Data in the form (x,y) are found to have a linear correlation coefficient of -0.

Question

Data in the form (x,y) are found to have a linear correlation coefficient of -0.90. We can conclude:

a. y values are physically connected with the x values (i.e x causes y)

b. x and y are independant

c. y can be determined from the inverse of x

d. None of the above

The data in the previous question are fitted to be a straight line by linear least squares regression. What fraction of the variability in the y data can be explained by the linear rel;ationship between x and y?

a 0.81

b. -0.81

c. 0.90

d. There is not enough infomation to say

Explanation / Answer

1. a) As x and y has a correlation coffiecient of -0.9. Implies, both are highly correlated in a negative way, meaning when x increases/decreases, y decreases/increases. Hence, we can say that x causes y, in a negative way.

2. a) R2 = (Pearson coefficient)2 = (-0.9)2 = 0.81

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