Notes10 - Correlation and Regression Analysis of Continuous...

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1 Correlation and Regression Analysis of Continuous Independent Variables and Non-experimental Data 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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2 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 . 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.
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3 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 - Tampa.

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Notes10 - Correlation and Regression Analysis of Continuous...

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