By default, Minitab includes a constant term for fitted line plots and regression models. To remove this term and have the model go through the origin, follow these steps.
Suppose the predictor variable (X) is in C1 and the response variable (Y) is in C2.
Suppose the predictor variable (X) is in C1 and the response variable (Y) is in C2;
When Minitab fits the model with the constant term, the R-squared is the proportion of the initial variation, as measured by the sum of squares around the mean of Y, which is explained by the regression. For the model without the constant term, R-squared is the proportion of the variation around the origin (that is, around the value zero) explained by the regression. This means the values of R-squared for the intercept and no-intercept models are not comparable.
Specifically, R-squared for regression through the origin tends to be larger than R-squared for regression with an intercept, even if the quality of fit is not better. The intercept model calculates the variations in the numerator (Ssreg) and denominator (Sstotal) of R-squared are calculated around the response mean, while in the non-intercept model those variations are calculated around zero. Such statistics cannot be used for performance comparison with the intercept model because the R-squared of the non-intercept model tends to be larger than the R-squared of the intercept model. This is because uncorrected (around zero) sum of squares are used. If R-squared was calculated around the response mean in the non-intercept model it can sometimes be negative.