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PSYC 51A (16)
Lee Yoona (16)
Lecture 16

PSYC 51A Lecture 16: Psyc 51A: Ch.16: Regression
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Department
Psychology
Course
PSYC 51A
Professor
Lee Yoona
Semester
Spring

Description
Correlation ● Describe association b/w two variables ○ The order of association does not matter ● One statistics (r) combines slope and scatter ● r statistics is independent of the scale of the variables ● Order of the two variables does not matter Regression ● Predict exact value of one variable Y from other variable X ○ Order matters ● Three statistics (b, a anY.X quantify slope (b), y-intercept (a), and scY.X,r (s separately ● Regression statistics are dependent on the scale of variables ● Order of two variables matter Questions from Univariate Statistics vs. Regression ● Is there any mean difference on weight loss depending on different treatments? ○ Within subject design ○ Correlation: Consider all individual score ■ Positive/negative correlation ● Univariate statistics don’t indicate anything except that the groups don’t differ. Mean differences (not all scores taken into consideration). Each statistic (Mean and SD) summarizes information about just one variable ● Need a summary statistic that is computed using information from two variables. What if we want to ask a question, “if someone lost 3 lbs using drug, what is the predicted range of their weight loss with behavioral therapy? (Here, we want to predict the possible changes in Y by changes in X. In this example, Y=behavioral therapy & X=drug). ● PS. Correlation: X variable is positively/negatively correlated with Y variable ● Curvilinear relationship ● Linear relationship - straight line relationship ○ We will only deal with this type of relationship ○ Need a statistic that captures the information in a scatter plots like this ● The general form of a predictive equation for a straight line relationship is: (weight loss with Therapy) = b(weight loss with No Drug) + a ● Ŷ = bX +a ● Where ○ Y - dependent variable X ○ Ŷ - estimate of dependent variable (values predicted by the line equation) ○ X - independent variable ○ b - slope ○ a - y-intercept ● Slope = b = ΔY = Y1-Y2 ΔX = X1-X2 ● slope is positive or negative direction; magnitude = +∞ ● y-intercept = a ; Y value where X= 0 (where the line crosses the Y axis) How do we calculate b and a? 1. Scatter (error from the predicted line) ● For univariate distributions we computed variability using squared deviation between sampled values and the mean, SS = Σ(X-M ) and SS = Σ(Y-M ) 2 X X Y Y ● For bivariate distributions we use the squared deviation between the sampled values and the value predicted by the straight line equation, residual(Y- 2 Ŷ) ● The criterion for the best fitting line is to minimize the sum of squared
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