## Correlation Examples in Statistics

The example of the positive correlation includes calories burned by exercise where with the increase in the level of the exercise level of calories burned will also increase and the example of the negative correlation include the relationship between steel prices and the prices of shares of steel companies, wherewith the increase in prices of steel share price of the steel companies will decrease.

In Statistics, the Correlation is used mainly to analyze the strength of the relationship between the variables that are under consideration and further it also measures if there is any relationship i.e. linear between the given sets of data and how well they could be related. One such common measures that are used in the field of statistics for correlation is the Pearson Correlation Coefficient. The following Correlation example provides an outline of the most common correlations.

### Example #1

Vivek and Rupal are siblings, and Rupal is elder to Vivek by 3 years. Sanjeev their father is a statistician and he was interested in conducting research on the linear relationship between height and weight. Hence, since their birth he was noting down their height and weight at various ages and has arrived at below data:

He tries to identify if there is any correlation between age, height, and weight, and is there any differentiation between them?

**Solution:**

>We will first plot a scatter chart and we get below result for Rupal’s and Vivek’s age, height, and weight.

As the age increases, height increases, and also weight increases, so there appears to be a positive relationship, in other words, there is a positive correlation between height and age. Further, he observed that weight is fluctuating and is not stable it could either increase or decrease marginally but however he observed that there is a positive relationship between height and weight that is when height increases weight also tends to increase.

Thus, he observed that there are two important relationships here, with age – height increases and with height increase weight also increases, hence all three-carry positive correlation.

### Example #2

John is excited about summer vacation. However, his parents are worried since the teenager would be sitting home and playing games on mobile and would be switching on Air condition the whole time. The noted the various temperature and the units consumed by them during last year and found interesting data and they wanted to anticipate their upcoming may month bill and they are expecting the temperature to be near 40*C, but they want to know is there any correlation between Temperature and electricity bill?

**Solution:**

Let’s analyze this as well through a chart.

** **

We have plotted electricity bills and temperature and noted their various points. There appears to be a correlation between the temperature and electricity bill when the temperature is cold, the electricity bill is under control which makes sense as the family would be using less of air condition and as and when temperature increases, the use of air condition, geyser would increases which would hit them with a higher cost which is evident from the above graph where the electricity bill rises up heavily.

From this, we can conclude that there is no linear relationship but yes there is a positive correlation. Hence, the family can again expect a bill amount for may in the range of 6400 to 7000.

### Example #3

Tom has started a new catering business, where he is first analyzing the cost of making a sandwich and what price should he sell them. He has gathered below information after talking to various cooks who are currently selling the sandwich.

Tom was convinced that there is a positive linear relationship between No of sandwiches and the total cost of making it. Analyze if this statement is true?

**Solution:**

After plotting the points between the number of sandwiches prepared versus the cost of making them, there is definitely a positive relationship between them.

And it can be seen from the above table, yes there is a positive linear relationship between and if one runs correlation it will come +1. Hence, as he makes more sandwich the cost will increase, and it appears to be valid as the more sandwich are made, the more vegetables will be required and so as bread would be required. Hence, this has a positive perfect linear relationship based on the given data.

### Example #4

Rakesh has been investing in ABC stock for quite a long time. He wants to know whether ABC stock is a good hedge for the market. As he has also invested in an ETF fund that tracks a market index. He has gathered below data for the past 12 monthly returns on the stock ABC and Index.

Using correlation, identify the kind of relationship ABC stock has with the market and whether it hedges the portfolio?

**Solution:**

Using the correlation coefficient formula below treating ABC stock price changes as x and changes in markets index as y, we get correlation as -0.90

This is clearly a close to perfect negative correlation or in other words negative relationship.

Therefore, as the market rises, the stock price of ABC falls and when the market falls, the stock price of ABC rises, hence it is a good hedge for the portfolio.

### Conclusion

It can be concluded that there could be a correlation between two variables but not necessarily a linear relationship. There could be exponential correlation or log correlation, hence if one gets a result stating that there is a positive or negative correlation, then it should be judged by plotting the variables on the graph and find out if there is truly any relationship or there is spur correlation.

### Recommended Articles

This has been a guide to Correlation Examples in Statistics. Here we discussed the various examples to understand the correlation between two variables which can positive or negative. You can learn more financing from the following articles –

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