# How to find the correlation coefficient

**A. Colin Cameron, Dept. of Economics, Univ. of Calif. - Davis**

This January 2009 help sheet gives information on - Correlation coefficient.
- Calculation using the Data Analysis Add-in.
- Calculation using the CORREL function.

CORRELATION COEFFICIENT

The **correlation coefficient** between two series, say x and y, equals

Covariance(x,y) / [Sqrt(Variance(x)) * Sqrt(Variance(y))]

where

- Covariance(x,y) is the sample covariance between x and y: (1/(n-1)) × Σ
_{i}(x_{i}- xbar)(y_{i}- ybar) - Variance(x) is the sample variance of x: (1/(n-1)) × Σ
_{i}(x_{i}- xbar) 2 - Variance(x) is the sample variance of y: (1/(n-1)) × Σ
_{i}(y_{i}- ybar) 2

**CALCULATION USING THE DATA ANALYSIS ADD-IN**

The data used are

in carsdata.xls

- In the Data Group select the Data Analysis Add-in
- Select Correlation
- Fill out the Correlation dialog box as below

Hit enter yields

This can be extended to several series.

For example if there are data in columns A, B, C, D and E then the array chosen is A1:E6 and produces a 5 x 5 table of correlations.

CALCULATION USING THE CORREL FUNCTION

This does not require the Data Analysis Add-in

- Click on the cell you want result to appear on.
- On the Formula Tab select the Function Library group and More Functions and Statistical
- Select Correlation and fill out the dialog box as below

Source: cameron.econ.ucdavis.edu

Category: Forex