The regression equation is an algebraic representation of the relationship between the response and predictor variables. For hierarchical models, Minitab displays the coefficients in uncoded units. For non-hierarchical models, Minitab displays the coefficients in coded units. Use Stat > DOE > Factorial > Predict to calculate the predictions and confidence intervals for predictor values that you specify.

The regression equation takes the form of:

Response = constant + coefficient * predictor + ... + coefficient * predictor

or y = bo + b1X1 + b2X2 + ... + bkXk

Where:

·    Response (Y) is the value of the response.

·    Constant (bo) is the value of the response variable when the predictor variable(s) is zero. The constant is also called the intercept because it determines where the regression line intercepts (meets) the Y-axis.

·    Predictor(s) (X) is the value of the predictor variable(s). The predictor can be a polynomial term.

·    Coefficients (b1, b2, ... , bk) represent the estimated change in mean response for each unit change in the predictor value. In other words, it is the change in Y that occurs when X increases by one unit.

For the insulation data, the response variable is Strength. The model includes the covariate, the main effects, and the two-way interactions. The regression equation is:

Strength = 52.7 - 1.229 (MeasTemp) + 10.43 (Material) + 0.216 (InjPress) + 0.007 (InjTemp) - 1.357 (CoolTemp) -0.0096 (Material*InjPress) - 0.0683 (Material*InjTemp) - 0.0104 (Material*CoolTemp) - 0.00149 (InjPress*InjTemp) - 0.00007 (InjPress*CoolTemp) + 0.01288 (InjTemp*CoolTem)

You can interpret each slope value for each predictor as the change in strength when the predictor increases by 1. For example, when injection pressure increases by one unit, strength increases by 0.216.  However, in this case, you also have to include the interaction effect. The interactions indicate that the effect of injection pressure depends on the other predictors.

You can interpret the intercept value as the predicted value of strength when each predictor is zero. Because no values are near 0 in the data, the intercept is likely to be nonsensical or extrapolated so far that the intercept is inaccurate. For the insulation data, insulation made when the ambient temperature is 0 degrees, from a material that doesn't exist, with no injection pressure, injected at 0 degrees, and cooled at 0 degrees would have a strength of 52.7.