Coefficients

The numbers by which the variables in an equation are multiplied. For example, in the equation y = -3.6 + 5.0X1 - 1.8X2, the variables X1 and  X2 are multiplied by 5.0 and -1.8, respectively, so the coefficients are 5.0 and -1.8.  

The size and sign of a coefficient in an equation affect its graph. In a simple linear equation (contains only one x-variable), the coefficient is the slope of the line.

When calculating a regression equation to model data, Minitab estimates the coefficients for each predictor variable based on your sample and displays these estimates in a coefficients table. For example, a coefficients table below is shown in the output for a regression equation HeatFlux = 389 + 2.12 East + 5.32 South - 24.1 North, which predicts the heat flux in a home based on the position of its focal points. The coefficient values for the equation appear in the second column:

Each coefficient estimates the change in the mean response per unit increase in X when all other predictors are held constant. For example, in  the output above, if the North variable increases by 1 and the other variables stay the same,  heat flux decreases by about 24, on average.

If the p-value (P) of a coefficient is less than the chosen a-level, such as 0.05, the relationship between the predictor and the response is statistically significant. Note that Minitab also includes a value for the constant in the equation in the Coef column.