Respuesta :
Answer:
See explanation below.
Explanation:
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
By definition the covariance "is a measure of the variability of two random variables". The covariance between x and y is defined as:
[tex] Cov(x,y) =\frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar y)}{n}[/tex]
And we have the following relation between the covariance and the correlation coefficient:
[tex] r= \frac{Cov(X,Y)}{\sigma_x \sigma_y}[/tex]
[tex] r = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{\sqrt{\sum_{i=1}^n (x_i-\bar X)^2 (y_i -\bar Y)^2}}[/tex]
So then we see that the correlation coeffcient is dependent of the covariance. If the covariance is + the r is + and if the covariance is - then r is negative, and the reasonis because if we see the last expression obtained the denominator can't be negative.
