## Correlation

### What is need of correlation?

- Is there any association between hours of study and grades?
- Is there any association between number of temples in a city & murder rate?
- What happens to sweater sales with increase in temperature? What is the strength of association between them?
- What happens to ice-cream sales v.s temperature? What is the strength of association between them?
- How to quantify the association?
- Which of the above examples has very strong association?
**Correlation**

## Correlation coefficient

- It is a measure of linear association
- r is the ratio of variance together vs product of individual variances.

Correlationcoefficient(r)=CovarianceofXYSqrt(VarianceX∗VarianceY)

- Correlation 0 No linear association
- Correlation 0 to 0.25 Negligible positive association
- Correlation 0.25-0.5 Weak positive association
- Correlation 0.5-0.75 Moderate positive association
- Correlation >0.75 Very Strong positive association

### Practice : Correlation Calculation

- Dataset: AirPassengers\AirPassengers.csv
- Find the correlation between number of passengers and promotional budget.
- Draw a scatter plot between number of passengers and promotional budget
- Find the correlation between number of passengers and Service_Quality_Score

In [1]:

```
import pandas as pd
air = pd.read_csv("datasets\\AirPassengers\\AirPassengers.csv")
air.shape
```

Out[1]:

In [2]:

```
air.columns.values
```

Out[2]:

In [3]:

```
#Find the correlation between number of passengers and promotional budget.
import numpy as np
np.corrcoef(air.Passengers,air.Promotion_Budget)
```

Out[3]:

In [4]:

```
#Draw a scatter plot between number of passengers and promotional budget
import matplotlib.pyplot as plt
%matplotlib inline
plt.scatter(air.Passengers, air.Promotion_Budget)
```

Out[4]:

In [5]:

```
#Find the correlation between number of passengers and Service_Quality_Score
np.corrcoef(air.Passengers,air.Service_Quality_Score)
```

Out[5]:

### Beyond Pearson Correlation

- Correlation coefficient measures for different types of data

Variable Y\X | Quantitative /Continuous X | Ordinal/Ranked/Discrete X | Nominal/Categorical X |

Quantitative Y | Pearson r | Biserial rb | Point Biserial rpb |

Ordinal/Ranked/Discrete Y | Biserial rb | Spearman rho/Kendall’s | Rank Biserial rrb |

Nominal/Categorical Y | Point Biserial rpb | Rank Biserial rrb | Phi, Contingency Coeff, V |