# Correlation

Now we are going to look at the linear relationship between two variables! Visually, we can use a **scatter plot** to show the relationship between two variables (X and Y). The variable on the x-axis is known as the *independent variable* and the variable on the y-axis is known as the *dependent variable*.

We can use `df.plot.scatter()`

to create scatter plots in Python.

In addition to looking at two variables graphically, we can also calculate a statistic that mathematically represents the linear relationship between X and Y. We can measure the strength of this linear relationship using the **Correlation Coefficient.**

## CORRELATION COEFFICIENT ( r )

The correlation coefficient (often represented by the letter, r) measures the strength of the linear association between two variables (X and Y). It measures how tightly points are clustered around a line. It is relevant when the scatter plot forms a linear trend.

*The correlation coefficient is always between –1 and 1.*

The closer the points hug a line with a positive slope, the closer r is to +1. The closer the points hug a line with a negative slope the closer r is to -1.

If there is no association between x and y then the correlation coefficient is 0 and the scatter plot has no linear pattern.

### In other words,

- A correlation of 1 or -1 means you can perfectly predict one variable knowing the other.
- A correlation of 0 means that knowing one variable gives you no information about the other.

Here are some examples below:

## How to mathematically calculate the correlation coefficient:

*In words:*

- Convert x-values and y-values to standard units (z-scores). Z-scores tell you how many SDs a value is above or below average.
- Multiply each x-value (in standard units) by each corresponding y-value (in standard units)
- The correlation coefficient is the sum of the products divided by n-1.

*In symbols:*

## Correlation in Python

In Python, the following code will display the correlation coefficient for every numeric column (variable) in a DataFrame:

`df.corr()`

The output is called a **correlation matrix.** Finding the correlation matrix can be an important part of *Exploratory Data Analysis* to see if there are any linear relationships between two variables!

# Example Walk-Throughs with Worksheets

### Video 1: Correlation Examples

### Video 2: Outliers Impact on Correlation

### Video 3: Correlation Coefficient in Python

# Practice Questions

**Q1**: Which of the following cannot be a correlation coefficient?

**Q2**: The diamond dataset has 10 variables in total( including 3 categorical variables and 7 numeric variables). What is the sum of all elements in the diagonal of the correlation matrix?