**Regression and correlation** analysis can be used to describe the nature and strength of the relationship between two continuous variables. Correlation focuses primarily on an association, while regression is designed to help make predictions.

**CORRELATION**

A simple relation between two or more variables is called as correlation. If the change in one variable effect the change in another variable, then the variables are said to be correlated.

**Example:** Price and Demand of a certain commodity.

**TYPES OF CORRELATION**

There are 3 types of correlation depending on nature, they are as follows.

**1. Positive Correlation:** If both the variable deviate in the same direction, then it is said to be the Positive correlation.

**Example:** Income and Expenditure of the certain family.

**2. Negative Correlation:** If both the variables deviate in the opposite directions, then it is said to be the Negative correlation.

**Example:** Price and Demand of a commodity.

**3. Zero Correlation:** If the change in one variable does not depend on the another variable, then the correlation between these variables is said to be Zero Correlation.

**Example:** Heights of students and their marks.

**METHODS OF CORRELATION**

The following methods are commonly used for finding the Correlation Coefficient.

1. Karl Pearson’s correlation coefficient.

2. Spearman’s Rank correlation coefficient.

3. Least Squares Method.

**REGRESSION**

Regression literally means going back or stepping back towards the average. Regression analysis is a mathematical measure of an average relationship between two or more variables in terms of original units of data.

In regression analysis, there are two variables.The variable whose value is influenced it is called as “Dependent Variable” and the variable which influences the value of the other variable is called as “Independent Variable”.

**Example:*** Controlling the supply of goods may affect the price of the good.*

**REGRESSION LINES**

1. Regression line of X on Y

2. Regression line of Y on X

**TYPES OF REGRESSION**

There are various types of regressions based on their functionality, some of them are as follows.

**1.Simple linear Regression:** Simple linear regression is a statistical method that helps to summarize and study relationships between two continuous variables: one Dependent variable and one

Independent variable.

**2.Multiple linear Regression:** Multiple linear regression examines the linear relationships between one Dependent variable and two or more Independent variables.

**COMPARISON TABLE**

Now let us see some of the differences between CORRELATION and REGRESSION below given table.

CORRELATION | REGRESSION |
---|---|

The main purpose of correlation analysis is to predict which are the most dependable forecasts. | The main purpose of regression analysis is to predict or estimate the unknown variable with the help of known variable. |

Scope | |

Correlation analysis has limited applications. | Regression analysis has wider applications. |

Nature of variables | |

In correlation both the variables are mutually dependent. | In regression one variable is dependent and other variable is independent. |

Range | |

Correlation coefficients can range from -1.00 to +1.00. | In regression anlysis if byx > 1, then bxy |

Responding Nature | |

The correlation coefficient is independent of the change of Origin or change of Scale. | The regression coefficient is independent of the change of Origin but dependent on the change of Scale. |

Nature of Coefficient | |

The correlation coefficient is symmetrical and also mutual. | Regression coefficient is not symmetrical. |

Exceptional Cases | |

Sometimes there may exist Non-sense correlation in the correlation analysis. | There is no such thing as a Non-sense regression in regression analysis. |

Measures | |

Correlation measures the degree to which two variables move together, | Regression describes the fundamental level the nature of any linear relationship between two variables. |

Association | |

The correlation coefficient measures the extent and direction of a linear association between two variables. | Linear regression allows us to describe one variable as a linear function of another variable. |

Relationship | |

Correlation is confined to the linear relationship between variables only. | Regression studies linear and Non-linear relationships also. |