Answer :
0.64 or 64% of the variance for the y scores is predicted by its relationship with x.
What is coefficient of determination?
The percentage of the variation in the dependent variable that can be predicted from the independent variable is known as the coefficient of determination, abbreviated R2 or r2, in statistics.
How to find the variance for the y scores?
given that
A set of n = 25 pairs of scores (x and y values) has a pearson correlation of r = 0.80.
now we have to find the variance for the y scores.
here, r=0.80 then [tex] {r}^{2} = 0.64[/tex]
which means 0.64 or 64% of the variance for the y scores is predicted by its relationship with x.
[tex]r = \sqrt{ {r}^{2}} \: or \: \sqrt{ {r}^{2}} \\ 0.80 = \sqrt{ {0.80}^{2} } \\ 0.80 = 0.80[/tex]
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