2. Explained and unexplained variance
SStotal = SSexplained + SSunexplained
SStotal = SSexplained SSunexplained N

3. Explained and unexplained variance
r2XY = 1 -
σ2Y’ [ =unexplained]
σ2Y [ =total]

4. Explained and unexplained variance
r2XY = 1 -
σ2Y’ [ =unexplained]
σ2Y [ =total]
σ2Y - σ2Y’ =
σ2Y
r2 is the proportion explained variance to the total variance.

5. What is r? r

6. 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.

7. 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.