It is one of the most common questions asked in a Data Science and Analytics interview. Before we directly jump to the definitions, we will first try to understand how correlation differs from correlation coefficient.
Correlation studies the linear relationship between two variables, whereas correlation coefficient measures the strength and direction of a linear relationship, whether positive or negative. We will try to understand each one by one.
Correlation: Often, we encounter situations where information on two variables like height and weight, income and expenditure etc., are available. Our interest is to study the relationship between these two variables, which is where correlation comes to the rescue.
Correlation studies the linear relationship between two variables.
And the best way to determine correlation potentiality is to use a Scatter diagram. It may not tell the exact relationship between the two variables, but it indicates whether they are correlated or not.
Types of Correlation:
Positive Correlation: If the values of one variable increase, the values of another variable also increase, and if the values of one variable decrease, the values of another variable also decrease. e.g., height and weight of a group of people, advertising expenditure and sales revenue.
Negative Correlation: If the values of one variable increase, the values of another variable decrease, and if the values of one variable decrease, the values of the other variable increase. e.g., price and demand of goods, literacy and poverty in a country etc.
Correlation coefficient:
A scatter diagram tells us whether variables are correlated or not but does not indicate the extent to which they are correlated, and this is where the correlation coefficient comes into the picture. It measures the strength of a linear relationship and the direction of positive or negative correlation. It is denoted by a small ‘r’ and can take a range of values from +1 to -1.
· A value of 0 (Zero) indicates no association between the two variables
· A value greater than 0 indicates a positive association; that is, as the value of one variable increases, so does the value of the other variable
· A value less than 0 indicates a negative association; that is, as the value of one variable increases, the value of the other variable decreases.
Different coefficient correlation values and interpretations are as below:
What is Linear regression, and how it differs from correlation?
Prediction or estimation is a major problem in most human activities. Like prediction of rainfall, price of goods, births etc., it helps us to plan for the future. If two variables are correlated significantly, it is possible to predict or estimate the values of one variable from the other. And this leads to the fundamental concept of regression analysis.
In fact, regression analysis is a statistical technique used to investigate the relationship between variables. The effect of price increases on demand and changes in advertisement expenditure on business sales are a few examples of regression analysis.
Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered an explanatory or independent variable, and the other is considered a dependent or response variable. For example, a modeler might want to relate the weights of individuals to their heights using a linear regression model where a particular value of height can be used to predict weight.
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References:
· http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm
· https://www.jmp.com/en_in/statistics-knowledge-portal/what-is-correlation.html
· https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/pearsons-correlation-coefficient/