In this article, we will learn the steps to make the Regression Model. In the previous article of this series, we learned how to calculate the values of coefficients, a test of slope coefficients and Hypothesis.
Let us continue where we left out
Here in this article, we will learn about:
- Coefficient of Determination
Let’s start with ANOVA:
What is ANOVA?
A basic idea about ANOVA, that of partitioning variation, is a fundamental idea of the experimental idea of experimental statistics. The ANOVA belies its name in that it is not concerned about analyzing variances but rather with analyzing the variances of mean.
There are two types of ANOVA:
- One way ANOVA
- Two way ANOVA
What is the Coefficient of Determination?
The coefficient of determination denoted by R² or r² and pronounced as R-squared, it is a ratio of the sum of squared.
R² or r²=SS(reg)/SS(t)
- R² is a statistic that will give some information about the goodness of fit of a model.
- R², the coefficient of determination measure of how good is the relationship between the dependent and independent variable.
- R² lies between [0,1].
- An R² of 1 indicates that there is a 100% relationship between variables.
- If R² = 0.8 explain 80% variability between variables.
- An R² of 0 indicates that there is no relationship between the variables.
- R² does not tell you that the independent variable is the cause of change independent variable.
- R² does not tell you whether the correct regression model was used.
R² increase or decrease on adding of any extra regressor variable, so we can not much dependent on R².
If this isn’t a solution then there might be another way to find the coefficient of determination of model. Yes, there is a solution known as Adjusted R².
The above properties for R² and Adjusted R² will remain the same.
- The adjusted R2 can be negative, and its value will always be less than or equal to that of R2.
- The adjusted R2 increases only when the increase in R2 (due to the addition of a new regressor variable)
The adjusted R2 is defined as
- p is the total number of regressor variables in the model (not including the constant term)
- n is the sample size.
Adjusted R2 can also be written as
- dft is the total degrees of freedom.
- n– 1 of the estimate of the population variance of the dependent variable.
- dfe is the degrees of freedom of the regression model.
- n – p – 1 of the estimate of the underlying population error variance.
Next is Model Adequacy checking, Multicollinearity and selecting significant explanatory variables.
We will discuss these remaining topics in the next article of this series. Till then, if you have any doubt or suggestion please feel free to shoot me an email on firstname.lastname@example.org or mention in the comment.
Article originally posted