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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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**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…**• 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!**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**When they are imperfectly correlated, i.e., rxy ≠ 1 or -1**zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (sy / sx) aYX = Y - bYXX _ _**When they are imperfectly correlated, i.e., rxy ≠ 1 or -1**zy’ = rxyzx Y’ = bYXX + aYX bYX = rYX (sy / sx) aYX = Y - bYXX _ _**Assumptions**• Linearity • Homoscedasticity**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.**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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