Respuesta :
The standard deviation of the residuals is (actual values of y - predicted values of y) is 0
What does correlation coefficient tells?
The correlation coefficient is the degree of association between two quantities in terms of linear relation.
The range of correlation coefficient is -1 to 1
If the correlation is -1, then that means as the one quantity increases, the other quantity decreases (linearly)
If the correlation is 0, then there is no linear relationship between two variables.
If the correlation is 1, then that means as the one quantity increases, the other quantity increases(linearly) and vice versa for decrement.
Thus, if the correlation coefficient of two variables is 1 or -1, then that means they are linearly related.
For this case, we're given that:
- Correlation coefficient of x and y is -1
That shows that:
[tex]y = mx + c[/tex] (a linear relation between x and y).
Now, since there was a line fit, that fit would exactly match with the real line y = mx +c
Thus, the actual values and predicted values both will overlap, due to which, there would be no difference between them.
That means:
Residuals = actual values of y - predicted values of y = 0
All values of residuals = 0, thus, mean of residuals is 0 too.
Since all the values of the residuals is 0 = their mean, there is no deviation of residuals from their mean.
Thus, the standard deviation of the residuals in this case is 0.
Learn more about correlation coefficient here:
https://brainly.com/question/10725272
