Correlation

Correlation and Linear regression

Think back to our copier example.

Only 10 sales people were sampled.

Could our strong correlation coefficient be due to chance?

How can we tell?

Sounds Fun - Right?

t-Test For the Correlation Coefficient

... with n-2

degrees of freedom

Practice!

A sample of 25 mayoral campaigns in medium-sized cities with populations between 50,000 and 250,000 showed that the correlation between the percent of the vote received and the amount spent on the campaign by the candidate was .43. At the .05 significance level, is there a positive association between the variables?

Remember the Steps!

A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be .86. At the .05 significance level, can we conclude that there is positive correlation in the population?

How strong is the correlation between the # of sales calls and the # of copiers sold?

Correlation Analysis

Regression Analysis

Regression equation - An equation that expresses the linear relationship between two variables

A group of techniques to measure the relationship between two variables.

What do we do first?

Graph something (of course!)

Remember Spurious Correlations?

Independent Variable

Dependent Variable

Correlation Coefficient

A measure of the strength of the linear relationship between two variables.

1. Sample correlation coefficient

identified by r.

2. Shows direction and strength.

3. Ranges from -1 to +1.

So ... let's make some predictions.

Correlation Coefficient

Remember sample standard deviation?

Some stuff you really don't need to know just yet...