# crov - Correlation Regression 1 Correlation and Regression...

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Correlation & Regression 1 Correlation and Regression There are two major different types of data analysis, depending on the type of IV Nominal IVs use t or ANOVA Continuous IVs use correlation or regression Linear correlation The correlation coefficient is a number that summarizes the direction and degree (closeness) of linear relations between two variables. The correlation coefficient is also known as the Pearson Product-Moment Correlation Coefficient . The sample value is called r , and the population value is called ρ (rho). The correlation coefficient can take values between -1 through 0 to +1. The sign (+ or -) of the correlation affects its interpretation. When the correlation is positive ( r > 0), as the value of one variable increases, so does the other. For example, on average, as height in people increases, so does weight. N Ht. In. Wt. Lbs. 1 60 102 2 62 120 3 63 130 4 65 150 5 120 6 68 145 7 69 175 8 70 170 75 72 69 66 63 60 Height 210 180 150 120 90 Weight Plot of Weight by Height 9 72 185 10 74 210 Example of a Positive Correlation If the correlation is positive, when one variable increases, so does the other.

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Correlation & Regression 2 If a correlation is negative, when one variable increases , the other variable decreases . N Study Time Minutes # Error 1 90 25 2 100 28 3 130 20 4 150 5 180 15 6 200 12 7 220 13 8 300 10 400 300 200 100 0 Study Time 30 20 10 0 Errors Plot of Errors by Study Time 9 350 10 400 Example of a Negative Correlation If the correlation is negative, when one variable increases, the other decreases.
Correlation & Regression 3 If there is no relationship between the two variables, then as one variable increases, the other variable neither increases nor decreases. In this case, the correlation is zero. 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 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 9 650 1.9 10 700 1.7 Example of a Zero Correlation Note that as either toe size or SAT increases, the other variable stays the same on average. The sign of the correlation indicates the direction of the relationship The absolute value of the correlation indicates the strength of the relationship Some other examples of positive, negative, and zero correlations: Variable X Variable Y Correlation Salary Taxes paid Positive Shyness N of people greeted at party Negative Price of car Prestige of car Positive Price of tennis shoe Foot support Zero Time of use of flashlight Battery life Negative Weight in lbs.

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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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crov - Correlation Regression 1 Correlation and Regression...

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