Correlation Analysis
How do you measure correlation?
- Association (linear relationship) between variable 1 and 2 - magnitude of the direction (positive or negative relation) of the association
What are the properties of the correlation coefficient
-1 <= r > = 1 if r < 0, X and Y are negatively correlated if r>0 then X and Y are positively correlated if r=0 then X and Y are NOT correlated the closer r is to -1 or 1 the stronger the correlation
How do you get correlation?
Divide covariance by standard deviations
What does correlation measure?
Measures the DEGREE to which there is an association between TWO INTERVAL SCALED VARIABLES
Does correlation imply a causal relationship?
NO
Can you make predictions from correlations?
NO . only from regressions
What scales can be used with correlation?
ONLY interval and ratio
What is an example where you'd use correlation?
Price and consumer's purchase intention
What does association measure?
The strength of the relationship between two or more variables
What does regression do?
Used to understand the NATURE of the relationship between two or more variables
Does covariance change based on use of measurement?
YES, correlation fixes this by standardizing it
What does covariance measure
measure of association
What does partial correlation coefficient measure?
provides a measure of association between two variables after controlling for the effects of one or more additional variables
What is r (correlation) independent of?
sample size and units of measurement
What is positive correlation
tendency for a high value of one variable to be associated with a high value of the second
What is negative correlation
tendency for a high value of one variable to be associated with a low value in the second
Why do you divide the covariance by n-1
to ensure that measure doesn't increase just because sample size increased
What type of test is correlation always?
two tail
