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Monday, October 8 Wednesday, October 10. Correlation and Linear Regression. z y = z x When X and Y are perfectly correlated. We can say that z x perfectly predicts z y. z y ’ = z x Or z y = z x. ^. When they are imperfectly correlated, i.e., r xy ≠ 1 or -1. z y ’ = r xy z x.

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## Monday, October 8 Wednesday, October 10

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**Monday, October 8 Wednesday, October 10**Correlation and Linear Regression**zy = zx**When X and Y are perfectly correlated**We can say that zx perfectly predicts zy**zy’ = zx Or zy = zx ^**When they are imperfectly correlated, i.e., rxy ≠ 1 or -1**zy’ = rxyzx**Example from hands…**• Let’s double-check our understanding of what a correlation coefficient is with respect to z-scores on X and Y variables.**When we want to express the prediction in terms of raw**units: zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (σy / σx) aYX = Y - bYXX _ _**SStotal = SSexplained+SSunexplained**N N N Explained and unexplained variance SStotal = SSexplained + SSunexplained**σ2Y’ [ =unexplained]**σ2Y [ =total] Explained and unexplained variance r2XY = 1 - σ2Y - σ2Y’ = σ2Y r2 is the proportion explained variance to the total variance.

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