IA Type II -- G-Force Tolerance

[Pandemonium]

Thanks for defining the parameters; that definitely helped a ton.

I'm having trouble deriving the equation (although, of course, I can/have easily obtained it using PowerRegression), how can it be derived? Is it using the points (I think somebody mentioned this above)?

Also, just to clarify, "using technology" means you can legitamately use a Regression, without having to derive or anything, correct?

Yep, using the points will certainly give you what you need. And using technology technically means you can do so and leave out your own work, but solving analytically will certainly give you a boost--it gives you something to compare to, something to talk about, and shows a thorough understanding of how a model/parameters are obtained. It can only help to say "here is what I found, here is what the calculator says."

So, I have the points, but I'm a bit puzzled as to what to do with them, lol =/..

Like, I know that the general equation for Power Functions (which seems to be the best-fitting-model-function for the given set of data) is f(x) = a*x^b... You can easily plug in two points, but I'm not sure how to obtain the other part.

I tried to be a bit sneaky here and research how to derive a power function (Power Law -> Least Squares Fitting -> Haven't taken stats, yet -> :-( ). So, yeah, that didn't work out so well.

Any suggestions or aid would be so much appreciated.

Well...you need a and b, yes? And you have plenty of x and y to choose from. I'd pick a couple points and set up a system of equations, then solve. As in, you need two equations with points plugged in. And I don't know anything about stats lol, I always use a regression from the GDC to compare to my results.

Yeah, right after I typed that I was like "OH WAIT.." and figured it out; however, I was approached today by a few people and was a bit puzzled -- should g-force be the dependent or independent variable? I was trying to think of it logically, because instinctively I made time my independent variable. However, after thinking it over, I began to rationalize "Time is calculated FROM g-force," meaning, to obtain the time, you must see how long the person can undergo g-force value 40 (for argument's sake). Using that logic, g-force would be the independent variable, and that would make sense.

Let me know, maybe I'm thinking too deep into it =)

[lil romany]

Thanks for defining the parameters; that definitely helped a ton.

I'm having trouble deriving the equation (although, of course, I can/have easily obtained it using PowerRegression), how can it be derived? Is it using the points (I think somebody mentioned this above)?

Also, just to clarify, "using technology" means you can legitamately use a Regression, without having to derive or anything, correct?

Yep, using the points will certainly give you what you need. And using technology technically means you can do so and leave out your own work, but solving analytically will certainly give you a boost--it gives you something to compare to, something to talk about, and shows a thorough understanding of how a model/parameters are obtained. It can only help to say "here is what I found, here is what the calculator says."

So, I have the points, but I'm a bit puzzled as to what to do with them, lol =/..

Like, I know that the general equation for Power Functions (which seems to be the best-fitting-model-function for the given set of data) is f(x) = a*x^b... You can easily plug in two points, but I'm not sure how to obtain the other part.

I tried to be a bit sneaky here and research how to derive a power function (Power Law -> Least Squares Fitting -> Haven't taken stats, yet -> :-( ). So, yeah, that didn't work out so well.

Any suggestions or aid would be so much appreciated.

Well...you need a and b, yes? And you have plenty of x and y to choose from. I'd pick a couple points and set up a system of equations, then solve. As in, you need two equations with points plugged in. And I don't know anything about stats lol, I always use a regression from the GDC to compare to my results.

Yeah, right after I typed that I was like "OH WAIT.." and figured it out; however, I was approached today by a few people and was a bit puzzled -- should g-force be the dependent or independent variable? I was trying to think of it logically, because instinctively I made time my independent variable. However, after thinking it over, I began to rationalize "Time is calculated FROM g-force," meaning, to obtain the time, you must see how long the person can undergo g-force value 40 (for argument's sake). Using that logic, g-force would be the independent variable, and that would make sense.

Let me know, maybe I'm thinking too deep into it =)

I see the logic of that, and have considered it...however my Physics teacher last year beat into our heads "TIME GOES ON THE X AXIS, NO MATTER WHAT" so that's what I based my selection on. I don't know if there are applications where this is not so...but I sure do remember the 50% on the lab my group failed because we thought time could be the dependent variable.....there's an argument for either side, I don't know the "official" verdict on whether it is permissible....do what you've been taught and go with your instinct....

[Rafael]

So, er... how'd you guys start off with this? I mean how'd you graph the data? What programs did you use? If you did it in the calculator, how?

Sorry, I'm rather technologically challenged. I figured Excel would help me make the graph, but I had no idea how to make it create the graph like I wanted it. Help would be very appreciated!

EDIT: Heh, nevermind, I was being silly. I figured out that you need to use a scatter plot graph as opposed to a line graph.

Edited December 22, 2010 by Rafael

[---ooo---]

I have read earlier posts and few people asked this but no one really answered but what does it mean

Define appropriate variables and parameters, and identify any constraints for the data.

Is there anyone who knows this and could give me advice how to solve this. Anything really. I know the values can't be negative and that is it.

Anyone ???

Variables: as simple as stating x and y. What are they? What units? How are they measured?

Parameters: things you know about this data

-why are x and y what they are (what axis does time usually go on)

-you know time can't be negative--what does that say about the nature of the function that will model this data?

-will the model ever lose accuracy? (presumably toward infinity)

-do you have enough given data to even create a model?

-is the given data valid? (cross cultural, age, weight?)

-most importantly, once you pick a function, what are the constants? (say it is exponential, what are the values of "a" and "b"?)

It seems really dumb to repeat much of what seems obvious, but basically it is asking you to meditate on the information and the implications--using what you are given and what you know, they want you to state ideas you have about potential function behavior---basically just clarify what EVERYTHING means. For instance, differences in notation are important (we have two data sets here, all you have to do is recognize that somewhere in word form!)

And in clarifying parameters....what are you trying to do? If you give a table, a function, maybe a graph, lovely---but why are you doing that? What is the goal? Those are the types of things you need to answer

Thank you so much. This was really helpful

What type of function models the behaviour of the graph? - Does this mean that we state what equation we used: power equation, exponential equation and so on??

Use technology to find another function that models the data. - To find wheter was it exponential or power I used GDC so does this mean I first had to do it by hand and besides power equation I need to come up with new one?

Please I am stuck and this is due two days, so any hint would be helpful

[dessskris]

What type of function models the behaviour of the graph? - Does this mean that we state what equation we used: power equation, exponential equation and so on??

Use technology to find another function that models the data. - To find wheter was it exponential or power I used GDC so does this mean I first had to do it by hand and besides power equation I need to come up with new one?

Please I am stuck and this is due two days, so any hint would be helpful

Is it due today? Sorry if I'm too late to help. I'm not doing this portfolio but I guess I could just help, perhaps?

What type of function models the behaviour of the graph? - Does this mean that we state what equation we used: power equation, exponential equation and so on??

I think so

Use technology to find another function that models the data. - To find wheter was it exponential or power I used GDC so does this mean I first had to do it by hand and besides power equation I need to come up with new one?

What did you do in GDC to find the equation type? Remember it first asked you to explain why you chose that function.. So you first must guess from the shape (I think, not sure. again I'm not doing this task)

Like if the shape is like that, what function does it remind you of?

Then when they ask for another function, it asks for another type of function perhaps. You do this one with GDC! If GDC tells you it's a power function, then in the first part you should have guessed it was a logarithmic function

[dfmarty]

did anyone get a power regression???

[dessskris]

did anyone get a power regression???

I am not doing this task but I just want to help people around..

When I tried to plot a graph, yes I got a power regression

[OneMistake]

Can someone please tell me whether time is on the x axis or y axis, because it can be argued that it can go on both axis. It would be greatly appreciated (:

[dessskris]

Can someone please tell me whether time is on the x axis or y axis, because it can be argued that it can go on both axis. It would be greatly appreciated (:

I would personally say put time on the x axis and +G on the y axis.

[tinkerbell927]

Can someone please tell me whether time is on the x axis or y axis, because it can be argued that it can go on both axis. It would be greatly appreciated (:

I would personally say put time on the x axis and +G on the y axis.

I am working on the same task right now. I am a bit confuse with the variables, why do you chose time as the independent and +G as the dependent. thanks

[dessskris]

Can someone please tell me whether time is on the x axis or y axis, because it can be argued that it can go on both axis. It would be greatly appreciated (:

I would personally say put time on the x axis and +G on the y axis.

I am working on the same task right now. I am a bit confuse with the variables, why do you chose time as the independent and +G as the dependent. thanks

Whoa I never expected such questions and I am not doing this task so I cannot comment much on it, but I hope you don't mind hearing some opinions from me.

Let me define some terms first.

Independent variable is the one which is manipulated. Meaning you can decide what their values are. The result of this manipulation leads to the measurement of the dependent variable.

Dependent variable is the one which is measured. Its values depend on the values of the independent variable.

First impression when I saw the table: time is independent and G is dependent. Why? Because most tables are organised in such a way that the first column is usually the independent variable and the second column is usually the dependent variable.

Then, the trend in the values. If you notice, the times are 0.01, 0.1, 1, 10 and also 0.03, 0.3, 3, 30 min. Don't you see the trend? But for G: 35, 28, 20, 15, 11, 9, 6, 4.5... I do not really notice any pattern in the values of G.. And if you are to choose the values of the independent variable, would you choose random numbers like 35, 28, 20, 15, 11, 9, 6, 4.5; or would you rather choose numbers in which there is a trend, like 0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30?

Last, the values of time in the first and second tables. The values are exactly the same. Thus I'd say time is the independent variable.

If you are still unsure, you may argue with me and I will try to justify my opinion

[tinkerbell927]

anyone have any idea about which function should i use? is it power function, exponential or the others? thanks so much

[dessskris]

anyone have any idea about which function should i use? is it power function, exponential or the others? thanks so much

Which do you think fits the data points best?

I would suggest power function btw

[lil romany]

Can someone please tell me whether time is on the x axis or y axis, because it can be argued that it can go on both axis. It would be greatly appreciated (:

I would personally say put time on the x axis and +G on the y axis.

I am working on the same task right now. I am a bit confuse with the variables, why do you chose time as the independent and +G as the dependent. thanks

Whoa I never expected such questions and I am not doing this task so I cannot comment much on it, but I hope you don't mind hearing some opinions from me.

Let me define some terms first.

Independent variable is the one which is manipulated. Meaning you can decide what their values are. The result of this manipulation leads to the measurement of the dependent variable.

Dependent variable is the one which is measured. Its values depend on the values of the independent variable.

First impression when I saw the table: time is independent and G is dependent. Why? Because most tables are organised in such a way that the first column is usually the independent variable and the second column is usually the dependent variable.

Then, the trend in the values. If you notice, the times are 0.01, 0.1, 1, 10 and also 0.03, 0.3, 3, 30 min. Don't you see the trend? But for G: 35, 28, 20, 15, 11, 9, 6, 4.5... I do not really notice any pattern in the values of G.. And if you are to choose the values of the independent variable, would you choose random numbers like 35, 28, 20, 15, 11, 9, 6, 4.5; or would you rather choose numbers in which there is a trend, like 0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30?

Last, the values of time in the first and second tables. The values are exactly the same. Thus I'd say time is the independent variable.

If you are still unsure, you may argue with me and I will try to justify my opinion

Beautiful explanation. Absolutely perfect.

[CristinaV]

Whoa I never expected such questions and I am not doing this task so I cannot comment much on it, but I hope you don't mind hearing some opinions from me.

Let me define some terms first.

Independent variable is the one which is manipulated. Meaning you can decide what their values are. The result of this manipulation leads to the measurement of the dependent variable.

Dependent variable is the one which is measured. Its values depend on the values of the independent variable.

First impression when I saw the table: time is independent and G is dependent. Why? Because most tables are organised in such a way that the first column is usually the independent variable and the second column is usually the dependent variable.

Then, the trend in the values. If you notice, the times are 0.01, 0.1, 1, 10 and also 0.03, 0.3, 3, 30 min. Don't you see the trend? But for G: 35, 28, 20, 15, 11, 9, 6, 4.5... I do not really notice any pattern in the values of G.. And if you are to choose the values of the independent variable, would you choose random numbers like 35, 28, 20, 15, 11, 9, 6, 4.5; or would you rather choose numbers in which there is a trend, like 0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30?

Last, the values of time in the first and second tables. The values are exactly the same. Thus I'd say time is the independent variable.

If you are still unsure, you may argue with me and I will try to justify my opinion

See, that's what I thought in the beginning, that it's in the first column and that there's an actual pattern between the numbers and so on. But the thing is that, as you pointed out, the dependent variable is the one that you can't control; it's the one that's affected by the independent variable.

The time column in this case is the time a human can tolerate a specific G-force for, and you can't (or at least I don't think you can) just decide how long a person is going to be able to tolerate the G-force until they lose consciousness and then check what the exact G-force was. You would have to change the G-force yourself (not really yourself, but you know what I mean) and then check how long they lasted for.

I've always believed that time should be independent and in the x-axis, but here I don't see how it would be possible for anyone to willingly change it, because it's a direct result from the G-force itself. G-force, on the other hand, I find more believable to change. Now, as for why the time numbers seem so neat and organized (0.01, 0.03, 0.1...), I have no idea. That's what threw me off.

Ok and question, I plotted the one for horizontal G-force, and by checking the R value on excel, I saw that the power trend line was almost perfect, very close to 1. That's the reasoning I did to choose the power function. But I'm very confused by how it asks to find another function... I already used technology in the first method, and to me it is the best one. So why would I want to show another formula that's less correct in finding a pattern?

I know I could just randomly guess the first one, put exponential, and leave the R value thing and the power function for the next, but I would have no way of justifying why I chose it other than "it looks good". And even if it did look good... to me it doesn't look as good as power. I pretty much just use the R value...

Help, anyone? :-)

I find this portfolio to be very vexing...

And another thing!

When I found the equation by hand, I used the points (1,11) and (10,6) (or (11,1) and (6,10) if you have the axes the other way like I do ) and I solved for a and b. I already saw what the formula was with Microsoft Excel, because it's really awesome and tells me R value together with the function's equation. The b I got is very similar, but the a is off by about 2436 hahah

I know why I have different results, because I've taken two points instead of looking at the entire function and points like Excel did. Now, do you guys think I should put the Excel formula, which is probably more accurate although I didn't "prove" it, or use my formula, which is less accurate but was calculated by myself? I guess I also have the possibility of including both somewhere, but which one should I put as the "ideal function"?

Or maybe you guys could tell me any two points that would lead to a far more accurate result?

Thanks

Edited January 8, 2011 by Desy ♫

[dessskris]

See, that's what I thought in the beginning, that it's in the first column and that there's an actual pattern between the numbers and so on. But the thing is that, as you pointed out, the dependent variable is the one that you can't control; it's the one that's affected by the independent variable.

The time column in this case is the time a human can tolerate a specific G-force for, and you can't (or at least I don't think you can) just decide how long a person is going to be able to tolerate the G-force until they lose consciousness and then check what the exact G-force was. You would have to change the G-force yourself (not really yourself, but you know what I mean) and then check how long they lasted for.

I've always believed that time should be independent and in the x-axis, but here I don't see how it would be possible for anyone to willingly change it, because it's a direct result from the G-force itself. G-force, on the other hand, I find more believable to change. Now, as for why the time numbers seem so neat and organized (0.01, 0.03, 0.1...), I have no idea. That's what threw me off.

I dont really understand this G-force thingy TBH!! The explanation on the paper is weird, I still don't get how they measure the force and time. I actually also thought so, Chris. Like when G=x, they human can only tolerate that force for y min. And yes it is more logical for us to control G instead of time. But I still think that if they meant to make G the independent variable, why did they put G on the right column instead of the left one? Why did they put time with pattern and random G, why not the other way round? I think a Psychology student could explain this but idk since I'm not taking Psych. If I were you I would still put time on the x-axis and G on the y-axis.

Actually if you think about it, would it matter much if you put G on the x-axis and time on the y-axis? Well firstly your answers would be different, obviously, but then aren't the equations just the inverse of one another? Just pick one that you think is more logical and do it.. If I were you I would contact my teacher and ask for as many clues as possible. Or if there are more than one Math classes with different teachers, ask the other teacher! It should be fine.. The Math SL class in my grade hasn't done any IA, though, so even if I try to approach their teacher and ask, he wouldn't answer me directly with confidence. Not my HL teacher also because she has not read the SL tasks (and why bother, anyways?) so she would take some time to read/try doing it too.

[dessskris]

Ok and question, I plotted the one for horizontal G-force, and by checking the R value on excel, I saw that the power trend line was almost perfect, very close to 1. That's the reasoning I did to choose the power function. But I'm very confused by how it asks to find another function... I already used technology in the first method, and to me it is the best one. So why would I want to show another formula that's less correct in finding a pattern?

I know I could just randomly guess the first one, put exponential, and leave the R value thing and the power function for the next, but I would have no way of justifying why I chose it other than "it looks good". And even if it did look good... to me it doesn't look as good as power. I pretty much just use the R value...

And another thing!

When I found the equation by hand, I used the points (1,11) and (10,6) (or (11,1) and (6,10) if you have the axes the other way like I do ) and I solved for a and b. I already saw what the formula was with Microsoft Excel, because it's really awesome and tells me R value together with the function's equation. The b I got is very similar, but the a is off by about 2436 hahah

I know why I have different results, because I've taken two points instead of looking at the entire function and points like Excel did. Now, do you guys think I should put the Excel formula, which is probably more accurate although I didn't "prove" it, or use my formula, which is less accurate but was calculated by myself? I guess I also have the possibility of including both somewhere, but which one should I put as the "ideal function"?

Or maybe you guys could tell me any two points that would lead to a far more accurate result?

Thanks

I find this task very vexing too btw haha I hope my type II task won't be as vexing as this one!

For your first question, right, TBH I have no experience in type II IA yet while I have done two type I IAs (one is a practice, the other one is a real IA) so idk much how exactly you are supposed to do it.

But from the questions in the IA, I think they firstly want you to plot the graph, comment on any apparent trends, make a mathematical guess based on the apparent trend (so in this stage you haven't used technology to find the function yet), compare that model function with your data points (tell them whether your function fits the data points well) and THEN use technology to find another function which fits the data points better!

I tried plotting time against G just now and the only function that fits is power. Another one is logistic but it was in the form of:

y= m/(n+p*e^f(x))+q

where m, n, p and q are real constants

and f(x) is a linear function

So I think it's too complicated for you to guess a function like this. Then I plotted G against time and there are also only 2 functions that fit: power and logarithmic! This logarithmic function is in the form of:

y=a+b*ln(x)

where a and b are real constants

If I were you in the first part I would plot G against time then! And try to find a logarithmic function that fits the data points even though it does not fit well.. It makes more sense to find that simple ln function than to find a complicated e function. And you are not taught anything about the power function right? Only linear, polynomial, logarithmic, exponential and sin cos tan functions. So do not use power lah.. Then I would talk about how bad the ln function fits the curve and say technology could prob find a better function.. After that use TI software to draw the power function and compare the graphs.

For the other question, what did you mean by 'by hand'??? That's not the way you find a function! idk if you should go in this depth in SL portfolio but I think you should mathematically find it!!

Let's say you want to find the y=a+b*ln(x) function. You have more than 2 points already so you should be able to find the function mathematically!

If my explanations are not clear just ask. Any other doubt just ask also.

[aposton]

What type of function models the behaviour of the graph? - Does this mean that we state what equation we used: power equation, exponential equation and so on??

Use technology to find another function that models the data. - To find wheter was it exponential or power I used GDC so does this mean I first had to do it by hand and besides power equation I need to come up with new one?

Please I am stuck and this is due two days, so any hint would be helpful

Is it due today? Sorry if I'm too late to help. I'm not doing this portfolio but I guess I could just help, perhaps?

What type of function models the behaviour of the graph? - Does this mean that we state what equation we used: power equation, exponential equation and so on??

I think so

Use technology to find another function that models the data. - To find wheter was it exponential or power I used GDC so does this mean I first had to do it by hand and besides power equation I need to come up with new one?

What did you do in GDC to find the equation type? Remember it first asked you to explain why you chose that function.. So you first must guess from the shape (I think, not sure. again I'm not doing this task)

Like if the shape is like that, what function does it remind you of?

Then when they ask for another function, it asks for another type of function perhaps. You do this one with GDC! If GDC tells you it's a power function, then in the first part you should have guessed it was a logarithmic function

I'm still confused as to how to come up with another equation model. /:

[dessskris]

What did you do in GDC to find the equation type? Remember it first asked you to explain why you chose that function.. So you first must guess from the shape (I think, not sure. again I'm not doing this task)

Like if the shape is like that, what function does it remind you of?

Then when they ask for another function, it asks for another type of function perhaps. You do this one with GDC! If GDC tells you it's a power function, then in the first part you should have guessed it was a logarithmic function

I'm still confused as to how to come up with another equation model. /:

Ok first you need to model a logarithmic function. You do this mathematically, substituting values of x and y to get the function. If you need more information I can explain this further.

Then you use your GDC to actually find a more accurate function. Plot the graph and make your software show the equation of the graph (I suggest a power function). Done!

If you are still in doubt I don't mind explaining this more clearly..

[Bjork]

after plotting the datas in excel, it is obvious that this is an logarithmic function, but then what? what is the next thing that we should do??? ıf anyone knows please help me!!

I plotted it, and it seems like an exponential function! Am I on the right track?

It is an exponential graph as the g-force value will never be negative of zero and the time survived will always delay even the smalest amount of time, so it will never be zero or negative as well.