Correlation is a term used to describe the relationship between the variables in a multivariate data distribution. The relationship found in Bivariate data between the independent and dependent variable is called a simple relationship. A simple relationship in turn is categorized in terms of direction, strength and shape.

The direction based categorization of correlation is consists of two types.
1. Positive Correlation
2. Negative Correlation

Negative Correlation Definition

If the independent and dependent variables vary in opposite directions, then their relationship is described as a negative correlation. This means as the value of one variable increases the value of the other will decrease and vice versa.

The Scatter plot drawn for the data set will display a pattern falling down from left to right. The slope of the fitting line or curve for the data set will be negative at any point on the line or curve.

Scatter Plot Negative Correlation

Scatter plot is a powerful tool used in correlation analysis which visually describe the nature of the relationship. The scatter plot drawn for a bivariate data distribution with negative correlation will show a pattern, where the points falling down the coordinate plane in clusters from left to right.

Example:
The following scatter plot shows the Hours exercised in a week against the LDL Cholesterol Level.

The Number of hours worked is the independent variable plotted along the horizontal axis and the LDL level in mg/dl is measured along the vertical axis. The dots plotted show a falling pattern from left to right. This indicates a negative correlation between the two variables. This means more the number of hours exercised results in less LDL Cholesterol level.

Scatter Plots for data sets can be made easily using graphing calculators or technology like MS Excel. These utilities also have features to show the fitting line or curve as desired.

Negative Correlation Coefficient

The correlation coefficient is a measure that determines the direction and strength of the relationship between the two variables. The symbols r and ρ represent correspondingly the correlation coefficient of sample and population data. The value of correlation coefficient ranges from -1 to 1 both inclusive. If the value of the correlation coefficient is negative, then the correlation is termed negative.

Strong Negative Correlation

When the value of correlation coefficient is close to -1, then the relationship is described as strong negative correlation.

Generally the value of r satisfying the inequality -1 < r < -0.8, is considered to indicate strong negative correlation.

In the scatter plot shown the pattern of dots seems to lies close to a line with a negative slope. This plot shows a strong negative correlation.

Perfect Negative Correlation

When the correlation coefficient is equal to -1, the relationship between the two variables is said to be a Perfect negative correlation.

The above scatter plot displays bivariate observations with perfect negative correlation. It can be noted that all the data plots lie on a straight line with negative slope.

Low Negative Correlation

The negative correlation between two variables is considered to be weak when the value of correlation coefficient is between -0.5 and -0.2, If the correlation coefficient is greater than -0.2 but less than 0, it can be termed that no correlation exists between the two variables studied.

Negative Correlation Graph

The fitting line used to estimate the linear relationship can be found using different methods.

1. Eye estimation

The eye estimation or a rough estimation of the graph of the fitting line cant be found using two approaches. In the first method the number of points above and below the line are kept the same. In the second method, the total deviations (errors ) on either side are kept equal.

2. Median Method

In the median method the entire plot is partitioned into three or four equal parts and the median point in each partition is identified. The line joining the median points is the straight line fit for the data set.

3. Using Graphing Calculator

When technology is used to make the scatter plot, the built in feature to find the line of best fit can be used. The graphing calculator not only display the line of best fit, but also returns the regression equation. The line of best fit for the data on Hours walked and Cholesterol level is shown below.

Negative Correlation Examples

Below you can see few examples for Negative Correlation,

Example 1:
Describe the correlation between the two variables X and Y as seen in the scatter plot given.
 The plot shows a corridor of points fallingfrom left to right. So here we observe a negativecorrelation between two variables X and Y. The pointsare seen distributed evenly on either side of the fittingline and no point lies on the line. The strength of the correlation can be described as moderate. Thescatter plot hence exhibits a moderate linear correlationbetween the two variables x and Y.

Example 2:
What kind of relationship do you expect between the number of hours worked per week and time spent on recreation activities?
A person working more number of hours per week will have less time for recreation than the one who works less. Hence we expect a negative correlation between number of hours worked and the time spent on recreation.