What is the difference between regression analysis and response surface analysis?
When should one use response surface?
Solved – Regression analysis and response surface analysis
experiment-designregression
Related Solutions
This is a central composite design so I assume you're fitting a full second-order model for the mean response $\mathrm{E}(Y)$ on continuous predictors $x_1$, $x_2$, & $x_3$
$$\mathrm{E}(Y)= \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \beta_{12} x_1 x_2 + \beta_{13} x_1 x_3 + \beta_{23} x_2 x_3 + \beta_{11} x_1^2 +\beta_{22} x_2^2 +\beta_{33} x_3^2$$
& estimating the coefficients $\beta$ by ordinary least squares.
I fitted the model: the estimated mean response has a stationary point, a maximum, of $\mathrm{E}(Y)=102$ at $x_1=0.62, x_2=-0.11, x_3=0.13$. (You can check for yourself by differentiating the equation for the response with respect to each predictor, setting each derivative to zero (all slopes are zero at a stationary point), & solving the resulting simultaneous equations.) Contour plots at slices through the stationary point are a good way of visualizing the fitted model:
The $95\%$ confidence interval for $\mathrm{E}(Y)$ at the maximum is $(89,114)$, & the $95\%$ prediction interval for $Y$ at the maximum is $(68,136)$. These are rather wide compared to the range of the response across the whole design. Indeed the residual standard deviation is $14$ (just look at the spread of responses over your centre points). I don't know the context of your experiment, but in many situations this would be cause for concern—are there other factors significantly contributing to process variability that you haven't taken into account?
Have a look at the rsm package in R and the companion paper in 2009 Journal of Statistical Software by its author, Russell Lenth.
Best Answer
I'm assuming that you are asking about Multiple regression method and Response surface method. Below is the simple explanation about both methods and their applications. As you read through, you will understand the difference between these two methods.
Multiple regression:
Regression analysis is used to investigate and model the relationship between a response variable and one or more predictors
Multiple regression method may be employed to
Response surface method:
Response surface methods are used to examine the relationship between a response variable and a set of experimental variables or factors. These methods are often employed after you have identified a "vital few" controllable factors and you want to find the factor settings that optimize the response. Designs of this type are usually chosen when you suspect curvature in the response surface.
Response surface methods may be employed to
Hope this helps !