IA Type II -- G-Force Tolerance

[Lev]

I seem to be getting an inverse power function, since a regular power function results in a quadratic, cubic, etc. The inverse works well with my data points, so is it correct?

Equation is y=a[1/(x^b)]

[dessskris]

I seem to be getting an inverse power function, since a regular power function results in a quadratic, cubic, etc. The inverse works well with my data points, so is it correct?

Equation is y=a[1/(x^b)]

Umm if it fits then why not?

Btw equation is y=a/(x^b) or y=ax^-b easier to see than that..

[rabyl123]

daisy, when i try to find the exponential regression on my GDC it gives me a and b but when i plot it dosent cross any points?

[vira.may]

I want to graph with excel, but I just can't do it! It is making me crazy right now. Does anyone know how to graph it? Please help!!!!!

Which graph? The very first bit, yeah?

I suggest using your GDC.. If you have TI, use it.

But if you still want to use excel, you can tabulate it first and then create a scatter graph. However you'll need to use a graphing software to find a logistic regression (the researcher's model) later. Excel can't do this. TI GDC can do this

Let me know if you don't know how to plot a graph in excel or TI and I'll write you an instruction/guide

If I'm using the GDC, do I use the "screen capture" to get screenshots for my math portfolio? Or is there another way?

The screen captures aren't particularly clear, and they don't look very nice either... Is it supposed to be this way?!

[dessskris]

daisy, when i try to find the exponential regression on my GDC it gives me a and b but when i plot it dosent cross any points?

I didn't recommend exponential, did I? I plot the data using TI-Nspire but it cannot give the exponential regression. It says: "Two or more arguments must have matching dimensions. For example [1, 2]+[1, 2, 3] is a dimension mismatch." try another function type then

If it doesn't pass through any point but it fits the data series in overall, just continue

---

If I'm using the GDC, do I use the "screen capture" to get screenshots for my math portfolio? Or is there another way?

The screen captures aren't particularly clear, and they don't look very nice either... Is it supposed to be this way?!

What GDC software do you use? I use TI-Nspire Student Software. It has this camera icon (Takes a Screen Capture of the active view) which I usually use to take screenshots, and the captures are always clear. Or you can go to Tools>Take Screen Capture, or just press Ctrl+J if you use Windows. That capture can be copied to your word document.

Another way is to press PrtSc SysRq on your keyboard (idk if it's the same for Mac though I use Windows) and paste it in your word document.

Or if you have Windows Vista or Windows 7, go to Start Menu, just type Snipping Tool and snip a capture of the graph

[2Busy4Name]

okay thanks that helps! But i just noticed (correct me if i'm wrong) x represents the time of tolerance and y the G force. So anyways for the limitations I am changing the x and y since they represent t and G! I also just added how i did not have to do a test if the function works with a negative t since time can not be negative ect...

Last question! ( sorry but i really want this over) Does a negative G force exist? Since G force is about acceleration, and a negative acceleration is deceleration so wouldnt that have its own force? This question sounds more clear in my head but I hope you can understand!

Actually many people argued that time can be y and G-force can be x. However I would go with time on the x-axis and G-force on the y-axis so yeah you are right

Good good!

Umm the tables actually say +Gx and +Gz right? Then +Gx and +Gz cannot be negative. I actually don't really get what this G-force thing is in real life so I cannot make a rational guess but how did you define G? I think -Gx and -Gz might exist. And yes it would be a deceleration.

So +Gx and +Gz cannot be negative

But Gx and Gz might be negative -- or -Gx and -Gz might exist

Sorry I really can't help much in this task because I myself haven't done any type 2 IA and this task is tricky. Good luck with it anyways! If you still want to ask just post your question and I'll look at it.

In my opinion, time should be dependent since the time is referring to the duration of human tolerence to the G-forces. And with limited physics knowledge, I think that G-force is basically a force that acts on your body with relation to gravity. One possible explaination i can think of is unequal acceleration of your internal organs, since our bodies aren't rigid, it is quite possible that there is a lot of "flinging" going on in our organs, which is a possible reason why G-forces are bad for us.

And in the case of the portfolio, I would think that +Gx and +Gz should not go into negatives, cuz if you think about it, the "smaller" it goes into the negatives, our models show that the duration only increases, however, that is not the case as it is previously stated by the "eyeballs-out" scenario.

also, I would use exponential if time is dependant since the dependant value cannot go below 0, which in this case works with time. However, I'm currently not sure what to do as +Gx approaches 0, since that in theory should have time approach 0. So would the proper model be the reciprocal model? Or even a reciprocal model within an absolute value one?

f(x) = |(1/x)| ?

[reaching4thestars]

How do you define the parameters and constraints for the data BEFORE plotting the data points and finding the equation by hand????

[Soozy]

I used G-force as my independent variable and time as my dependent variable. Then I tried some regressions on the GDC and looked at the diagnostic (r^2). The closest one was a power function which had an r^2 of 0.997 and an exponential function which had an r^2 of 0.934. I also tried a log function as some of you guys suggested and the r^2 was 0.587. Something weird I discovered was that the cubic function had an even more accurate regression than the log function of an r^2 of 0.85. So right now the two functions that I am considering are power and exponential.

Am I on the right track?

I am still confused about how we can define our parameters before we actually find the model function. Can anybody help?

Edited February 25, 2011 by Soozy

[dessskris]

So would the proper model be the reciprocal model? Or even a reciprocal model within an absolute value one?

f(x) = |(1/x)| ?

Well, I think reciprocal is a good one, it might fit well. I don't think you need to think so much about that because you need to define x (whatever you put in the x-axis). maybe you'll say x>0. then why bother about the value of y when x<0? just pick either with smart considerations

---

How do you define the parameters and constraints for the data BEFORE plotting the data points and finding the equation by hand????

I think that simply means something like:

Let t be time in minutes

Let +Gx be positive acceleration in the horizonal direction in g

t>0 min

+Gx>0 g

and whatnot...

So you can do it before plotting but if there is any other limitation that you find after plotting, just state it later when you give the model function.

---

I used G-force as my independent variable and time as my dependent variable. Then I tried some regressions on the GDC and looked at the diagnostic (r^2). The closest one was a power function which had an r^2 of 0.997 and an exponential function which had an r^2 of 0.934. I also tried a log function as some of you guys suggested and the r^2 was 0.587. Something weird I discovered was that the cubic function had an even more accurate regression than the log function of an r^2 of 0.85. So right now the two functions that I am considering are power and exponential.

Am I on the right track?

I am still confused about how we can define our parameters before we actually find the model function. Can anybody help?

I recommend power and logistic. Logistic is hard to model analytically, though, so go for power.

I tried finding a cubic regression using technology but it doesn't fit. So if yours fits, just go for it then because of the greater R-squared value. But if it's just the R-squared value but the curve does not fit, don't use cubic.

and for the last part I guess I answered that with my answer to reaching4thestars' question

[Soozy]

Logistic doesn't work using technology. Are reciprocal functions and power functions the same thing?

Another question...when the task says "Use technology to find ANOTHER function that models the data.", can it be another power function with slightly different a and b values that you calculated by hand in the first part? Or does the function have to be a completely different type? Thanks

Edited February 26, 2011 by Soozy

[dessskris]

Logistic doesn't work using technology. Are reciprocal functions and power functions the same thing?

Another question...when the task says "Use technology to find ANOTHER function that models the data.", can it be another power function with slightly different a and b values that you calculated by hand in the first part? Or does the function have to be a completely different type? Thanks

it does work! look at this picture below:

it's a logistic regression generated using technology

Reciprocal is a form of power function.

Reciprocal function is a power function but power function is not a reciprocal function..

Power: y=ax^b

Reciprocal: y=a/x which is y=ax^-1 so in a reciprocal function, the b is -1

well it's a bit vague as the task does not clearly mention the type of function

looking at the question I think you can model the same type of function. but I personally recommend modelling a different type of function, to demonstrate your broad knowledge in types of function

[reaching4thestars]

hey desy

how did you solve the function by hand for a power function??

I get the part where you use the general formula where y= a(x^b) and thn you would substitute in points to find your a and b values

but then when you substitute in different points, you would get different values, so how do you conclude which a and b value to use for your model???

I think that simply means something like:

Let t be time in minutes

Let +Gx be positive acceleration in the horizonal direction in g

t>0 min

+Gx>0 g

and whatnot...

So you can do it before plotting but if there is any other limitation that you find after plotting, just state it later when you give the model function.

I'm still confused about the parameters and how to define them

I was told that the parameters are the transformation of your base functions

Doesn't that mean that your parameters would be specific values??

and so you can't define those values before actually finding the model??

Edited February 26, 2011 by Desy ♫

[dessskris]

hey desy

how did you solve the function by hand for a power function??

I get the part where you use the general formula where y= a(x^b) and thn you would substitute in points to find your a and b values

but then when you substitute in different points, you would get different values, so how do you conclude which a and b value to use for your model???

I'm still confused about the parameters and how to define them

I was told that the parameters are the transformation of your base functions

Doesn't that mean that your parameters would be specific values??

and so you can't define those values before actually finding the model??

What do you mean by 'by hand'?

I don't know if there is actually a method to determine which point to use, but if I were you I would just plot the data in my GDC and show power regression and see which 2 points the curve fits best then choose those 2 points.

Btw you substitute in x and y in order to solve for a and b. Not the other way round

If still unclear just ask again!

Ok well it says 'Define appropriate variables and parameters.'

TBH I am not so sure about parameters either, sorry, but I would say if there is no parameter yet in the beginning (and I think there isn't) just leave that.. Discuss your variables and constraints first.

Then after you start modelling and stuffs, you define the relevant parameters as you find each one along the portfolio that is what I would do.

[reaching4thestars]

What do you mean by 'by hand'?

I don't know if there is actually a method to determine which point to use, but if I were you I would just plot the data in my GDC and show power regression and see which 2 points the curve fits best then choose those 2 points.

Btw you substitute in x and y in order to solve for a and b. Not the other way round

If still unclear just ask again!

Ok well it says 'Define appropriate variables and parameters.'

TBH I am not so sure about parameters either, sorry, but I would say if there is no parameter yet in the beginning (and I think there isn't) just leave that.. Discuss your variables and constraints first.

Then after you start modelling and stuffs, you define the relevant parameters as you find each one along the portfolio that is what I would do.

By hand I mean without technology because that is what the first part of the question is asking you to do, finding the model of the function without technology

haha yea that's what I mean for the substitution part

and how did you explain which type of function you choose to model the behaviour of the function???

and since we have to explain which type of function we choose does that mean that we only need to include the one that we chose and not the others?? i.e. we choose power then we dont have to test log and exponential

also what did you comment for the trends??? did you include asymptotes and if so how did you explain them???

I'm still a bit confused about what to plot on my axis

I've heard a lot of people saying that g-force is the x axis and time is the y axis because time is dependent on the g-force ..

However, the chart given, the left hand side, which would normally be your x axis is time and the right hand side, which would normally be your y axis, is the positive acceleration in horizontal direction (for the first part)

Would they (the people who made the question) purposefully switch the columns of the chart???

And if you input the data as shown in the question, when excel graphs time is automatically ur independent variable....

As well, there have been published physics articles about g-force and their graph shows that time is the independent variable??

So doesn't it make sense that the independent is time??

Can someone explain this to me????

Edited February 26, 2011 by Desy ♫

[Soozy]

Ohh I see. Thanks desy! BTW what program did you use to graph that?

[dessskris]

@reaching4thestars

Disclaimer: I am not doing this IA task.. and not going to because I am in Math HL I am posting here just to help people without any experience on doing Type 2 Portfolio. so I still do not know how to correctly do some parts of this task.

When choosing the type of regression, you need to consider the ‘characteristics’ of each regression type. TBH idk what to say either but I am sure it is something along those lines. This should demonstrate your knowledge in types of functions so you should mention a lot of theoretical things in here, like the existence of asymptote in this type of function, the shape of the curve of that function and whatnot...

Yeah you don’t need to discuss the other types of function. However if you feel like it you may suggest why this type of function will not fit the data or why that type of function cannot be modelled for this data. If you want to go the extra mile that is

The trends, just describe the graph as if you are describing a graph in science. At the beginning is the value of y increasing or decreasing? How fast? After that does it keep decreasing? Faster or slower? At the end what happen? What value does it approach? Something like that... yes include asymptotes. The ‘HOW’ is subjective. You need to be creative and think of how you can write a good portfolio – just like writing a good essay – you need to make it flow smoothly, nicely. Do not forget mathematical terminologies very important..

As for what to put in x-axis and in y-axis, I would suggest that both should be acceptable. But I prefer time on the x-axis and G on the y-axis. Anyhow if you put it the other way round it is also reasonable. Thus both should be acceptable. It’s up to you!

---

Ohh I see. Thanks desy! BTW what program did you use to graph that?

You are welcome! TI-Nspire Student Software

[vira.may]

I've found my function, and I want to see how well it corresponds to the plotted points. how do I do that?!

I don't know how to do this with Excel or my GDC (T1-83). is there any way I can plot the data points, and then enter the equation of my function, and then find the correlation coefficient (of how well the points correlate to my function)?

[afrocomb]

How did you guys get to the equation...?

I just plotted it into Excel and grabbed the exponential function.

Can someone explain to me why it isn't Power but it is Exponential?

Power seems to fit even better too.

And how would you derive that equation by hand...

I also noticed someone talking about R-squared value... what is that?

To get the equation all you do is right click on the trendline of your graph and select "Format Trendline" and then at the bottom of the box that will appear, there are two check boxes. One will say "Display Equation on chart" and the other "Display R-squared value on chart". Once you've done that, click Close and it should appear on your graph (usually bottom right).

And I also think that it is Power because Exponential or Log don't even fit properly.

---

I've found my function, and I want to see how well it corresponds to the plotted points. how do I do that?!

I don't know how to do this with Excel or my GDC (T1-83). is there any way I can plot the data points, and then enter the equation of my function, and then find the correlation coefficient (of how well the points correlate to my function)?

I'm actually trying to figure out how to do that too right now but if you have a graphic calculator you can just type in your equation and compare it to your graph on excel

[Mark Eatman]

For any Apple iWork users (Numbers '09 or later), enter the plots into a table in Numbers, and make a graph (bar graph with trendline) by clicking the graph icon. A plot with the points will appear. Click the "inspector" icon, then under the graph tab, click the "series" icon. Click "advanced" at the bottom, then click "trendline." Choose "power" in the drop-down box, then click "show equation."

[dessskris]

I've found my function, and I want to see how well it corresponds to the plotted points. how do I do that?!

I don't know how to do this with Excel or my GDC (T1-83). is there any way I can plot the data points, and then enter the equation of my function, and then find the correlation coefficient (of how well the points correlate to my function)?

Plot them both on the same axes. I highly don’t recommend Excel. Uhh do you have a software for that TI-83? I think there is… however I do not have it so I cannot teach you how to use it to plot :/ anyhow I have TI-Nspire Student Software and I guess they are a bit similar? In TI-Nspire what you need to do is:

---

How to Use Technology to Plot A Function with the Data on The Same Axes

This procedure below is meant for TI-Nspire™ calculators.

1. Add Lists & Spreadsheet

2. Put in the values of your variables in column A and B

3. Insert a new page

4. Add Data & Statistics

5. Plot Properties > Add X Variable > choose your independent variable

6. Plot Properties > Add Y Variable > choose your dependent variable

7. Data series will appear

8. Analyze > Plot Function.

9. Type in the function and press enter

10. You are done

---

However I don’t think TI can find the correlation coefficient there is no perfect software in the world.. however you can just comment on it by describing how well the curve fits each point.

Edited February 27, 2011 by Desy ♫