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Lecture

Linear regression and correlation.docx

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Department
Psychology
Course
PSYB07H3
Professor
Dwayne Pare
Semester
Winter

Description
Linear regression and correlation: -regression line, least sq, best-fit line, trend line -linear model -age (x,IV) predicts weight (y,DV) Regression lien: -how to find— -Y is actual data point Minimize sum(y-y^)2 Calculating regression line; -y^=bx +a -y^-predicted y value b=slope a= y-intercept b: -amount of y^ changes by one unit change of x -1 unit change in x? how much change in y^ 2 -b=cov xy x Eg.) x(line on top)=6.5 y (line on top)=8 sx=12.02 COX =XY58 b= 0.63 COV= sum (x-x[line ontop]) (y-y[line ontop])/n-1 =(1-6.5) (5-8) + (1-6.5) (6-8) +…….+(12-6.5) (14.4-8)+ (12-6.5) (14.9-8)/120-1 =7.58 b = COV/S =x7.58/12.02 = 0.63 a: -y-intercept Eg) y^=bx+a =0.63x+a a=y[line on top]-bx[line on top] =y[line on top] – 0.63x[line on top] =8-0.63(6.5)=3.94 y^=bx+a =0.63x+3.94 Draw regression line: -Always needs 2 points -(x[line on top],y[lie on top]) and (0, a) Prediction; Eg) 2.5 month-old-- y^=0.63(2.5)+3.94=5.52 5-year old compared to 60 month-old-- Y^= 0.63(60+3.94=41.81 ---not really accurate---b/c--Over-generalization Over-generalization Linearity: Correlation: -how good is our prediction? -the
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