## Correlation Statistics

Metric | Formula | Description | Result |
---|---|---|---|

Pearson Correlation Coefficient / R Correlation |
| where, x̄ is the mean of x, ȳ is the mean of y and xi,yi are the individual values in sets of x and y | 0.9424 |

Count of dataset 1 | Count = n | where, n is the Number of items in dataset 1 | 18 |

Count of dataset 2 | Count = n | where, n is the Number of items in dataset 2 | 18 |

Sample Std Deviation | S = Square root((1/ n - 1 ) * ∑ i( x i - x ¯ ) 2) | where, n is Number of observations in sample, xi is individual values in sample and x ¯ is Sample mean | 6.546 |

## Correlation Analysis / Inference

Correlation Range | Description |
---|---|

1 | 100% Positive Correlation |

>= 0.7 < 1 | Strong Positive Correlation |

>= 0.5 < 0.7 | Moderate Positive correlation |

>= 0.3 < 0.5 | Low Positive Correlation |

> 0 <= 0.3 | No Correlation |

0 | No Correlation |

< 0 >= -0.3 | No Correlation |

>= -0.3 < -0.5 | Low Negative Correlation |

>=-0.5 < -0.7 | Moderate Negative Correlation |

>= -0.7 < - 1 | Strong Negative Correlation |

-1 | 100% Negative Correlation |

## What is Coefficient Correlation and R?

Correlation Coefficient is the strength and relationship between two variables and the direction of it (+ve or -ve).

For example: Age vs Height have a positive correlation during the growing period.

Calories Consumed vs Weight has a positive correlation.

Relative Humidity and Temperature have a negative correlation

Density and Volume have a negative correlationR stands for Regression and is the correlation Coefficient between 2 sets of variables.

R value ranges from -1 to 1. A value of 0 for R indicates that there is no correlation between 2 sets of variables.

## Significance of R

Significance of R is a measure of reliability. It is used to indicate if there is significant linear relationship between the variables and if it can be used for predictions

If R is significant, it indicates that the coefficient value and Scatter plot can be used for prediction of outcomes.based on the significant linear relationship between 2 variables

If R is NOT SIGNIFICANT, it means insignificant relationship between the variables and it cannot be used reliably to predict any outcome

This is used as a pre-requisite test before applying the Pearson's coefficient formula and analyzing

## Frequently Asked Questions on R Calculator

correlation coefficient r = Σ(xi - x̄)(yi - ȳ) / √(Σ(xi - x̄)2Σ(yi - ȳ)2 ).

where,where, x̄ is the mean of x, ȳ is the mean of y and xi,yi are the individual values in sample sets of x and y.

It ranges between -1 to 1

1 or -1 depending on the variables under consideration

1 (positive) and -1 (negative)

Strong Negative Correlation

Moderate Positive correlation

Negligible or No Correlation