Coefficients are 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.
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, the following coefficients table is shown in the output for a regression equation:
This equation predicts the heat flux in a home based on the position of its focal points, the insolation, and the time of day. Minitab displays the coefficient values for the equation 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 regression equation, if the North variable increases by 1 and the other variables remain the same, heat flux decreases by about 22.95 on average.
If the p-value of a coefficient is less than the chosen significance level, such as 0.05, the relationship between the predictor and the response is statistically significant. Minitab also includes a value for the constant in the equation in the Coef column.
The term coefficient can also be used to denote a calculated numerical value used as an index, such as a coefficient of correlation, a coefficient of determination, or Kendall's coefficient.