The Correlation Coefficient
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Who created the Product-Moment Correlation Coefficient?
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 non-linear relationship)
What is the probability formula for the coeffient?
- The square root of r2If 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 R2?
- R2 must be expressed as a proportion when taking the square root (not a percentage)
- r varies between -1.0+1.0 whereas R2 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
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