The Correlation Coefficient
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Who created the ProductMoment Correlation Coefficient?
Karl Pearson

What is the correlation coefficient?
 A model dependent measure of the strength of relationship between two variables
 It provides an appropriate measure of the strength of a relationship only within the context of linear regression

What happens if the relationship between variables is non linear?
The use of the correlation as a descriptive statistic is misleading

What does the interpretation of the coefficient assume?
 An underlying bivariate normal distribution
 Normally distributed condition distributions
 Homogeneity of variance

What are the relationship denotations for the correlation coefficient?
 When there is a perfect positive linear
 relationship, r = 1.0
 When there is perfect negative linear
 relationship, r = 1.0
 When r = 0.0 there is either no relationship,
 (or possibly a nonlinear relationship)

What is the probability formula for the coeffient?
 The square root of r^{2}
 If the regression coefficient is negative the r value should also be made negative
 This means the correlation coefficient is the square root of the proportion of variability accounted for by the straight line regression

What must be remembered when using R^{2}?
 R^{2} must be expressed as a proportion when taking the square root (not a percentage)
 r varies between 1.0+1.0 whereas R^{2} varies between 0.0+1.0

Give a formula to relate the correlation coefficient to the regression coefficient
r= slope x the square root of the sum of squares of x over the sum of squares of y

What happens if X and Y are converted into standard scores (M=0.00, SD=1.0)
 The value of the coefficient will not be affected
 The SD will be the same for both