In statistics, the

**correlation coefficient**r measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and –1. A perfect downhill (negative) linear relationship. –0.70. A**strong**downhill (negative) linear relationship.How do you know if its a positive or negative correlation?

The direction of a

**correlation**is either**positive or negative**. In a**negative correlation**, the variables move in inverse, or opposite, directions. In other words, as one variable increases, the other variable decreases. For example, there is a**negative correlation**between self-esteem and depression.1

## Is a strong correlation?

In statistics, the

**correlation**coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. A perfect downhill (negative) linear relationship. –0.70. A**strong**downhill (negative) linear relationship.2

## Can you use correlation to predict?

Never

**do**a regression analysis unless**you**have already found at least a moderately strong**correlation**between the two variables. In general, Y is the variable that**you**want to**predict**, and X is the variable**you**are**using**to make that**prediction**.3

## What R value is considered a strong correlation?

Coefficient of Correlation

Value of r | Strength of relationship |
---|---|

-1.0 to -0.5 or 1.0 to 0.5 | Strong |

-0.5 to -0.3 or 0.3 to 0.5 | Moderate |

-0.3 to -0.1 or 0.1 to 0.3 | Weak |

-0.1 to 0.1 | None or very weak |

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## What is a positive correlation?

**Positive correlation**is a relationship between two variables in which both variables move in tandem. A

**positive correlation**exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.

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## What does Pearson's correlation coefficient tell you?

The

**Pearson correlation coefficient**, r, can take a range of values from +1 to -1. A value of 0 indicates that there is no association between the two variables. A value greater than 0 indicates a positive association; that is, as the value of one variable increases, so**does**the value of the other variable.6

## Why would you use a correlation coefficient?

In summary,

**correlation coefficients**are used to assess the strength and direction of the linear relationships between pairs of variables. When both variables are normally distributed**use**Pearson's**correlation coefficient**, otherwise**use**Spearman's**correlation coefficient**.7

## What is the Pearson correlation coefficient?

The

**Pearson**product-moment**correlation**coefficient is a measure of the strength of the linear relationship between two variables. It is referred to as**Pearson's correlation**or simply as the**correlation**coefficient. A perfect positive linear relationship, r = 1.8

## What is the difference between a positive and a negative correlation?

The direction of a

**correlation**is either**positive**or**negative**.**In**a**negative correlation**, the variables move**in**inverse, or opposite, directions.**In**other words, as one variable increases, the other variable decreases. For example, there is a**negative correlation between**self-esteem and depression.9

## What is an example of a positive correlation?

**Positive Correlation Examples**. A

**positive correlation**is a relationship between two variables where if one variable increases, the other one also increases. A

**positive correlation**also exists in one decreases and the other also decreases.

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## What is an example of a negative correlation?

In other words, as one variable increases, so does the other. For

**example**, there is a positive**correlation**between smoking and alcohol use. When two variables have a**negative correlation**, they have an inverse relationship. This means that as one variable increases, the other decreases, and vice versa.11

## What does it mean to have a weak correlation?

Strong

**Correlation**: A**weak correlation means**that as one variable increases or decreases, there is a lower likelihood of there being a relationship with the second variable.12

## What is a large correlation?

A

**correlation**coefficient of .10 is thought to represent a weak or small association; a**correlation**coefficient of .30 is considered a moderate**correlation**; and a**correlation**coefficient of .50 or larger is thought to represent a strong or**large correlation**.13

## What are the different types of correlation?

**Correlation**

- Positive Correlation: as one variable increases so does the other. Height and shoe size are an example; as one's height increases so does the shoe size.
- Negative Correlation: as one variable increases, the other decreases.
- No Correlation: there is no apparent relationship between the variables.

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## What does the correlation matrix tell you?

A

**correlation matrix**is a table showing**correlation**coefficients between sets of variables. Each random variable (X_{i}) in the table is**correlated**with each of the other values in the table (X_{j}). This allows you to see which pairs have the highest**correlation**.15

## What is the definition of no correlation?

If there is a

**correlation**between two sets of data, it means they are connected in some way. We have seen that as the temperature increases, the number of ice-creams sold increases. The results are approximately in a straight line, with a positive gradient.16

## What is a linear relationship?

A

**relationship**of direct proportionality that, when plotted on a graph, traces a straight line. In**linear relationships**, any given change in an independent variable will always produce a corresponding change in the dependent variable.17

## What is a significant Pearson correlation?

Output of a Pearson's correlation in Stata

Coefficient Value | Strength of Association |
---|---|

0.1 < | r | < .3 | small correlation |

0.3 < | r | < .5 | medium/moderate correlation |

| r | > .5 | large/strong correlation |

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## How is the correlation coefficient used?

In general,

**correlation**tends to be**used**when there is no identified response variable. It measures the strength (qualitatively) and direction of the linear relationship between two or more variables. The Pearson**correlation coefficient**measures the strength of the linear association between two variables.19

## What does it mean to have a negative correlation?

**Negative correlation**is a relationship between two variables in which one variable increases as the other decreases, and vice versa. In statistics, a perfect

**negative correlation**is represented by the value -1.00, a 0.00 indicates no

**correlation**, and a +1.00 indicates a perfect positive

**correlation**.