Correlation relating the linear relationship between two variables; in regression, we can forecast the relationship between more than two variables and can use it to classify which variables x can forecast the consequence variable y.

**Correlation** is a statistical quantity that designates the extent to which two or more variables vary together. An optimistic **correlation** designates the extent to which those variables increase or decrease in similar; a negative **correlation** designates the extent to which one variable increases as the other decreases. A mutual relationship between two or more things.

A correlation coefficient is a statistical quantity of the degree to which variations to the value of one variable forecast change to the value of another. When the variation of one variable dependably forecasts a similar variation in another variable, there’s frequently a propensity to think that means that the variation in one reasons the change in the other. However, correlation does not suggest causation. For example, an unidentified factor that effects both variables correspondingly.

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**Correlation Types**

Correlation is a measure of association between two variables. The variables are not designated as dependent or independent.

The value of a correlation coefficient can fluctuate from minus one to plus one. A minus one designates a perfect negative correlation, while a plus one designates a perfect positive correlation. A correlation of zero means there is no association between the two variables. When there is a negative correlation among two variables, as the value of one variable raises, the value of the other variable falls.

The standard error of a correlation coefficient is used to define the confidence intervals about a true correlation of zero. If your correlation coefficient falls outer of this range, then it is expressively dissimilar than zero. The standard error can be calculated for interval or ratio-type data.

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__Example__

__Example__

A company desired to know if there is an important association between the total number of sales people and the total number of transactions. They gather data for five months.

Variable 1 |
Variable 2 |

207 |
6907 |

180 |
5991 |

220 |
6810 |

205 |
6553 |

190 |
6190 |

Correlation coefficient = .921

Standard error of the coefficient =..068

t-test for the significance of the coefficient = 4.100

Degrees of freedom = 3

Two-tailed probability = .0263

__Another z__

Respondents to a survey were asked to judge the excellence of a creation on a four-point Liker scale (outstanding, rational, and poor). They were also asked to judge the status of the company that made the creation on a three-point scale (good, rational, and poor). Is there an important association among defendant’s perceptions of the company and their perceptions of excellence of the product?

The first variable is the score for the excellence the product. Reactions are coded as 4=excellent, 3=good, 2=fair, and 1=poor. Another variable is the perceived status of the company and is coded 3=good, 2=fair, and 1=poor.

Variable 1 |
Variable 2 |

4 |
3 |

2 |
2 |

1 |
2 |

3 |
3 |

4 |
3 |

1 |
1 |

2 |
1 |

Correlation coefficient rho = .830

t-test for the significance of the coefficient = 3.332

Number of data pairs = 7

March 09, 2018