what is an inverse correlation 
an inverse correlation also known as negative correlation is a contrary relationship between two variables such that when the value of one variable is high then the value of the other variable is probably low for example with variables a and b as a has a high value b has a low value and as a has a low value b has a high value in statistical terminology an inverse correlation is often denoted by the correlation coefficient r having a value between 1 and 0 with r 1 indicating perfect inverse correlation graphing inverse correlationtwo sets of data points can be plotted on a graph on an x and y axis to check for correlation this is called a scatter diagram and it represents a visual way to check for a positive or negative correlation the graph below illustrates a strong inverse correlation between two sets of data points plotted on the graph example of calculating inverse correlationcorrelation can be calculated between variables within a set of data to arrive at a numerical result the most common of which is known as pearson s r when r is less than 0 this indicates an inverse correlation here is an arithmetic example calculation of pearson s r with a result that shows an inverse correlation between two variables assume an analyst needs to calculate the degree of correlation between the x and y in the following data set with seven observations on the two variables there are three steps involved in finding the correlation first add up all the x values to find sum x add up all the y values to find sum y and multiply each x value with its corresponding y value and sum them to find sum x y sum x 55 37 100 40 23 66 88 409 begin aligned text sum x 55 37 100 40 23 66 88 409 end aligned sum x 55 37 100 40 23 66 88 409 sum y 91 60 70 83 75 76 30 485 begin aligned text sum y 91 60 70 83 75 76 30 485 end aligned sum y 91 60 70 83 75 76 30 485 sum x y 55 91 37 60 88 30 26 926 begin aligned text sum x y 55 times 91 37 times 60 dotso 88 times 30 26 926 end aligned sum x y 55 91 37 60 88 30 26 926 the next step is to take each x value square it and sum up all these values to find sum x2 the same must be done for the y values sum x2 552 372 1002 882 28 623 text sum x 2 55 2 37 2 100 2 dotso 88 2 28 623sum x2 552 372 1002 882 28 623sum y2 912 602 702 302 35 971 text sum y 2 91 2 60 2 70 2 dotso 30 2 35 971sum y2 912 602 702 302 35 971noting there are seven observations n the following formula can be used to find the correlation coefficient r r n sum x y sum x sum y n sum x2 sum x 2 n sum y2 sum y 2 r frac n times text sum x y text sum x times text sum y sqrt n times text sum x 2 text sum x 2 times n times text sum y 2 text sum y 2 r n sum x2 sum x 2 n sum y2 sum y 2 n sum x y sum x sum y in this example the correlation is the two data sets have a correlation of 0 42 which is called an inverse correlation because it is a negative number 