=== Optimization: yield ===
Direction: maximize

Best observed run: #3
  temperature = 200
  pressure = 5
  catalyst = B
  Value: 89.26

RSM Model (linear, R² = 0.9615, Adj R² = 0.9471):
  Coefficients:
    intercept                      +72.4500
    temperature                    +7.5783
    pressure                       +6.3333
    catalyst                       -0.4562

RSM Model (quadratic, R² = 0.9988, Adj R² = 0.9933):
  Coefficients:
    intercept                      +25.0608
    temperature                    +7.5783
    pressure                       +6.3333
    catalyst                       -0.4562
    temperature*pressure           -0.0817
    temperature*catalyst           +0.2537
    pressure*catalyst              -0.0088
    temperature^2                  +25.0608
    pressure^2                     +25.0608
    catalyst^2                     -4.0987

  Curvature analysis:
    temperature                    coef=+25.0608  convex (has a minimum)
    pressure                       coef=+25.0608  convex (has a minimum)
    catalyst                       coef=-4.0987  concave (has a maximum)

  Predicted optimum (from quadratic model, at observed points):
    temperature = 200
    pressure = 5
    catalyst = B
    Predicted value: 89.0125

  Surface optimum (via L-BFGS-B, quadratic model):
    temperature = 200
    pressure = 5
    catalyst = A
    Predicted value: 89.0152

  Model quality: Excellent fit — surface predictions are reliable.

Factor importance:
  1. temperature  (effect: 15.2, contribution: 46.8%)
  2. pressure  (effect: 12.7, contribution: 39.1%)
  3. catalyst  (effect: 4.6, contribution: 14.1%)

=== Optimization: cost ===
Direction: minimize

Best observed run: #2
  temperature = 100
  pressure = 1
  catalyst = A
  Value: 13.24

RSM Model (linear, R² = 0.9947, Adj R² = 0.9926):
  Coefficients:
    intercept                      +16.4267
    temperature                    +0.8700
    pressure                       +2.2050
    catalyst                       -0.1837

RSM Model (quadratic, R² = 0.9958, Adj R² = 0.9771):
  Coefficients:
    intercept                      +5.4625
    temperature                    +0.8700
    pressure                       +2.2050
    catalyst                       -0.1838
    temperature*pressure           +0.0050
    temperature*catalyst           -0.0937
    pressure*catalyst              +0.0113
    temperature^2                  +5.4625
    pressure^2                     +5.4625
    catalyst^2                     +0.0588

  Curvature analysis:
    temperature                    coef=+5.4625  convex (has a minimum)
    pressure                       coef=+5.4625  convex (has a minimum)
    catalyst                       coef=+0.0588  negligible curvature

  Predicted optimum (from linear model, at observed points):
    temperature = 200
    pressure = 5
    catalyst = A
    Predicted value: 19.6854

  Surface optimum (via L-BFGS-B, linear model):
    temperature = 100
    pressure = 1
    catalyst = B
    Predicted value: 13.1679

  Model quality: Excellent fit — surface predictions are reliable.

Factor importance:
  1. pressure  (effect: 4.4, contribution: 67.7%)
  2. temperature  (effect: 1.7, contribution: 26.7%)
  3. catalyst  (effect: 0.4, contribution: 5.6%)

