**In a heated argument, the regression shouted at correlation, “You are dumbass, you don’t even know the cause and effect of this argument”**

**Correlation**is used to measure strength of the relationship between two variables. It can be positive, negative or zero.

**Positive Correlation :**Both variables tend to move in the same direction: If one variable increases, the other tends to increase. If one decreases, the other tends to decrease.

**Negative Correlation :**Both variables tend to move in the opposite directions: If one variable increases, the other tends to decrease, and vice-versa.

*Note: The correlation coefficient may take on any value between +1 and -1.*

**Examples**

1: How are sales of ABC Company and GDP related?

2: How are annual returns on Treasury Bills and Bonds related?

**What is correlation matrix?**

When you need to calculate correlation between more than two variables, it is generally called correlation matrix. It is also called multiple correlation coefficient. Let's solve it with a case study.

*Suppose you would like to know whether there is a relationship between grades and number of hours you spend studying.*

*You can*

**download the workbook**used in this example and practice what you learn.

**Using Excel:**

**1. If you haven’t already installed the**

**Analysis ToolPak**, Click the

**Microsoft Office**button, then click on the

**Excel Options**, and then select

**Add-Ins**, Click

**Go**, check the

**Analysis ToolPak**box, and click

**Ok**.

**How to Install Analysis ToolPak**

2. Select

**Data**tab, then click on the

**Data Analysis**option, then selects

**Correlation**from the list and Click

**Ok**.

**[Data tab >> Data Analysis >> Correlation]***3. Select the*

**data range**(both independent and dependent variable) in the

**Input Range**box.

4. Check

**Labels in first row**and enter range in the

**Output Range**box and Click on

**Ok**.

Excel : Multiple Correlation Coefficient |

Output : Correlation Coefficient |

**Interpretation:**

As you see the correlation between the grades and number of hours you spend studying is a very positive correlation (84%). This means as more number of hours students study their grades improve.

Understand Correlation |

*Calculate correlation coefficient with CORREL function*

**Syntax:**

**=CORREL (range1, range2)**

For the above problem the syntax would be

*=CORREL($A$2:$A$500,*

*$B$2:$B$500*

*)*

**To calculate multiple correlation coefficient with Excel Formula, visit this link :**

**Formula Explained:Correlation Matrix****Do You Know?**

**How to deal with outliers when doing correlation?**Solution: Look at the residuals from a regression by plotting the points to a scatter diagram. If they are not normally distributed around 0 the realibility of the Pearson correlation could be unreliable.

Hi, I would like to produce a complete correlation matrix (not the diagonally halved one with 1s running down the top margin). How do I generate it in Excel or any open source Stat package? Thx

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