Respuesta :
Answer:
r=0.4 (Same value)
Step-by-step explanation:
The correlation coefficient is unaffected by the scale of relation.
Correlation is a "statistical measure that indicates the extent to which two or more variables fluctuate together". And is always between -1 and 1. 1 indicates perfect linear relationship and -1 perfect inverse linear relationship. The formula for the correlation is given by:
[tex]0.4=r=\frac{b(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2-(\sum y)^2]}}[/tex]
Applying this formula we got that the correlation coeffcient it's 0.4. Now if we multiply all the x values by 2 we have this:
[tex]r_f=\frac{2b(\sum xy)-2(\sum x)(\sum y)}{\sqrt{4[n\sum x^2 -(\sum x)^2][n\sum y^2-(\sum y)^2]}}[/tex]
And symplyfing we see this:
[tex]r_f=2\frac{b(\sum xy)-(\sum x)(\sum y)}{2\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2-(\sum y)^2]}}[/tex]
We can cancel the 2 on the numerator and denominator and we got the same formula equal to 0.4.
[tex]r_f=\frac{b(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2-(\sum y)^2]}}=0.4[/tex]
So for this reason the correlation coefficient it's not affected by scale changes on the independent or dependent variables.
