Linear regression - Basic Statistics for Behavioral Sciences - Lecture Notes, Study notes of Statistics for Psychologists

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Basic Statistics for

The Behavioral Sciences

LECTURE NOTES

Ch. 17. Linear regression I. Relationship between correlation and regression A. Correlation; no prediction is involved, just have two sets of scores, no time gap between two tests. B. Regression; we are interested in prediction of Y using X scores. X is called predictor variable, Y is criterion variable. C. Formula for a linear regression line Y ˆ^ = bX + a where, Y ˆ^ = criterion variable X = predictor variable b = slope of the line = ΔY/ΔX

vertical rise = ────────────── horizontal run

a = Y-intercept.

II. Situation A. In the behavioral or social sciences, we hardly find a perfect linear line where all points are on the line (e.g.). B. The regression problem is to find the "best" line through a swarm of points to reflect a linear relationship between two variables because there are infinitely many lines reflecting linear relationship. C. We define the "best" line based on the Least Squares Criterion; this least squares line minimizes the sum of squared errors about the prediction line.

Y = Y ˆ^ + e ───> e = Y - Y ˆ Σe = Σ(Y - Y ˆ^ ) = 0 Σe² = Σ(Y - Y ˆ^ )² ≤ Σ(Y - Y ˆ^ + C)²