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Monday, October 8 Wednesday, October 10

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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  1. Monday, October 8 Wednesday, October 10 Correlation and Linear Regression

  2. zy = zx When X and Y are perfectly correlated

  3. We can say that zx perfectly predicts zy zy’ = zx Or zy = zx ^

  4. When they are imperfectly correlated, i.e., rxy ≠ 1 or -1 zy’ = rxyzx

  5. 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.

  6. When we want to express the prediction in terms of raw units: zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (σy / σx) aYX = Y - bYXX _ _

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

  8. 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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