Coefficient of correlation.

#1
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.
 
#12
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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#13
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.)
 
#14
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).