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Lecture 5

Lecture 5 - Linear Regression - October 11.docx

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Department
Psychology
Course
PSY201H1
Professor
Kristie Dukewich
Semester
Fall

Description
October 11, 2012. Lecture 5 – Linear Regression Dividing what we can and can’t explain using r xy  For any given person o Explainable + Unexplainable = Deviation Score o (Y’ - Ῡ) +i(Y – Y’i = (Y - Ῡ) 2 2 2 o ∑(Y’ - Ῡ) + ∑iY – Y’) = i(Y - Ῡ)  Standard error of the estimate o Across all our participants, what’s the average amount of unexplained variation in Y, given X? o Interpret like a standard deviation o E.g., 68% of scores fall +/-1 SE around the regression line  Interpreting the Standard Error of the Estimate (SE) o Standard deviation assumes you have scores that are normally and equally distributed around the mean. o Standard error assumes you have scores that are normally and equally distributed around the regression line? (refer to slides)  Homoscedastic  Less homoscedastic when distribution along regression line varies Least Squares Regression Equation  Line that best fits scattered scores o Smallest SE possible when using X to predict Y o Maximizes ability to predict Y using X o Ensures only one line can fit  “Least Squares” Criterion2 o Minimizes ∑(Y – Y’) o Y’ = predicted scores Practical Comparison  Correlation o Can’t manipulate variables (either for ethical or practical reasons o Measure relationships among variables o No causation o
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