended up graphing models and everything, however I am now trying to find out how to create my own model to fit the data. If I try to use the sine regression function asin(bx+c)+d, I plug in 4 x-values and then create a matrix to try to figure out what a, b, c, and d are in my model. The only problem is, when I try to take the inverse of the matrix of the x values, it won't work because it is apparently a singular matrix. I used "1" as the x value for a, c, and d. My matrix is something like this:

[1, 1985, 1, 1

1, 1990, 1, 1

1, 1995, 1, 1

1, 2000, 1, 1]

I need to find the inverse of this matrix and multiply it by my matrix of y-values to get a,b,c, and d. Does anyone have any ideas about how to solve this. Or another way of finding out a, b, c, and d?

Thanks,

-Noxen

[dessskris]

hey Noxen,

can you get me a soft copy of this task paper? I can try to help you.

if you can get the original PDF that would be great or you can just scan the task paper and attach it here.

I can try to help you!

---

Just went through your problem and I apparently don't need to know the task to be able to help you but anyway I still want the task paper! If you have it please do attach it here. Thanks!

You don't do matrices to solve sinusoidal equations. Substitute in values of x and y to the general equations and solve for the constants manually...algebraically.

Btw the general sinusoidal function seems to be:

y = a sin(bx + c)

Let me check though and I'll confirm this tomorrow.

Never mind, your equation is right

y = a sin(bx + c) + d

Edited April 30, 2011 by dessskris

[Noxen]

I ended up figuring out how to do it. Turns out it is not as hard as I thought it to be. Making a model can be as easy as modifying some of the parameters of a regression function . Also, I am going to post the task paper below for anyone who is interested.

Thanks for all your help,

-Noxen

SL Math IA Type II.tiff

[El Che]

When we plot the data on a graph, it is kind of fluctuating. So, what can I suggest as a suitable model? It can't be a quadratic equation, and it looks more like a sine function to me, if I'm not mistaken.

[dessskris]

Geez! It's really weird! This task is a hard one I'd say. When I plotted the data, gosh, I wanted to faint. This is so random! And the task suggests us to use a combination of functions. What I don't understand is, do they mean a combination of functions as in

y = f1(x) + f2(x) + f3(x) + etc

OR

y = f1(x) when a≤x≤b. y = f2(x) when c≤x≤d. y = f3(x) when e≤x≤f

?

If it's the first one, it's really hard! I'd say I might not be able to do it... But if it's the second one, I think it can be done with a lot of effort.

Anyways... So yeah. I'd split the graph according to how the task splits the data (first table, second table, third table).

Data from the first table:

Looks like tangent graph. I suggest modelling a tangent function whose general formula is y=a*tan(bx+c).

Data from second table:

Quite random, but it still looks like a sine function with general formula y=a*sin(bx+c) where a is negative.

Data from third table:

I honestly don't know! It's very random. The easiest would be cos though. But I'm not sure.

I'm playing around with the data. If I get something interesting I'll let you know!

[dessskris]

I ended up figuring out how do do it. You have to create a table with a whole bunch of x and y values. Basically, make a column with all of your x values. Then next to it you create y values by typing in the equation in the formula box. For example, the equation you would type for a quadratic regression is this " =((0-0.1950435771)*(A79^2))+((777.1864334)*(A79))+(0-773674.6726) ". A79 is the cell of the x-value you are putting into the equation. You only have to do this for one cell, then you can just drag the cell down and it will apply the equation to whatever cells you drag it through. Then you select all the points and create a smooth scatter plot, copy the actual graph part of the plot and paste it into a graph with all of your original data points you are applying the regression to.

is x the year here? and why do you 'create' your y values? you are supposed to model the data given in the table aren't you? and where do you get the quadratic equation from? isn't that kind of random? I don't understand...

[El Che]

I also split the graph according to how the task splits it. First graph looks like a quadratic to me although I am not so sure. Maybe it is tangent, but is there a way to check it via GDC? Because I don't think my calculator has such regression option. For the second table, I think sine function works, however interestingly I have a positive value for a. For the last table, I honestly don't have an idea. When I get the constants by using regression, it doesn't work for all of the data.

[dessskris]

I seem to be not really helpful here...

I don't think it looks much like a quadratic :/ it's not parabolic it just looks like a 'broken' tangent curve

what GDC do you have? I use TI-Nspire and it can find the best fit curves but I'm not sure how to do it in other TI calculators. sorry

hmmm what did you do to find the sine function? did you do it analytically or using technology? you can just roughly estimate the amplitude and modify the x right, actually? but okay, if that's what you got.

yeah the last table is very random...

you know in lower levels (e.g. IGCSE, this is what we did), there used to be some questions which give the random data of x and y but then we are asked to 'modify' it to get a straight line. the new x-axis and y-axis can become like xy, ln(y), 1/y, x/y etc... I thought of doing something like that but I didn't get anything for the last data from the last table

[El Che]

In fact, it does look like a "broken" tangent curve. I have TI-84 Plus. I found the sine function by using technology. After that I substituted these constants to check whether they apply to the amplitude (and etc) or not. As a result, they pretty much did but that's all.

It's fine it is just for practice, not a real one and thanks for your effort to help me though! =)

[LittleJ.]

I have a question to this task. I dont really understand what do they mean by: analytically develop a model that fits the data points. Can some one help me,please?

[dessskris]

you have to create/model a function that fits the data points best, but you have to do it analytically/algebraically/using algebra/mathematically. meaning you cannot simply plot the data in a graphing software or in your GDC and find the best regression, this is for the second part.

tips: start with the general formula of the type of function that you want to model and then substitute in some data points coordinates and solve for the constants.

[LittleJ.]

Ohh ok!Thank youu Now my only problem is the fish farm plot... its weird, I mean it is slowly increasing then it is decreasing and increasing again... & I dont know if i should count it as sine function or not... (

[dessskris]

no... I'd go with a polynomial.

[LittleJ.]

no... I'd go with a polynomial.

Ohh... yeah... i guess i forgot about that one... thanks Edited June 4, 2011 by Austin Glau
no text speak

[3bbasi12]

I dont get how this works. Can we define a function for each table? Or do we have to combine all the functions together? And if so, how do we do that?

[Mija]

Oh gosh, this is SO complicated...

Do you know what to do with the data from the third table? I seriously cannot find any trend in there, it is so random. I think the first one is either tangent or cubic. For the second one I'd go with a sine but the third...

(EDIT) I used a program called Graph (http://www.padowan.dk/graph/) and it has an option of giving you the predicted forumla for the fuction. It didn't find anything suitable for the third one though. Please, do you have any clue what it could be?

Edited June 12, 2011 by Mija