dessskris Posted November 9, 2011 Report Share Posted November 9, 2011 Thanks, and when they ask to discuss implications of each of these models do they refer only to researcher's model and the original data or to my model also?that would be the implications of your analytical model and the researcher's model. Reply Link to post Share on other sites More sharing options...
alexandranielsen Posted November 15, 2011 Report Share Posted November 15, 2011 Hey youcandoit and alex, I finally wrote it already! Here it is. How to Model a Quartic Function I think you should be able to model other polynomial functions from there because the idea is about the same. FYI if you don't want to use rref, you can actually solve for a, b, c and d using elimination and substitution. Also, you can use inverse to solve the matrices instead of transforming it into an augmented matrix and doing rref. Be careful, just find the inverse using calculator, don't do it yourself because finding the inverse of 3x3 or 4x4 matrix is not as easy as finding the inverse of 2x2 matrix. I will try to figure out the IMF modification thing..and youcandoit if you still have problems please ask again, specify your question, I will try to help! I tried using this system and it worked for a 4x4 but since i want it to be more accurate i tried a 6x6 and i just cant get i to work. I double check tht it is rigth by multiplying the matrix with its inverse and then getting a identity, but somehow i just end up with some 1&0 and the rest just being tiny numbers. I've checked the numbers like 100000 times but it still wont work.. any advice? Reply Link to post Share on other sites More sharing options...
dessskris Posted November 15, 2011 Report Share Posted November 15, 2011 have you converted the years to small integers like 0, 1, 2, 3, and so on and so forth?when I first did it I got the same result as you because I used those big values of year, but then I figured out that we need to convert the year first to smaller numbers and then the matrices will work. Reply Link to post Share on other sites More sharing options...
DKMikey Posted November 16, 2011 Report Share Posted November 16, 2011 have you converted the years to small integers like 0, 1, 2, 3, and so on and so forth? when I first did it I got the same result as you because I used those big values of year, but then I figured out that we need to convert the year first to smaller numbers and then the matrices will work. So I've read all 37 pages, and I must say that you people are all true lifesavers. One quick question though. As I do my sextic equation on Microsoft Excel, I am receiving E values. What do these mean? Am I supposed to have these? (I do know that I have to solve the equation analytically, but I don't want my graph to be wrong). Basically, I put the graph onto an XY Scatterplot, and created an x^6 polynomial trend line. Reply Link to post Share on other sites More sharing options...
dessskris Posted November 16, 2011 Report Share Posted November 16, 2011 So I've read all 37 pages, and I must say that you people are all true lifesavers. One quick question though. As I do my sextic equation on Microsoft Excel, I am receiving E values. What do these mean? Am I supposed to have these? (I do know that I have to solve the equation analytically, but I don't want my graph to be wrong). Basically, I put the graph onto an XY Scatterplot, and created an x^6 polynomial trend line. thank you! glad to hear that basically so yeahh hmm for your analytical model (first model), you're not supposed to do that. you HAVE to do it analytically (algebraically, mathematically) so you need to use matrices as in my attachment above (quoted in post #722) instead of just finding best regression (technologically) because for yuor second model (the researcher's model) you have to find it technologically. Reply Link to post Share on other sites More sharing options...
DKMikey Posted November 16, 2011 Report Share Posted November 16, 2011 (edited) So I've read all 37 pages, and I must say that you people are all true lifesavers. One quick question though. As I do my sextic equation on Microsoft Excel, I am receiving E values. What do these mean? Am I supposed to have these? (I do know that I have to solve the equation analytically, but I don't want my graph to be wrong). Basically, I put the graph onto an XY Scatterplot, and created an x^6 polynomial trend line. thank you! glad to hear that basically so yeahh hmm for your analytical model (first model), you're not supposed to do that. you HAVE to do it analytically (algebraically, mathematically) so you need to use matrices as in my attachment above (quoted in post #722) instead of just finding best regression (technologically) because for yuor second model (the researcher's model) you have to find it technologically. I plan to develop it analytically later, mainly because I have trouble inputting the matrices into my calculator and using rref to solve for the equation. We were never taught this in class, and I really doubt that my teacher will teach it to us, but this is what I put into the calculator (TI-83): This is what I try to do based on your example: ---------------------------------------------------------------------------------- Matrix A: [(1950)^6 (1950)^5...(1950)...554.8] [(1955)^6 (1955)^5...(1955)...609.0] [(1960)^6 (1960)^5...(1960)...657.5] [(1965)^6 (1965)^5...(1965)...729.2] [(1970)^6...] [(1975)^6...] [(1980)^6...] [(1985)^6...] [(1990)^6...] When I rref it, I get an INVALID DIM. I planned to use the R^2 value and equation in Excel to justify why I was using an x^6 equation as opposed to x^2 or linear, exponential, etc. Edited November 16, 2011 by DKMikey Reply Link to post Share on other sites More sharing options...
dessskris Posted November 16, 2011 Report Share Posted November 16, 2011 So I've read all 37 pages, and I must say that you people are all true lifesavers. One quick question though. As I do my sextic equation on Microsoft Excel, I am receiving E values. What do these mean? Am I supposed to have these? (I do know that I have to solve the equation analytically, but I don't want my graph to be wrong). Basically, I put the graph onto an XY Scatterplot, and created an x^6 polynomial trend line. thank you! glad to hear that basically so yeahh hmm for your analytical model (first model), you're not supposed to do that. you HAVE to do it analytically (algebraically, mathematically) so you need to use matrices as in my attachment above (quoted in post #722) instead of just finding best regression (technologically) because for yuor second model (the researcher's model) you have to find it technologically. I plan to develop it analytically later, mainly because I have trouble inputting the matrices into my calculator and using rref to solve for the equation. We were never taught this in class, and I really doubt that my teacher will teach it to us, but this is what I put into the calculator (TI-83): This is what I try to do based on your example: ---------------------------------------------------------------------------------- Matrix A: [(1950)^6 (1950)^5...(1950)...554.8] [(1955)^6 (1955)^5...(1955)...609.0] [(1960)^6 (1960)^5...(1960)...657.5] [(1965)^6 (1965)^5...(1965)...729.2] [(1970)^6...] [(1975)^6...] [(1980)^6...] [(1985)^6...] [(1990)^6...] When I rref it, I get an INVALID DIM. I planned to use the R^2 value and equation in Excel to justify why I was using an x^6 equation as opposed to x^2 or linear, exponential, etc. lol of course, your matrix is incomplete well use inverse? Reply Link to post Share on other sites More sharing options...
DKMikey Posted November 16, 2011 Report Share Posted November 16, 2011 lol of course, your matrix is incompletewell use inverse?I think I figured out the problem with the matrix. It has to be a square [7x7] to do an rref. However, I'm getting some REALLY weird numbers now...In the end, I've decided to do substitution and elimination instead. However, I am completely stuck as to how to solve a system of equations with 9 different equations. Do you think you could help me?(The problems I'm having is how to isolate variables, or how to approach the system of equations, etc.). Reply Link to post Share on other sites More sharing options...
dessskris Posted November 16, 2011 Report Share Posted November 16, 2011 no I couldn't... why do you think matrices were invented?? because people couldn't manage to solve 9 equations with 9 variables simultaneously with substitution and elimination!! I'm even too lazy to do 4 equations...with 9 equations? I'll die. I can guide you with forming the matrices though if you've realised how much like a suicide solving for 9 variables with substitution and elimination is. you're indeed supposed to get weird numbers, it's very rare to get nice numbers when you have lots of random data like that. Reply Link to post Share on other sites More sharing options...
alexandranielsen Posted November 16, 2011 Report Share Posted November 16, 2011 have you converted the years to small integers like 0, 1, 2, 3, and so on and so forth? when I first did it I got the same result as you because I used those big values of year, but then I figured out that we need to convert the year first to smaller numbers and then the matrices will work. yep, did 0,5,10 and so on but decided to go for onyl a cubic and quartic and then like discuss which one works best cause i dont feel like putting down too much time when i'm gonna go for the researcher's model in the end, but thanks Reply Link to post Share on other sites More sharing options...
Console Posted November 16, 2011 Report Share Posted November 16, 2011 Could someone please give me the vertex form of the function for the first set of data as a cubic. I just started, and dont have a clue how to write an expanded formula into vertex form. Thanks a bunch! Reply Link to post Share on other sites More sharing options...
DKMikey Posted November 16, 2011 Report Share Posted November 16, 2011 (edited) I can guide you with forming the matrices though if you've realised how much like a suicide solving for 9 variables with substitution and elimination is. you're indeed supposed to get weird numbers, it's very rare to get nice numbers when you have lots of random data like that.- Post edited so I wouldn't go against the rules and give away any answers. I PM'd you. Edited November 16, 2011 by DKMikey Reply Link to post Share on other sites More sharing options...
Reginald Jones Posted November 17, 2011 Report Share Posted November 17, 2011 Hey I'm having difficulty with "developing one model function" how do I go about doing that? Any suggestions? Reply Link to post Share on other sites More sharing options...
DKMikey Posted November 17, 2011 Report Share Posted November 17, 2011 Hey I'm having difficulty with "developing one model function" how do I go about doing that? Any suggestions?Basically, try different equations until you find the best line of fit for the original function. The words "regression equations" should come in handy, you might want to google that. If you read earlier in the thread, there are programs that can graph those regression lines, no technical work involved. 1. First, find out the function you want to graph (sin wave, polynomial, linear, etc.)2. Compare and contrast characteristics that would make this function appropriate for your original model.3. Solve the equation for that model analytically ONLY (as in no technology) - To do this, plug in the X and Y values and go on from there. I can't give you specific instructions after that because it is based on what kind of function you decided to use.Good luck! 1 Reply Link to post Share on other sites More sharing options...
dessskris Posted November 17, 2011 Report Share Posted November 17, 2011 Could someone please give me the vertex form of the function for the first set of data as a cubic. I just started, and dont have a clue how to write an expanded formula into vertex form. Thanks a bunch!what vertex form? use matrices Reply Link to post Share on other sites More sharing options...
DKMikey Posted November 17, 2011 Report Share Posted November 17, 2011 Hit another roadblock. Many people are saying that the researcher's model for the logistic function is dead on, but I am not getting that (despite using the calculator, putting values in list with L1, L2, Y1 and calculating the logistic regression). Is this true? Reply Link to post Share on other sites More sharing options...
dessskris Posted November 17, 2011 Report Share Posted November 17, 2011 Hit another roadblock. Many people are saying that the researcher's model for the logistic function is dead on, but I am not getting that (despite using the calculator, putting values in list with L1, L2, Y1 and calculating the logistic regression). Is this true?what do you mean? the researcher's model part is indeed easy, just plot the data in yout GDC and generate the logistic regression that's it. Reply Link to post Share on other sites More sharing options...
DKMikey Posted November 17, 2011 Report Share Posted November 17, 2011 Hit another roadblock. Many people are saying that the researcher's model for the logistic function is dead on, but I am not getting that (despite using the calculator, putting values in list with L1, L2, Y1 and calculating the logistic regression). Is this true?what do you mean? the researcher's model part is indeed easy, just plot the data in yout GDC and generate the logistic regression that's it.Yep, that's what I did. I was just confused because when I read those 37 pages of lots of information, many people on the forums were saying that the researcher's model matched exactly with the data points of the graph, so I felt like I was doing it wrong. I'm probably just overthinking this. Reply Link to post Share on other sites More sharing options...
dessskris Posted November 17, 2011 Report Share Posted November 17, 2011 Yep, that's what I did. I was just confused because when I read those 37 pages of lots of information, many people on the forums were saying that the researcher's model matched exactly with the data points of the graph, so I felt like I was doing it wrong. I'm probably just overthinking this.ohh. I think the researcher's model is indeed the best model but it doesn't really go through EVERY single point exactly. it's just the shape is really fitting the data. Reply Link to post Share on other sites More sharing options...
codiambo Posted November 17, 2011 Report Share Posted November 17, 2011 Hi all,I was wondering what difference it would make in the values of k,l and m in the logistic function if the x variable which is in years is set as follows:1950 is set as 0, 1955 set as 5 etc.?What would be the consequence? Reply Link to post Share on other sites More sharing options...
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