Purpose: The researcher generalizes regression of three variables to n-variable by induction method with the help of cofactor of a matrix so that it assist to the predictor and estimator to estimate and predict dependent variable with the help of independent variables as applied in the relationship between dependent variable GDP and independent variables agriculture, industry, and service sector by using the n-variable regression model at initial condition. This seems a highly applied tool. So, its verification for validity is most and it is attemped here. Design/methodology/approach: To verify the n-variable linear model, both the methods are applied for the same data and estimated the best fit of the line and checked after applying the correlation coefficient matrix method and multiple regression equation using deviations from mean, zero order correlation coefficients, and standard deviation, do the fluctuation existed in the line or not, is estimated. Findings/result: The estimation of dependent variable with the help of independents variables can be estimated through the regression model found to be valid. Originality/value: It is pure research and a useful tool for estimation for multiple variables has been developed and validated.
