-2-1

01

23

z_est

-4 -2 0 2 4z_act

Explained and unexplained variance

SStotal = SSexplained + SSunexplained

SStotal = SSexplained + SSunexplained

N N N

Explained and unexplained variance

r2XY = 1 -

σ2Y’ [ =unexplained]

σ2Y [ =total]

Explained and unexplained variance

r2XY = 1 -

σ2Y’ [ =unexplained]

σ2Y [ =total]

= σ2

Y - σ2Y’

σ2Y

r2 is the proportion explained variance to the total variance.

What is r?

r

What is r?

• r is an expression of the linear relationship between two variables …

• Expressed in terms of standard deviation units, it puts a value on the predictability of one variable from the other.

• Expressed in terms of variance (r2), it is the term that maximizes the proportion of explained variance and minimizes the proportion of unexplained variance.

Spearman’s Rank Order Correlation

• A non-parametric test using ranked (ordinal) data.

• It does not estimate population parameters for means or variances – if you use ranked data, the parameters are known (the mean of 5 (1,2,3,4,5) ranks is always 3.