1
00:00:00,060 --> 00:00:08,070
This example is referring to the curve fitting problem, so we do have a set of points on a plane and,

2
00:00:08,070 --> 00:00:14,910
um, we want to find out, uh, second degree, uh, expression that.

3
00:00:16,330 --> 00:00:20,330
And approximates the behavior of these points in the best way.

4
00:00:20,710 --> 00:00:28,510
So it means that that line should be somehow representing these points.

5
00:00:29,230 --> 00:00:38,030
OK, so the input parameters are the locations of these points, let's call them and X and Y.

6
00:00:38,500 --> 00:00:46,390
And the question is, what are the coefficients of this expression, A, B, C, or the, um, decision

7
00:00:46,420 --> 00:00:47,150
variables?

8
00:00:47,170 --> 00:00:50,980
OK, so let's have a look at the.

9
00:00:52,490 --> 00:00:53,750
And Python code.

10
00:00:53,870 --> 00:00:55,640
OK, so this example.

11
00:00:56,730 --> 00:01:01,570
OK, so, uh, first of all, I import all the required packages.

12
00:01:02,130 --> 00:01:09,540
This is an abstract model, so and, uh, can be a number of, um, solutions.

13
00:01:10,060 --> 00:01:15,440
That's, um, the number of, uh, points that I want to draw a line between them.

14
00:01:16,530 --> 00:01:24,450
I is the sets that represent each node and also, um, A, B, C are the variables.

15
00:01:25,940 --> 00:01:32,690
And we have a model and that or F, which is going to be representing the objective function, which

16
00:01:32,690 --> 00:01:34,190
is the error of estimation.

17
00:01:34,220 --> 00:01:42,980
OK, so first of all, I, um, create some random points on the plane and then, uh, write down the

18
00:01:43,130 --> 00:01:49,820
objective function, which is model A, uh, multiplied by X, location A squared plus.

19
00:01:50,960 --> 00:01:57,220
Um, B dot model X location plus, C minus Y location.

20
00:01:57,430 --> 00:02:06,880
OK, a. it means that I'm trying to find A, B, C in a way that the difference between the line and

21
00:02:06,880 --> 00:02:09,940
those points are minimal.

22
00:02:11,350 --> 00:02:19,210
They square of that is minimal, and since it's a linear programming, I have to use IP iPod and then,

23
00:02:19,210 --> 00:02:23,250
um, I'm using the.

24
00:02:25,920 --> 00:02:26,520
Model that.

25
00:02:27,630 --> 00:02:28,020
Yeah.

26
00:02:28,960 --> 00:02:32,260
For this purpose and run it.

27
00:02:36,190 --> 00:02:43,540
OK, and the points are here and the line is, uh, true, all of them.

28
00:02:43,750 --> 00:02:44,220
OK.

29
00:02:45,210 --> 00:02:46,140
And that's it.

30
00:02:46,170 --> 00:02:46,680
Thank you.