How to Develop Regression Equation from Effects?
For quantitative independent variables (factors), an estimated regression equation can be developed from the calculated main effects and the interaction effects. The full regression model with two factors (two level for each factor) with the interaction effect can be written as Equation 1.
How to estimate the regression coefficients from the main and the interaction effects.
Using the -1/+1 coding system (Figure 8), the average comfort level increases by 6 ((9+5-2-0)/2=6) if the temperature is increased by two units (-1 to 0 and then from 0 to +1). Therefore, for one unit increase of the temperature, the comfort level is increased by 3. As the estimate for the coefficients, beta for an example is the increase of the response for every one unit increase of the factor level, the estimated regression coefficient is calculated as one-half of the respective estimated effect.
The regression coefficient is one-half of the calculated effect. The regression constant is calculated by averaging all four responses. Therefore, the regression equation can be written as in Equation.
Figure 8. How to estimate the regression coefficients from the main and the interaction effects.