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The Correlation Coefficient
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Who created the Product-Moment 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 non-linear 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
Author
camturnbull
ID
297182
Card Set
The Correlation Coefficient
Description
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Updated
2015-03-01T15:22:50Z
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