Correlation Examples

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 CorrelationCorrelationCorrelation is a statistical measure between two variables that is defined as a change in one variable corresponding to a change in the other. It is calculated as (x(i)-mean(x))*(y(i)-mean(y)) / ((x(i)-mean(x))2 * (y(i)-mean(y))2.read more 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 older than Vivek by three years. Sanjeev, their father, is a statistician, and he was interested in researching the linear relationship between height and weight. Hence, since their birth, he was noting their height and weight at various ages and arrived at the following:

AgeRupalVivek
    Height (in foot)     Weight (in Kgs)    Height (in foot)     Weight (in Kgs)
53.5203.622
73.11253.10127
94.1264.328
114.7324.732
134.11354.1140
155.1405.245
175.2455.450
195.3485.755
215.5505.964
235.55515.967
255.55555.970

He tries to identify 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 the result for Rupal’s and Vivek’s age, height, and weight.

correlation-example 1.2
correlation-example 1.3

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, Sanjeev observed that weight is fluctuating and is not stable; it could either increase or decrease marginally, but he observed a positive relationship between height and weight; that is, when height increases, weight also tends to increase.

Thus, he observed two crucial 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 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?

Temperature (in oC)Units ConsumedElectricity Bill (in Rs)
2480                          2,490.00
2782                          2,550.00
3084                          2,610.00
31101                          3,170.00
34110                          3,890.00
35115                          4,290.00
38140                          6,390.00
40142                          6,441.00
42156                          7,155.00
45157                          7,206.00

Solution:

Let’s analyze this as well through a chart.

EX 2.2

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, and 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 heavily.

Thus, 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 the below information after talking to various cooks who are currently selling the sandwich.

No of SandwichCost of BreadVegetableTotal Cost
1010030130
2020060260
3030090390
40400120520

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 a positive relationship between them.

EX 3.2

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 Tom makes more sandwiches, the cost will increase, and it appears to be valid as more the sandwich, 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 ETFETFAn exchange-traded fund (ETF) is a security that contains many types of securities such as bonds, stocks, commodities, and so on, and that trades on the exchange like a stock, with the price fluctuating many times throughout the day when the exchange-traded fund is bought and sold on the exchange.read more 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 relationship ABC stock has with the market and whether it hedges the portfolio?

MonthChange in Price of ABC StockChange in Price Index
Jan-4.00%2.00%
Feb-3.86%2.33%
Mar1.21%0.09%
Apr-0.33%1.01%
May6.00%-0.34%
Jun7.00%-3.40%
Jul4.55%-1.50%
Aug3.50%-1.09%
Sep1.50%2.50%
Oct-4.00%3.00%
Nov-3.50%2.89%
Dec-5.00%4.00%

Solution:

Using the correlation coefficient formulaCorrelation Coefficient FormulaCorrelation Coefficient, sometimes known as cross-correlation coefficient, is a statistical measure used to evaluate the strength of a relationship between 2 variables. Its values range from -1.0 (negative correlation) to +1.0 (positive correlation). read more below treating ABC stock price changes as x and changes in markets index as y, we get correlation as -0.90

correlation coefficient Formula

It is clearly a close to perfect negative correlationNegative CorrelationA negative correlation is an effective relationship between two variables in which the values of the dependent and independent variables move in opposite directions. For example, when an independent variable increases, the dependent variable decreases, and vice versa.read more or, in other words, a 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 a spur correlation.

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