Question

Assume that we have the usual Simple Linear Regression model given by: y = 0 + 1x +

Show that in this case:
2 = xy2
Where ₓᵧ is the correlation coefficient between x and y.

Answer 1

The connection between the correlation coefficient (r) and the linear regression model can be explained by noting that r measures the linear association between x and y, and its square (r²) represents the variance in y explained by x.

Step-by-step explanation:

The question seems to contain a typo, but the essence of the query is about showing the relationship between the correlation coefficient (notated as r) and the linear regression model y = β0 + β1x. The correlation coefficient, r, is a measure of the linear association between the independent variable x and the dependent variable y. The value of r lies between -1 and +1, where a positive r indicates that x and y tend to increase or decrease together, whereas a negative r indicates that as x increases, y decreases, or vice versa.

The coefficient of determination, denoted as r², is the square of the correlation coefficient and represents the proportion of the variance in y that can be predicted from x using the regression line. If we assume a simple linear regression model y = β0 + β1x, then the correlation coefficient r would be the standardized version of β1, and hence r² would represent the explanatory power of x on y in the regression model.