# Regression: Introduction–Question 3

A useful statistic associated with regression analysis and correlation is percentage of explained variance. The percentage of explained variance tells us how well one variable (Y) can be predicted from another variable (X) in terms of the variance of Y that can be explained by knowing scores on X. The percentage of explained variance is closely related to the correlation (r); in fact, to get the proportion of explained variance you just take the correlation and square it. The percent is that value times 100.

Question 3: For our example, we have a correlation of r = .90. What portion of the variance of Y could we say is explained here? Technically what we are looking at is the amount of variance in points scored that can be explained by attendance.

#### 90%

Incorrect.

90% of the variance would be explained if you had r = .95 because .95 squared is .9025. Maybe you forgot to square your correlation?

#### 81%

Correct!

81% is the variance explained when r = .90, because .9x.9 = .81 = 81%.

#### 95%

Incorrect.

95% of the variance would be explained if you had r = .97. Maybe you took the square root of the correlation instead of squaring it?

#### 0.81%

Incorrect.

0.81% of the variance would be explained if you had r = .09. Maybe you forgot to multiple by 100?

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