Question

Does anyone know how to construct a correlation matrix table?

Answer 1

x1 x2 x3 y
6.7 2.8 2.5 11.0
3.9 2.6 5.7 11.0
1.8 2.4 7.8 10.6
5.1 2.3 7.1 10.3
2.7 2.5 5.9 10.3
8.4 2.9 8.6 10.7
14.0 2.3 9.2 10.0
6.0 2.0 5.5 9.4
14.6 2.2 3.7 8.7
9.3 1.1 5.5 8.7

Answer 2

ok I couldn't find any calculator that could do everything in one step, but I did managed to find a correlation coefficient calculator

Answer 3

manage*

Answer 4

I found this: http://www.endmemo.com/statistics/cc.php

Answer 5

the idea is this:

for each cell, we're finding the correlation coefficient for the variables in the row and column headers

for example, in the cell that is in the row that starts with x3 and is in the column x1, we are going to input the correlation coefficient for the two variables x3 and x1

Answer 6

let corr(x,y) be a function that returns the correlation coefficient for the variables x and y

because corr(x,y) = corr(y,x), this means that we don't need to do the upper triangular half, which is why there are no boxes here

Answer 7

that sounds kinda confusing.
I did find this example but it's not very helpful.

Answer 8

I hate that. When they say "use technology", they're basically waving a magic wand to get things done and don't explain what's going on.

Answer 9

I'm assuming you are (somewhat) familiar with correlation right?

Answer 10

THAT'S WHAT I TOLD MY INSTRUCTOR!
And yes i'm kinda familiar with that.

Answer 11

but then again, doing this thing by hand will take forever, so I understand why they resort to "technology" (they fail to specify WHICH technology though)

Answer 12

anyways, let's just focus on the first two columns x1 and x2

Answer 13

of the original data set

Answer 14

I'm going to use this calculator: http://www.endmemo.com/statistics/cc.php

On that page, I'm going to paste in the first column x1 into the first big text input box on the left side

Then I'm going to paste in the second column x2 into the big text input box on the right side

Note: order doesn't matter and you can swap the two

doing so will give you this

Answer 15

what this calculator is doing is using the formula it shows at the bottom to calculate the correlation coefficient

in this case (on the image I posted), it's calculating the correlation coefficient between x1 and x2

Answer 16

That result of -0.24431755 gets rounded to -0.244, which is the answer that goes in the box where the x1 column and x2 row intersect

Answer 17

hopefully all that makes sense

Answer 18

kinda yah

Answer 19

its definitely a lot to take in and process since correlation coefficients are a pain on their own

Answer 20

I want you to use the calculator I posted and tell me what you get for the correlation coefficient between x1 and x3.

This is so you get some practice using it and so I know if you're on the right track or not.

Answer 21

good

Answer 22

that number (when rounded) goes in the cell that is in the x1 column, x3 row

Answer 23

So -0.018?

Answer 24

yep

Answer 25

the rest of the cells are done the same way (just with different combos of data sets)

Answer 26

so the next one would be x1 & y?

Answer 27

yep

Answer 28

so you can see why I had you copy/paste all that data

having to type it all in again would be a pain

Answer 29

i did have to type it all out again tho. lol

Answer 30

oh why is that? lol

what I did was have 4 groups of data on their own so I could easily copy/paste any column I wanted

you should give it a try

Answer 31

so that becomes -0.582

Answer 32

and that's the answer for the cell in the x1 column, y row

Answer 33

i typed it out here going down instead of across so when i tried to copy and past it does the whole row across.
But now i do x2 & x3?

Answer 34

i see, and yes, now you're doing x2 and x3

Answer 35

good, so it's 0.089 for the box in column x2, row x3

Answer 36

that's for x2 and y, good

Answer 37

so 0.817?

Answer 38

correct

Answer 39

good, so that is 0.199

Answer 40

and that's the only box left: column x3, row y

Answer 41

ok my math lab says the answers r right!
now i have this part.

Answer 42

let's hope so lol or else we'd have to find another calculator

Answer 43

according to your example, multicollinearity exists when the correlation coefficient between two explanatory variables is either smaller than -0.7 or larger than 0.7

Answer 44

so do you see any boxes that fit that description? if so, which one(s)?

Answer 45

don't all of them fit that?

Answer 46

how so

Answer 47

ok well x1 & x2 is smaller,x1 & x2 is Smaller, x1 & y is smaller. Then x2 & x3 is smaller, x2 & y is larger & x3 & y is smaller.
lol i think i'm reading that right.

Answer 48

but which (if any) are either less than -0.7 or greater than 0.7 ?

Answer 49

What?

Answer 50

didn't i just answer that?

Answer 51

you're on part b right now correct?

Answer 52

no its still a part of a)

Answer 53

i see, well only one box has a number that is larger than 0.7

what box am I referring to?

Answer 54

x2 & y

Answer 55

is y an explanatory variable?

Answer 56

yes?

Answer 57

no, y is actually a response variable

the x1, x2, x3 are explanatory variables

Answer 58

oh ok. so that means...?

Answer 59

that means that there is no high correlation between any two pair of explanatory variables

Answer 60

so no evidence of multicollinearity exists

Answer 61

YAY! it said it's right!
Now its part B

Answer 62

yikes this is a long problem lol (imagine if we didn't have a calculator....)

Answer 63

lol yah there's still 8 more parts to this question.

Answer 64

wow i thought it was just a-d

Answer 65

NoPe sadly not. Lol this is my final homework assignment.

Answer 66

i gotcha, so they just wanna go all out then

Answer 67

yah

Answer 68

ok go here: http://www.xuru.org/rt/MLR.asp

Answer 69

copy and paste this data set (as is)


6.7 2.8 2.5 11.0
3.9 2.6 5.7 11.0
1.8 2.4 7.8 10.6
5.1 2.3 7.1 10.3
2.7 2.5 5.9 10.3
8.4 2.9 8.6 10.7
14.0 2.3 9.2 10.0
6.0 2.0 5.5 9.4
14.6 2.2 3.7 8.7
9.3 1.1 5.5 8.7


into the text box, then hit calculate and show me what you get

Answer 70

so like this?

Answer 71

good

Answer 72

what result did you get

Answer 73

getting the same

Answer 74

now you have to do a bit of work to get the answers in the format they want

Answer 75

not too much though

Answer 76

ok what do i do?

Answer 77

notice how the first box has NO x variable next to it

Answer 78

yah i see that

Answer 79

this means that this is the constant

the constant of the result is 7.530451834

that rounds to 7.530 when rounded to 3 decimal places

Answer 80

so 7.530 goes in the first box

Answer 81

ok

Answer 82

the next box is the coefficient for the x1 variable

the result says -8.013546385·10^(-2) x1

but...they don't want the answer in scientific notation, so you have to convert it to standard notation to get

-8.013546385·10^(-2) = -0.08013546385

then you round that to 3 decimal places to get: -0.080

Answer 83

oh and nearly forgot, but they already supplied the negative out front of the box

so the answer for the second box is 0.080

Answer 84

ok

Answer 85

see how I'm getting all this?

Answer 86

yah

Answer 87

ok great