# Coefficient of correlation.

#### harshalishah

##### New Member
1) If the correlation coefficient between two random variables X and Y is 0.5, then the correlation coefficient between 2X-4 and 3-2Y is?
a. 1
b. 0.5
c. -0.5
d. 0

1) If the correlation coefficient between two random variables X and Y is 0.3, then the correlation coefficient between (2X+3)/5 and (4Y+7)/11 is?
a. 0.3
b. 0.3/(11*5)
c. (2*4*0.3)/(11*5)
d. None of the above.

#### Karabiner

##### TS Contributor
Well, to start with...what are your own ideas regarding the correct solutions?

With kind regards

Karabiner

#### harshalishah

##### New Member
Well, to start with...what are your own ideas regarding the correct solutions?

With kind regards

Karabiner
Well, to start with...what are your own ideas regarding the correct solutions?

With kind regards

Karabiner
I dont have any. I only know the basics of correlation.

#### Dason

##### Ambassador to the humans
What facts about correlation do you know

#### harshalishah

##### New Member
What facts about correlation do you know
it measures how the dependency between two variables.
Please just explain, I have a test coming up, and this is important.

Thank you

#### Stats fan

##### Member
At the bottom of this overview http://statkat.com/stattest.php?t=19 you can find a list of properties of the correlation coefficient. The property listed fourth can help you answering this question. Let me know if you can figure it out using this information.

#### harshalishah

##### New Member
At the bottom of this overview http://statkat.com/stattest.php?t=19 you can find a list of properties of the correlation coefficient. The property listed fourth can help you answering this question. Let me know if you can figure it out using this information.

So the answers would be:

1. c?
2. a?

C is the correct answer for 1 but B is the correct answer for 2.
Is it A or B for the second question?

#### Stats fan

##### Member
A is the correct answer for the second question. It seems like you get it!

#### harshalishah

##### New Member
A is the correct answer for the second question. It seems like you get it!
But the source from where I got the 2nd question says that B is the correct answer.

#### Stats fan

##### Member
Then I disagree with that source. I think they made a mistake.

#### harshalishah

##### New Member
Then I disagree with that source. I think they made a mistake.
Maybe they did. Thank you!

So the coefficient is only determined through the signs?

#### Stats fan

##### Member
Well, the coefficient is determined by the strength and the direction of the linear relationship between two variables. If there is a linear negative relationship between two variables, the coefficient is between 0 and -1. If there is a linear positive relationship between two variables, the coefficient is between 0 and 1. The stronger the relationship, the closer is the coefficient to -1 or 1.

But given that the correlation between two variables x and y is, say, 0.3, we know that the absolute size of the correlation between x and y won't change if x and/or y are linearly transformed. However, the sign will flip if we multiply x or y by -1.

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#### harshalishah

##### New Member
Well, the coefficient is determined by the strength and the direction of the linear relationship between two variables. If there is a linear negative relationship between two variables, the coefficient is between 0 and -1. If there is a linear positive relationship between two variables, the coefficient is between 0 and 1. The stronger the relationship, the closer is the coefficient to -1 or 1.

But given that the correlation between two variables x and y is, say, 0.3, we know that the absolute size of the correlation between x and y won't change if x and/or y are linearly transformed. However, the sign will flip if we multiply x or y by -1.

So the correlation won't change even if the numbers are divided by a positive number? (I'm talking about question 2 in this case.)

#### Stats fan

##### Member
That's correct. Also, note that dividing the values by 5 is the same as multiplying them by 1/5. So in de second question, the x values are multiplied by 2/5 (and 3/5 is added to them).