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# Monday, November 9

Monday, November 9. Correlation and Linear Regression. You will not leave the room until…. you have understood that a correlation is a systematic quantitative expression of the proportion of explained and unexplained co-variation of two variables. You will not leave the room until….

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## Monday, November 9

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1. Monday, November 9 Correlation and Linear Regression

2. You will not leave the room until… • you have understood that a correlation is a systematic quantitative expression of the proportion of explained and unexplained co-variation of two variables.

3. You will not leave the room until… • you have understood that a correlation is a systematic quantitative expression of the proportion of explained and unexplained co-variation of two variables … and you love knowing this fact!

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

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

6. Example from hands…

7. When they are imperfectly correlated, i.e., rxy ≠ 1 or -1 zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (sy / sx) aYX = Y - bYXX _ _

8. When they are imperfectly correlated, i.e., rxy ≠ 1 or -1 zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (sy / sx) aYX = Y - bYXX _ _

9. Assumptions • Linearity • Homoscedasticity

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

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

12. Point-biserial correlation rpb • A correlation coefficient r that is calculated when one of the variables being correlated has only two levels, which are assigned arbitrary values (e.g., 0, 1). • This coefficient is useful in expressing the effect size of an independent samples t-test, as the proportion of the variance in the dependent variable that is explained by the independent variable.

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