Interpret the key results for Response Optimizer

Complete the following steps to interpret Response Optimizer. Key output includes the optimization plot, fitted values, and the confidence intervals.

Step 1: Identify the optimal setting of each predictor

Use the optimization plot to determine the optimal settings for the predictors given the parameters that you specified.

The optimization plot shows how the variables affect the predicted responses. You can modify the variable settings directly on the plot by moving the vertical bars. The optimization plot contains the following:
  • A column for each variable.
  • The composite desirability, if shown, is the top row.
  • After the composite desirability, a row for each response variable.
  • Cells that show how the corresponding response variable or composite desirability changes as a function of one of the variables, while all other variables remain fixed.
  • Numbers at the top of the columns that show the current variable settings (in red) and the high and low variable settings in the data.
  • Predict link in the top left of the graph that calculates the prediction for the current variable settings.
  • At the left of each response row, are the following: the predicted response (y) at the current variable settings, and the individual desirability score.
  • In the top row and in the upper left corner, the composite desirability (D).
  • A label above the composite desirability that refers to the current setting and changes if you modify the variable settings. When you create the graph, the label is Optimal. If you change the settings, the label changes to New. If you find a new optimal setting, the label changes to Optimal.
  • Vertical red lines on the graph that represent the current settings.
  • Horizontal blue lines that represent the current response values.
  • Gray regions that indicate where the corresponding response has zero desirability.
The type of fitted response values that Minitab displays depends on the type of response variable in your model. Minitab displays the following types of fitted values:
  • Means for response variables that contain continuous measurements, such as length or weight.
  • Means for response variables that contain counts that follow the Poisson distribution, such as the number of defects per sample.
  • Probabilities for response variables that contain only two possible outcomes, such as pass/fail.
  • Standard deviations for models that are fit using Analyze Variability.

The optimization plot displays the fitted values for the predictor settings. However, you should examine the prediction intervals in the Session window output to determine whether the range of likely values for a single future value falls within acceptable boundaries for the process.

Key Result: Optimization plot

For the insulation data, the composite desirability is 0.7750. The first column of the graph shows the response values at each level of Material, which is a categorical variable. The current variable settings are Material = Formula2, InjPress = 98.4848, InjTemp = 100.0, and CoolTemp = 45.0. The goal was to Maximize Insulation. Its predicted value is 25.6075, and its individual desirability is 0.85386. The covariate, MeasTemp, is included in the model as an uncontrollable noise variable and it is held at 21.49. Further observations are as follows:
  • Material: The two points for each cell in this column represent the two levels of the categorical variable: Formula1 and Formula2. Formula2 appears to be the best material. Changing to Formula1 would decrease the insulative value and increase the density, which are both undesirable. However, because material type interacts with other factors, this trend might not hold at other settings. Consider whether you can find a local solution for Formula1. Or, change the settings for Formula1 directly on the graph by moving the vertical bars.
  • InjPress: Increasing the injection pressure increases all three responses. Therefore, the optimal setting is in the middle of the range (98.4848), which is a compromise between conflicting goals. The goal is to maximize insulative value, minimize density, and maximize strength.
  • InjTemp: Increasing injection temperature also increases all the responses. But the effect on density is minimal compared to the effect on insulative value. Therefore, you increase the composite desirability by maximizing the injection temperature. The optimal settings of injection temperature are at the maximum levels in the experiment. This result suggests that you should consider experimenting with higher temperatures.
  • CoolTemp: Increasing cooling temperature increases insulative value, but decreases both density and strength. The optimal settings of both injection temperature and cooling temperature are at the maximum levels in the experiment. This result suggests that you should consider experimenting with higher temperatures. The graphs show that higher cooling temperatures may be especially worth considering. If the graphs could be extrapolated, higher cooling temperatures would improve insulative value and density. However, strength would decrease.

Step 2: Identify the point estimate and the likely range of each response

Use the fit values to identify the point estimate of each response variable that is based on the settings that the optimization plot displays.

The type of fitted response values that Minitab displays depends on the type of response variable in your model. Minitab displays the following types of fitted values:
  • Means for response variables that contain continuous measurements, such as length or weight.
  • Means for response variables that contain counts that follow the Poisson distribution, such as the number of defects per sample.
  • Probabilities for response variables that contain only two possible outcomes, such as pass/fail.
  • Standard deviations for models that are fit using Analyze Variability.
Use the prediction intervals (PI) to assess the precision of the predictions. The prediction intervals help you assess the practical significance of your results. If a prediction interval extends outside of acceptable boundaries, the predictions might not be sufficiently precise for your requirements. In this case, consider the following options:
  • Adjust the predictor settings directly on the Optimization plot by moving the vertical bars. Then, click the Predict link on the Optimization plot to determine whether the new solution is acceptable.
  • Conduct additional research and consider increasing the sample size to obtain more precise predictions.

The prediction interval (PI) is a range that is likely to contain a single future response for a specified combination of variable settings. If you collect another data point at the same variable settings, the new data point is likely to be within the prediction interval. Narrower prediction intervals indicate a more precise prediction.

Response Fit SE Fit 95% CI 95% PI Strength 32.34 1.04 ( 29.45, 35.22) ( 27.25, 37.43) Density 0.6826 0.0597 (0.5167, 0.8484) (0.3899, 0.9753) Insulation 25.608 0.268 (24.863, 26.352) (24.294, 26.921)
Key Results: Fit, PI

In these results, the input variable settings on the optimization plot are associated with the following predicted means and prediction intervals:
  • The mean strength is 32.34 and the range of likely values for a single future value is 27.25 to 37.43.
  • The mean density is 0.6826 and the range of likely values for a single future value is 0.3899 to 0.9753.
  • The mean insulation is 25.608 and the range of likely values for a single future value is 24.294 to 26.921.

Use your knowledge of the process to determine whether the prediction intervals fall inside acceptable boundaries.

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