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Pearson Correlation Coefficient | Formula | Example | Calculation

Correlation Coefficient

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What is the Correlation Coefficient?

Pearson Correlation Coeffecient | Formula | Example | Calculation

Definition: Correlation coefficient is also known as Pearson correlation coefficient which is used to statistical measure the association or dependence of 2 numbers.

At the same time when 2 numbers move in the same direction then it said to be a positive correlation.

When the number of 1 series move up and other moves down then it said to be the negative correlation.

For track data and understand it in a better way correlation efficient is use.

The aftermath of the financial crises in 2008 for the simulate economy federal reserved lower the interest rate.

After lowering the interest rate there is an increase in the employment rate. From this, it is clear that the fed interest rate and the unemployment rate has a positive correlation.

Now we examine How to calculate the correlation coefficient.


For the correlation calculation, correlation coefficient formula is longer. Due to which professional use calculator to get the correlation output from the given data.

In the Excel spreadsheet, it can also be programmed.

Correlation numbers from -1 to 1. If 2 number has the same amount and same direction then these number has a positive correlation.

If 2 data set has the same amount but different direction then it said to be the negative correlation coefficient which is  -1, but if 2 number neither have same amount nor the same direction then the correlation coefficient of these number will be 0.

If we analyze the above example of FED lower interest then we observe that with low-interest rate unemployment will be which is the same direction but here the amount is not same so the correlation coefficient of these are -1.

lee is a good student. He analyzes that when he sleeps less than the result of the test is not good.

He compares the previous number of tests with the sleeping period of the previous night as he put the information in the Excel file as

Correlation Coefficient

Hours of sleep                                    Test Score

8                                                          81

8                                                          80

6                                                           75

5                                                            65

7                                                             91

6                                                             80

He uses the above information in Correlation formula (CORREL) within excel and gets the result of output is 0.65.

So the hour of sleep and test score of lee are positively correlated. 0.65 mean when the hour of sleep of lee increase then score in the test of lee increase also.

If the correlation coefficient is when then both increase with the perfectly same ratio.

If Lee hour sleep infected the score in inversely proportional which means that when sleeping time is increase then test score decrease. In this case, the relation is negatively correlated.

Analysis  and interpretation

For the analysis of public companies and for assets classes correlation coefficient is mostly use.

The analyst does the research to take investment which increases with the value of time and also finds the investment which has not the strong correlation with the stock market.

Correlation coefficient will be one of the which taken in the account. Because of this investor can diverse his or her investment.

Portfolio 1 is the US stock market which locks by itself due to which the correlation coefficient result is 1.

Portfolio 2 is the gold which is like the stock market but it is not increasing in the same way as the market increase.

With the change of other, there is no change in the class two assets.because of which low correlation coefficient is the result as 0.05.

Portfolio 3 is the long term government bond which increases or decrease inversely proportional to the stock market. The correlation coefficient of this will be -0.30.

For more Financial Ratio Check: 

Cash ratio

Compound annual growth rate (CAGR)

Contribution margin

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