Example of Multiple Regression

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. Open the Multiple Regression dialog box.
    • Mac: Statistics > Regression > Multiple Regression
    • PC: STATISTICS > Regression > Multiple Regression
  3. In Response, enter Rating.
  4. In Continuous predictors, enter Conc Ratio Temp Time.
  5. On the Graphs tab, do the following:
    1. Select Residual plots.
    2. Select Residuals versus variables, and enter Conc Ratio Temp Time.
  6. Click OK.

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 Equation
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Model Summary
S
R-sq
R-sq(adj)
Coefficients
Term
Coef
SE Coef
T-Value
P-Value
Fits and Diagnostics for Unusual Observations
Obs
Rating
Fit
Resid
Std Resid
 
R Large residual
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