Example of Fit Regression Model

A research chemist wants to understand how several predictors are associated with the wrinkle resistance of cotton cloth. The chemist examines 32 pieces of cotton cellulose produced at different settings of curing time, curing temperature, formaldehyde concentration, and catalyst ratio. The durable press rating, a measure of wrinkle resistance, is recorded for each piece of cotton.

The chemist performs a multiple regression analysis to fit a model with the predictors and eliminate the predictors that do not have a statistically significant relationship with the response.

  1. Open the sample data, WrinkleResistance.MTW.
  2. Choose Stat > Regression > Regression > Fit Regression Model.
  3. In Responses, enter Rating.
  4. In Continuous predictors, enter Conc Ratio Temp Time.
  5. Click Graphs.
  6. Under Residuals plots, choose Four in one.
  7. In Residuals versus the variables, enter Conc Ratio Temp Time.
  8. Click OK in each dialog box.

Interpret the results

The predictors temperature, catalyst ratio, and formaldehyde concentration have p-values that are less than the significance level of 0.05. These results indicate that these predictors have a statistically significant effect on wrinkle resistance. The p-value for time is greater than 0.05, which indicates that there is not enough evidence to conclude that time is related to the response. The chemist may want to refit the model without this predictor.

The residual plots indicate that there may be problems with the model.
  • The points on the residuals versus fits plot do not appear to be randomly distributed about zero. There appear to be clusters of points that could represent different groups in the data. The chemist should investigate the groups to determine their cause.
  • The plot of the residuals versus ratio shows curvature, which suggests a curvilinear relationship between catalyst ratio and wrinkles. The chemist should consider adding a quadratic term for ratio to the model.

Regression Analysis: Rating versus Conc, Ratio, Temp, Time

Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 4 47.9096 11.9774 18.17 0.000 Conc 1 3.9232 3.9232 5.95 0.022 Ratio 1 31.0216 31.0216 47.07 0.000 Temp 1 3.6031 3.6031 5.47 0.027 Time 1 1.9839 1.9839 3.01 0.094 Error 27 17.7953 0.6591 Lack-of-Fit 25 17.7836 0.7113 121.94 0.008 Pure Error 2 0.0117 0.0058 Total 31 65.7049
Model Summary S R-sq R-sq(adj) R-sq(pred) 0.811840 72.92% 68.90% 62.81%
Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -0.756 0.736 -1.03 0.314 Conc 0.1545 0.0633 2.44 0.022 1.03 Ratio 0.2171 0.0316 6.86 0.000 1.02 Temp 0.01081 0.00462 2.34 0.027 1.04 Time 0.0946 0.0546 1.73 0.094 1.00
Regression Equation Rating = -0.756 + 0.1545 Conc + 0.2171 Ratio + 0.01081 Temp + 0.0946 Time
Fits and Diagnostics for Unusual Observations Std Obs Rating Fit Resid Resid 9 4.800 3.178 1.622 2.06 R R Large residual
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