Engineers are developing a new ultrasonic cleaner. The engineers use a screening design to determine which potential factors affect the output power for the cleaner.

One of the engineers analyzes a definitive screening design to determine which of 7 factors have the greatest effect on the power output. Power output needs to be high enough to clean adequately. At the same time, power output needs to be low enough to clean without damaging the items.

- Open the sample data, ultrasonic_cleaner.MTW.
- Choose .
- In Responses, enter Power.
- Click Terms.
- In Include the following terms, choose Linear. Click OK.
- Click Graphs.
- Under Residual Plots, select Four in one.
- Check Residuals versus variables. Enter Quiet and Sweep.
- Click OK in each dialog box.

In the Pareto chart, the engineer sees that the largest main effects are for Train (A) and Quiet (D). From the screening experiment, the engineer concludes that these two factors deserve the most consideration for further analysis.

The residual versus fits plot shows a U-shaped curve. This pattern is an indication that the model could be missing square terms or interactions. The plots of the residuals against Quiet and Sweep show curves also. In the exploration of potential models, the engineer decides to consider the square terms for these factors.

Coded Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 657.8 12.4 53.22 0.000
Train 52.4 13.6 3.85 0.004 1.00
Degas 0.9 13.6 0.07 0.949 1.00
Burst 8.6 13.6 0.63 0.542 1.00
Quiet -39.6 13.6 -2.91 0.017 1.00
Center -2.4 13.6 -0.17 0.866 1.00
Bandwidth 3.5 13.6 0.26 0.803 1.00
Sweep 2.8 13.6 0.21 0.839 1.00

Model Summary
S R-sq R-sq(adj) R-sq(pred)
50.9634 72.56% 51.21% 4.50%

Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Model 7 61803.7 8829.1 3.40 0.046
Linear 7 61803.7 8829.1 3.40 0.046
Train 1 38451.1 38451.1 14.80 0.004
Degas 1 11.2 11.2 0.00 0.949
Burst 1 1040.6 1040.6 0.40 0.542
Quiet 1 21938.4 21938.4 8.45 0.017
Center 1 77.8 77.8 0.03 0.866
Bandwidth 1 171.5 171.5 0.07 0.803
Sweep 1 113.1 113.1 0.04 0.839
Error 9 23375.4 2597.3
Total 16 85179.2

Regression Equation in Uncoded Units
Power = 626.5 + 116.5 Train + 2.0 Degas + 1.92 Burst - 8.80 Quiet - 0.47 Center
+ 0.70 Bandwidth + 0.57 Sweep

Alias Structure (up to order 2)
Factor Name
A Train
B Degas
C Burst
D Quiet
E Center
F Bandwidth
G Sweep
Aliases
I + 0.82 AA + 0.82 BB + 0.82 CC + 0.82 DD + 0.82 EE + 0.82 FF + 0.82 GG
A
B
C
D
E
F
G