Regression Analysis

Regression analysis is a Statistical technique used to determine the best functional relationship between a dependent variable with one or more independent variables. The functional relationship of a dependent variable with one or more independent variables is called a regression equation. The relationship between a dependent variable Y and an independent variable X is linear, it is known as simple regression of Y on X. The relationship between a dependent variable with two or more independent variables is termed as multiple regression. The dependent variable is frequently termed as response or study variable and the independent variables are called explanatory variables. The aim of regression analysis is to estimate as best as possible, the dependent variable from the independent variables.

Linear regression model

The output of an experiment, called as dependent (or study) variable Y, depends on k independent (or explanatory) variables denoted by X₁, X₂, X₃…,X_k.. Suppose the performance of Y can be explained by a functional relation given by
Y = f(X₁, X₂, X₃………,X_k , β₁, β_2, β_{3,……….,}β_k) + ε , where f is some well-defined function and β₁, β_2, β_{3,,……….,}β_k  are the parameters which describe the role and input of X₁, X₂, X_3,…,X_k  respectively.  The term ε shows the stochastic nature of the relationship between Y and X₁, X₂, X_3,…,X_k  and indicates that such a relationship is not precise in nature. When ε = 0 then the relationship is called the mathematical model else the statistical model. The term “model” is generally in practice to specify the mechanism of interrelationship of independent variable on study variable in a Matrix. 

Illustration

• To estimate the sales (dependent variable) of an organization depends on expense of products (independent variable) and advertising activities (independent variable) the results from this regression analysis could provide a particular answer to what would happen to sales if prices were to upturn by 5% and promotional activities were to rise by 10%. Such precise answers can help (marketing) managers make sound conclusions. Moreover, by providing various circumstances, such as computing the sales effects of price increases of 6%, 10%, and 12%, managers can evaluate marketing procedures and create marketing policies.

• The yields of a crop depends on different doses of fertilizer, rainfall, irrigation, temperature etc.

• Future demand of food may be predicted with the help of regression analysis.

Steps of Regression Analysis

•    Consider the problem Statement  

•    Choice of important variables

•    Collection of data in important variable

•    Specification of regression model

•    Method for fitting the data

•    Fitting of proposed regression model

•    Validation of regression model

•    Interpretation & Conclusion