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Explained and unexplained variance

SS total = SS explained + SS unexplained. N. N. N. Explained and unexplained variance. SS total = SS explained + SS unexplained. σ 2 Y’ [ =unexplained]. σ 2 Y [ =total]. Explained and unexplained variance. r 2 XY = 1 -. σ 2 Y’ [ =unexplained]. σ 2 Y [ =total].

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Explained and unexplained variance

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

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

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

  4. What is r? r

  5. 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.

  6. 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.

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