## Introduction to Correlation Example

The following Correlation examples outline the most common set of Correlation examples:

**Example #1**

The height and weight of 5 students in a class are mentioned below:

Student Name |
Height (in cm) |
Weight (in kgs) |

Frank | 160 | 53 |

Leo | 165 | 61 |

Jerry | 172 | 74 |

Celeste | 150 | 51 |

Tracy | 180 | 82 |

Based on this simple data of Height and Weight of students we can observe a correlation pattern that is positive in nature. The data implies that with greater height weight also increase and inference drawn from the correlation implies that taller people are usually heavier in weight.

Similar types of examples can be observed in the correlation between Sales of Refrigerators and Increase in Temperature which highlights a Positive Correlation.

**Example #2**

Provided below are the speed of different trains and the amount of time taken to reach the same destination.

Train Name |
Speed (in km/hr) |
Time Taken (in hrs) |

A | 40 | 5 |

B | 50 | 4 |

C | 80 | 2.5 |

Here we can easily observe the Negative Correlation that Speed and Time are taken has. With greater the speed of Train, less the number of hours taken to reach the destination.

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### Example of Correlation (With Excel Template)

Let’s take an example to understand the calculation of the Correlation in a better manner.

#### Correlation – Example #1

**The following table exhibits the returns on two stocks held by ABC Limited in their Model Portfolio for the last 5 years. Based on the same let us calculate and interpret the correlation between the two stocks.**

**Solution:**

We will try to find the correlation between the two assets using the Pearson Correlation Coefficient which is one of the most popular methods used for measuring Linear Relationship between two variables which in our case is the two stocks namely: Facebook and Amazon.

Average Mean for 5 years is calculated as

Standard Deviation is calculated as

Sum of C*D is calculated as

Covariance is calculated as

Correlation is calculated using the given formula below

**Pearson Correlation Coefficient = ρXY = covXY / σXσY**

The Correlation of Negative 0.7501 implies a low to high Negative Correlation between the two stocks.

The correlation discussed through the above example is basically the Pearson Correlation Coefficient method and is helpful in measuring the linear relationship between the two variables which in our case was the two stocks in the model portfolio.

#### Correlation – Example #2

**Let’s take another example and understand correlation measure using other popular approach known as Spearman Rank Correlation. It is an Ordinal Correlation measure and correlation calculation is undertaken based on the relationship between the rank of the variables.**

**Solution:**

X is calculated as

Sum of (di^2) is calculated as

The following table exhibits the returns on two stocks X and Y for the last 5 months. Based on the same let us compute and interpret the correlation between the two stocks using the Spearman Rank Correlation method.

Correlation is calculated using the formula given below

**Spearman Correlation = ρ = 1 – [(6Σd ^{2}) / n(n^{2} – 1)]**

In order to calculate correlation using the Spearman Correlation method, we will first rank the returns of Stock X from lowest to highest in the second column and similarly, the returns for Stock Y are listed in the third column for each respective month. The fourth and fifth columns list the return for Stock X and Y rank-wise. In the sixth column, the difference in rankings for each month is listed and in the seventh column, the sum of squared differences in rankings is determined.

#### Correlation – Example #3

**The following data is observed from the medical reports of 10 patients categorized on the basis of their Age and Blood Pressure Level. Based on the same let us calculate the Correlation Coefficient.**

**Solution:**

Sum of is calculated as

Correlation is calculated using the formula given below

**r = NΣxy – (Σx)(Σy) / √ [NΣx ^{2} – (Σx)^{2}][NΣy^{2} – (Σy)^{2}]**

### Conclusion

Correlation examples can be encountered in our day to day life and are useful in understanding the relationship between two things. Researchers often use it for predicting purpose as well as to validate any relationship between different variables. The correlation coefficient varies from -1 to 1 values where -1 indicates a strong Negative Correlation and 1 indicates a strong Positive Correlation between the variables and a Correlation value of Zero indicates no relationship between the two variables. The above examples both simple and Practical ones are discussed to validate the Correlation concept and its relevance in statistical and other analytical studies.

### Recommended Articles

This is a guide to Correlation Example. Here we discuss how to calculate the Correlation by using its different methods with different examples. You may also look at the following articles to learn more –