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