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Type II -- Population Trends in China


Karl H T

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I am using a cubic function too. I already substituted each of the coordinates in the cubic model (ax + bx + cx + d....etc etc (imagine it with the exponents)) haha you get the idea. And i was thinking of using a matrix to obtain abcd...the problem is..I don´t really know how to use a matrix to do that. Any help? :S

Just set up a 4x4 matrix with all of the coefficients for a, b, c, and d, and multiply it by a 4x1 matrix of a b c d to get a 4x1 matrix of your y values... then can you solve from there?

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My school said no extra credit for using something we haven't learnt yet, and I would more likely lose marks for doing it wrong, so I should stick to something simple.

And I was going to use dry humor.

"Some of the limitations of this model are; that it relies on there being a large number of undead in China between x1 and x2, and on the PRC belief that before the PRC, there were no humans in China. As this sort of happening is preposterous, we can conclude that a model which would have to resort to such stipulations to be highly inaccurate etc."

Edited by Brad Johnston
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then modify it to fit the IMF data by translation and stretching

wasn't that clear enough?

well since the instruction on the task paper is not specific enough, I guess you could do anything you want. but if you use translation and stretching, it allows you to demonstrate more of your mathematical knowledge and it shows that you are familiar with various methods.

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hello, how do you get the parameters of K, L , M. I looked at the pdf posted on the first page but I am still confused o how to get the Parameters.. can someone please help me? :(

p.s What is regression??

Hey. If you have a GDC like TI-83 or TI-84 this should be easy. Go to STATS then then click on edit and enter all the data that was given. The years are too large and makes it harder to graph so you can input 0,5,10,15,20,25,30,35,40,45. These are the exact intervals as the years so the accuracy is fine. After you enter both the year and population value quit and then go back to STATS. Go across to CALC then scroll down all the way to logistic...which is B I believe then press enter then put L1 and L2. Then waalaa you have your parameters. :(

When I followed these instructions, it worked for me, however I even tried plotting it putting the values 1950-1955 instead of 0-45, and I get a different, must steepher graph. In my calculator, only the value for a changes. How come the two graphs are different? If the intervals are the same, shouldn't the graph go through the points? What explains the shape of this graph?

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I am using a cubic equation. I already arranged the result of substituting the coordinates in the cubic model and I have organized them in a Matrix. I used the Reduced Row-Echelon form to figure out the inverse Matrix, but the values that come up, when arranged in a cubic function, don´t give out any graph. What am I doing wrong?

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wrong model btw, it's supposed to be:

y=ax^3+bx^2+cx+d

remember when you need to generate a linear function, knowing two points?

for example, you have (1,2) and (3,4). your functions will be:

2=m+c

4=3m+c

then, construct matrices.

gif.latex?\begin{pmatrix} 1 & 1 \\ 3 & 1

then... you can use inverse to solve for m and c.

This is my matrix after plugging in coordinates in the cubic model:

0 0 0 1 554.8

8000 400 20 554.8 830.7

42875 1225 35 554.8 1070.0

91125 2025 45 554.8 1220.5

But when I apply the Reducer Row-Echelon form, the results are no good to draw a graph. What am I doing wrong?

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I am using a cubic function too. I already substituted each of the coordinates in the cubic model (ax + bx + cx + d....etc etc (imagine it with the exponents)) haha you get the idea. And i was thinking of using a matrix to obtain abcd...the problem is..I don´t really know how to use a matrix to do that. Any help? :S

Just set up a 4x4 matrix with all of the coefficients for a, b, c, and d, and multiply it by a 4x1 matrix of a b c d to get a 4x1 matrix of your y values... then can you solve from there?

No...I honestly don't get it. Sorry....

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@shyla I don't quite understand your question. try to use (x-1950) instead of x in your function?

@Olga sorry for taking so long to reply. I've been busy these days. use a different point for the first row in your matrix. and why do you always have 554.8 in your other rows? you do 3x4 matrix rref (alternatively you can use inverse) (3x4 means 3 rows, 4 columns). for KLM, just tabulate all your data in your GDC spreadsheet, then use the menu to find best logistic regression... I'm not sure what to press since we might be using different calculators, but if you use TI-Nspire let me know I can give you the instructions. it will then show the general equation form, which is the researcher's model and all the values of the parameters.

next time just quote me if you want a reply since I can't always check the forum due to exams coming up. so I will get a notification and can read your question.

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