Correlation and Regression

Correlation and Regression Analysis

Correlation analysis is applied in quantifying the association between two continuous variables, for example an dependent and independent variable or among two independent variables.

Regression analysis refers to assessing the relation between the outcome variable and one or more variables. The outcome variable is known as dependent or response variable and the risk elements, and cofounders are known as predictors or independent variables. The dependent variable is shown by “y” and independent variables are shown by “x” in regression analysis.

The sample of a correlation coefficient is estimated in the correlation analysis. It ranges between -1 and +1, denoted by r and quantifies the strength and direction of the linear association among two variables. The correlation among two variables can either be positive, i.e, a higher level of one variable is related to higher level of another) or negative, i.e, a higher level of one variable is related to lower level of the other.

The sign of the coefficient of correlation shows the direction of association. The magnitude of coefficient shows the strength of association.

For example, a correlation of r = 0.8 indicates a positive and strong association among two variables, while a correlation of r = -0.3 shows a negative and weak association. A correlation near to zero shows non-existence of linear association among two continuous variables.

Correlation and Regression Differences

Correlation and Regression Differences

There are some differences between Correlation and regression.

  • Correlation shows the quantity of the degree to which two variables are associated. It does not fix a line through the data points. You compute a correlation that shows how much one variable changes when the other remains constant. When r is 0.0, the relationship does not exist. When r is positive, one variable goes high as the other one. When r is negative, one variable goes high as the other goes down.
  • Linear regression finds the best line that predicts y from x, but Correlation does not fit a line.
  • Correlation is used when you measure both variables, while linear regression is mostly applied when x is a variable that is manipulated.

Comparison Table

Basis Correlation Regression
Meaning A statistical measure that defines co-relationship or association of two variables. Describes how an independent variable is associated to the dependent variable.
Dependent and Independent variables No difference Both variables are different.
Usage To describe linear relationship between two variables. To fit a best line and estimate one variable based on another variable.
Objective To find a value expressing the relationship between variables. To estimate values of random variable based on the values of fixed variable.

Correlation and Regression Statistics

The degree of association is measured by r after its originator and a measure of linear association. Other complicated measures are used if a curved line is needed to represent the relationship.

Correlation and Regression Statistics

The above graph represents correlation.

The coefficient of correlation is measured on a scale that varies from +1 to -1 through 0. The complete correlation among two variables is represented by either +1 or -1. The correlation is positive when one variable increases and so does the other; while it is negative when one decreases as the other increases. The absence of correlation is described by 0.

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Practise This Question

Solve the following pair of equations:
(where x0,y0)