A regression coefficient describes the size and direction of the relationship between a predictor and the response variable. Coefficients are the numbers by which the values of the term are multiplied in a regression equation.
MANOVA, Minitab displays coefficients for the constant and the covariates for each univariate analysis. To assess the categorical factors, see the Analysis of Variance table and the Means table.
The coefficient for a term represents the change in the mean response associated with a change in that term, while the other terms in the model are held constant. The sign of the coefficient indicates the direction of the relationship between the term and the response. The size of the coefficient is usually a good way to assess the practical significance of the effect that a term has on the response variable. However, the size of the coefficient does not indicate whether a term is statistically significant because the calculations for significance also consider the variation in the response data. To determine statistical significance, examine the p-value for the term.
For example, a manager determines that an employee's score on a job skills test can be predicted using the regression model, y = 130 + 4.3x. In the equation, x is the hours of in-house training (from 0 to 20) and y is the test score. The coefficient, or slope, is 4.3, which indicates that, for every hour of training, the mean test score increases by 4.3 points.