A correlation coefficient is used in statistics to describe a pattern or relationship between two variables. A negative correlation describes the extent to which two variables move in opposite directions. An in💝crease in X is associated with a decreaಌse in Y for two variables, X and Y.

A negative correlation coefficient is also referred to as an inverse correlation. Corꩵrelation reওlationships are graphed in scatterplots.

Correlation Coefficient Calculation

$\begin{aligned}&r=\frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum(x_i-\bar{x})^2\sum(y_i-\bar{y})^2}}\\&\textbf{where:}\\&r=\text{Correlation coefficient}\\&x_i=\text{Values of the $x$-variable in a sample}\\&\bar{x}=\text{Mean of the values of the $x$-variable}\\&y_i=\text{Values of the $y$-variable in a sample}\\&\bar{y}=\text{Mean of the values of the $y$-variable}\end{aligned}$​r=∑(xi​−xˉ)2∑(yi​−yˉ​)2​∑(xi​−xˉ)(yi​−yˉ​)​where:r=Correlation coefficientxi​=Values of the x-variable in a samplexˉ=Mean of the values of 💖🦋;the x-variableyi​=Values of the y-variable in a sampleyˉ​=Mean of the values of ꧅;the y-variable​

Negative Versus Positive Correlation

A negative correlation demonstrates a connection between two variables in the same way as a positive 澳洲幸运5开奖号码历史查询:correlation coefficient and the relative strengths are the same. A correl♑ation coefficient of 0.85 shows the same strength as a correlation coe🌄fficient of -0.85.

Correlation coefficients are always values between -1 and 1 where -1 shows a perfect, linear negative correlation and 1 shows a perfect, linear 澳洲幸运5开奖号码历史查询:positive correlation. This list shows what some correlation co𝓰efficient values indicate:

Exactly –1. A perfect negative, downward-sloping li✱near🎉 relationship

–0.70. A strong negative, d🐟ownward-sloping 💧linear relationship

–0.50. A m♏oderate negative, downhill-slop💦ing relationship

–0.30. A weak negativ♒e, downhill-sloping liꩲnear relationship

0. No linear relationship

+0.30. A weak positive, up💜war💮d-sloping linear relationship

+0.50. A moderate posi𓆏tive, upward-sloping linear relationship

+0.70. A strong positive, upward-sloping linea🔯r relationship

Exactly +1. A perfect positive, upward-sloping linear relatio🔯nship

Thinking about the nuℱmeric value of a correlation coefficient💦 as a percentage. A 20% move higher for variable X would equate to a 20% move lower for variable Y.

Extreme Correlation Coefficients

A correlation coefficient of zero or close to zero shows no meaningful relationship between variables. A coefficient of -1.0 or +1.0 indicates a perfect correlation. A change in one variable perfectly predicts the changes in the other. These numbers are rarely seen in reality because perfectly linear relationships are rare.

An example of a strong negative correlation would be -0.97.🔜 The variables would move in opposite directions in a nearly identical move. The values demo🍬nstrate the strength of a relationship as the numbers approach 1 or -1. Numbers of 0.92 or -0.97 would show a strong positive and negative correlation respectively.

Examples of Correlation Coefficients

The amount of snowfall decreases as the temperature increases outside. This shows a negative correlation and w♔ould have a negative correlation coefficient.

A positive correlation coefficient would be the relationship between temperature and ice cream sales. Ice cream sales i♎ncrease as temperature increases. This relationship would have a positive correlation coefficient.

A relationship with a correlation coefficient of zero or very close to zero might be temperature and fast food sales assuming there's zero correlation for illustrative purposes. Temperature typically has no bearing on whether people consume fast food.

The Bottom Line

A negative correlation can indicate a strong relationship or a 𒁏weak relationship. Many people think that a correlation of –1 indicates no relationship but the opposite is true. A correlation of -1 indicates a near-perfect relationship along a straight line. This is the strongest relationship possible. The minus sign simply indicates that the line slopes downwards and it is a negative relationship.