00:01
In this exercise, we are given the scores of five students in three different tests, and we have to find a correlation matrix.
00:09
So let's start by considering the matrix shown on the screen.
00:14
Each column represents a test and each one represents a student.
00:20
And in order to find a correlation matrix, our first step is to know how far these scores are from the average scores.
00:28
So we do that by subtracting the averages scores scores.
00:39
So we get the following matrix.
00:42
To the first column we will subtract 66, which is the score of the corresponding test.
00:49
This gives us minus 5, minus 3, 12, minus 1, minus 3.
00:56
Then to the second column, we will also subtract 266.
01:00
66 which is the averages score for the math test and we will get minus 13, 7, minus 5, 18 and minus 7.
01:13
And to the last colombo rules track 76.
01:17
That gives us minus 23, 2, 6, 20 and minus 5.
01:27
Now if we call this columns v1, v2 and v3, then we can view the new matrix by normalizing those columns.
01:45
Normalize.
01:48
So let's view this new matrix, which we will call v.
01:56
And the first column will v1 over the norm of v1 times v1.
02:02
The second column will be 1 over the norm of v2, times v2 and the 30 column will be 1 over the norm of v3 times v3.
02:15
If we define d this way, then the correlation matrix will be given by the product d transpose times d.
02:29
By doing the product carefully, we can see that the ith chain, i.
02:36
J and 3 of the matrix is going to be given by the inner product between v i and vj over the norm of v i times the norm of vj okay so we have to compute the norms of the viz and the inner product between them to find a correlation matrix and we'll do that here so the the norm of v1 is given by the square root of 25 plus 9 plus 12 square which is 144 plus 1 plus 9.
03:23
That is the square root of 188.
03:28
And similarly, the norm of v2 will be given by the square root of 169 plus 49 plus 49...