An electronics design engineer studies the effect of operating temperature and three types of face-plate glass on the light output of an oscilloscope tube.

To study the effect of temperature, glass type, and the interaction between these two factors, the engineer uses a general linear model.

- Open the sample data, LightOutput.MTW.
- Choose .
- In Responses, enter LightOutput.
- In Factors, enter GlassType.
- In Covariates, enter Temperature.
- Click Model.
- In Factors and covariates, select GlassType and Temperature.
- To the right of Interactions through order, select 2, and click Add.
- In Factors and covariates, select Temperature.
- To the right of Terms through order, select 2, and click Add.
- In Factors and covariates, select GlassType and, in Terms in the model, select Temperature*Temperature.
- To the right of Cross factors, covariates, and terms in the model, click Add.
- Click OK in each dialog.

In the Analysis of Variance table, the p-values for all of the terms are 0.000. Because the p-values are less than the significance level of 0.05, the engineer can conclude that the effects are statistically significant.

The R^{2} value shows that the model explains 99.73% of the variance in light output, which indicates that the model fits the data extremely well.

The VIFs are very high. VIF values that are greater than 5–10 suggest that the regression coefficients are poorly estimated due to severe multicollinearity. In this case, the VIFs are high because of the higher-order terms. Higher-order terms are correlated with main effect terms because the high-order tems also include the main effects terms. To reduce the VIFs, you can standardize the covariates in the Coding sub-dialog box.

Observations with large standardized residuals or large leverage values are flagged. In this example, two values have standardized residuals whose absolute values are greater than 2. You should investigate unusual observations because they can produce misleading results.

Method
Factor coding (-1, 0, +1)

Factor Information
Factor Type Levels Values
GlassType Fixed 3 1, 2, 3

Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Temperature 1 262884 262884 719.21 0.000
GlassType 2 41416 20708 56.65 0.000
Temperature*Temperature 1 190579 190579 521.39 0.000
Temperature*GlassType 2 51126 25563 69.94 0.000
Temperature*Temperature*GlassType 2 64374 32187 88.06 0.000
Error 18 6579 366
Total 26 2418330

Model Summary
S R-sq R-sq(adj) R-sq(pred)
19.1185 99.73% 99.61% 99.39%

Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -4969 191 -25.97 0.000
Temperature 83.87 3.13 26.82 0.000 301.00
GlassType
1 1323 271 4.89 0.000 3604.00
2 1554 271 5.74 0.000 3604.00
Temperature*Temperature -0.2852 0.0125 -22.83 0.000 301.00
Temperature*GlassType
1 -24.40 4.42 -5.52 0.000 15451.33
2 -27.87 4.42 -6.30 0.000 15451.33
Temperature*Temperature*GlassType
1 0.1124 0.0177 6.36 0.000 4354.00
2 0.1220 0.0177 6.91 0.000 4354.00

Regression Equation
GlassType
1 LightOutput = -3646 + 59.47 Temperature
- 0.1728 Temperature*Temperature
2 LightOutput = -3415 + 56.00 Temperature
- 0.1632 Temperature*Temperature
3 LightOutput = -7845 + 136.13 Temperature
- 0.5195 Temperature*Temperature

Fits and Diagnostics for Unusual Observations
Obs LightOutput Fit Resid Std Resid
11 1070.0 1035.0 35.0 2.24 R
17 1000.0 1035.0 -35.0 -2.24 R
R Large residual