In the last chapter, we studied about Regression analysis, its types and walked through concepts of univariate and multivariate analysis.
In this chapter, we are going to dive in further in Regression analysis while covering Linear Regression Analysis.
Linear Regression Analysis
Linear Regression Analysis or popularly called as, Linear analysis is a statistical technique to measure the effect and cause relationship between two variable represented by X and Y in Linear Regression Model;
- Dependent variable is Y
- Independent variable is X
Dependent variable (Y) is the one which is predicted under linear analysis and also called as criterion variable whereas
Independent variable (X) is used for predicting the x which is called as predictor variable.
If you have gone through the last chapter, there are two kinds of regression analysis, namely;
when 1 independent variable is used, analysis is called simple linear regression which comes under univariate analysis whereas when multiple variables are used in the study, it is called multiple linear analysis which falls under multivariate regression analysis.
Line of Best Fit in Linear Analysis
In linear analysis, first a plot is charted using the variable’s value and a line is plotted. This line is called line of best fit. It is used to join different values on the chart. You may have a situation where multiple lines could be drawn, in that case you will chose the one with minimum sum of squared errors.
You can use the graph shown here for better understanding the line of best fit. Other than line of best fit, you also need to know about;
Residual Value- It is the discrepancy between the actual and the predicted value.
Usage of R Square in Linear Regression
R2 (R Square) is based on line of best fit and is used to measure the strength of the relationship between variables in question.
- R2 is used in following;
- R2=0; No Linear Relationship
- R2=-1; Negative Linear Relationship
- R2=+1; Positive Linear Relationship
Let’s use a Linear Regression Analysis but before that let’s see how linear analysis is performed and rules to analyze it;
- Model p-value should be less than 0.05 which have earlier seen p test and anova related chapters.
- R Square should be greater than 0.06.
- Adjusted R Square should be closer to R square and there should not be much difference between them.
For this example, I have used excel to perform linear analysis along with following details as per screen shot;
I have highlighted the values in the embedded sheet in which i have performed the linear analysis;