To understand correlation and regression formula, we should first know about bivariate data. When the data is assembled for two variables concurrently, they are known as bivariate data. The corresponding frequency distribution produced by it is known as bivariate frequency distribution.
CORRELATION ANALYSIS
If there is a change in one variable due to a change in another variable irrespective of direct change or inverse change, these two variables are known as correlated. If there is no change in one variable due to a change in another variable, these two variables are uncorrelated.
TYPES OF CORRELATION
There are two types of correlation;
1. Positive correlation – if one variable increases/decreases and made the same effect on another variable, then they are positively correlated. Variables that are positively correlated move in the same direction. For example, a student’s marks in math and his rank, if his marks increase his rank in class also increase or profit and sale of a company, as much as sales increase profit also increase.
2. Negative correlation – if one variable increases/decreases and has the opposite effect on another variable, they are known as negatively correlated. Variables that are negatively correlated move in different directions. For example, if the price of an item increases, the demand for that item will decrease. In an uncorrelated variable, the change in one variable does not effect change in another variable. For example, weight and intelligence are uncorrelated.
METHODS TO MEASURE CORRELATION
• Scatter diagram: it is a diagrammatic method to know the correlation between variables. It helps differentiate between different types of correlation but can not measure the extent of the relationship between the variables.
• Karl Pearson’s product-moment correlation coefficient is the best method for finding a correlation between two variables. The formula for this method ;
r = rxy =cov(x,y)/sX x sy
• Spearman’s rank method: this method is used when we have to find a correlation between two qualitative characteristics. It provides rank to the data.
• Coefficient of concurrent deviation: it is a casual method of finding correlation when the magnitude of two variables doesn’t affect much.
rc= √(2c-m)/m
REGRESSION ANALYSIS
In regression analysis, we calculate the value of one variable based on the given value of another variable with the help of a mathematical relationship between two variables. It plays an important role in today’s activity; for example, a businessman wants to know how much profit he will make from the said investments.
When one variable depends on another variable, we get simple linear regression. Suppose two variables, x and y. If y depends on x, then y will be known as the dependent variable, and x will be the independent variable.
In the case of a simple regression, if y depends on x, then the regression line of y on x is given by y=a+bx. Here a and b are two constants known as parameters, and b is also known as the regression coefficient of y on x and is denoted by bxy. The regression coefficient remains unchanged due to a shift of origin but changed due to a scale shift.
DIFFERENCE BETWEEN CORRELATION AND REGRESSION
- Correlation is a statistical measure that tells the association of two variables, while regression tells how much two variables are related numerically.
- Correlation gives the linear relationship between two variables, and regressions fit the best line and estimate one variable based on another variable.
- Correlation finds the numeric value that tells the relationship between the two variables, and regression tells the value of the random variable based on the fixed variable.
- Correlation does not nominate variables as dependent or independent, and in regression, one variable is dependent, and another variable is independent.
- The correlation coefficient lies between -1 and 1, and in regression, only one regression coefficient can be greater than 1.
CORRELATION AND REGRESSION FORMULA
Formula to find correlation coefficient
Formula to find the least-squares of regression
Conclusion
Now you have understood the concept of regression and correlation, as well as are aware of the formula. It is time to practice some questions and drive the concepts home.
