10_corrnreg

# 10_corrnreg - Correlation and Regression Analysis of...

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Correlation and Regression Analysis of Continuous Independent Variables and Non-experimental Data

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Continuous vs Nominal IVs Nominal IVs are analyzed with t or ANOVA (e.g., trained vs. control) Continuous IVs are analyzed with correlation or regression (e.g., SAT scores predict GPA) Design. Variable assignment vs. variable measurement implication for inference.
Correlation Coefficient aka Pearson Product-Moment Correlation Coefficient. Correlation coefficient summarizes the relations b/t 2 variables, both direction and degree (closeness). Scattergram summary. Sample r; population ρ (Greek rho). Can take values from –1 thru 0 to +1. Sign tells direction (+ or -); magnitude or value tells closeness or degree.

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Positive Correlation 75 72 69 66 63 60 Height 210 180 150 120 90 Weight Plot of Weight by Height N Ht. In. Wt. Lbs. 1 60 102 2 62 120 3 63 130 4 65 150 5 65 120 6 68 145 7 69 175 8 70 170 9 72 185 Example of a Positive Correlation 10 74 210 When one variable increases, the other also increases.
Negative Correlation 400 300 200 100 0 Study Time 30 20 10 0 Errors Plot of Errors by Study Time N Study Time Minutes # Error 1 90 25 2 100 28 3 130 20 4 150 20 5 180 15 6 200 12 7 220 13 8 300 10 9 350 8 Example of a Negative Correlation 10 400 6 When one variable increases , the other decreases .

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Zero Correlation 1.9 1.8 1.7 1.6 1.5 Toe Size 700 600 500 400 SAT-V Plot of SAT-V by Toe Size N SAT- V Toe Size 1 450 1.7 2 480 1.8 3 500 1.6 4 510 1.8 5 520 1.9 6 550 1.7 7 600 1.6 8 630 1.7 9 650 1.9 Example of a Zero Correlation (*Strictly speaking, no linear relation.) 10 700 1.7 No relation*: when one variable increases , the other variable neither increases nor decreases.
Correlation Sign & Magnitude The sign indicates the direction of the relationship.

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## This note was uploaded on 05/21/2011 for the course PSY 3213 taught by Professor Staff during the Fall '08 term at University of South Florida.

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10_corrnreg - Correlation and Regression Analysis of...

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