Regression table – estimated regression equation for Regression with Life Data

The table estimates the best fitting regression equation for the model. The regression equation takes the following general form:

Prediction = constant + coefficient(predictor) + ... + coefficient(predictor) + scale (quantile function) or

Yp = β0 + β1x1 + ... + βkxk + σΦ-1(p)

  • Prediction (Yp): log failure time (Weibull, exponential, lognormal, and loglogistic models) or failure time (normal, extreme value, and logistic models).
  • Predictors (x1, x2 ... xk): the predictor variables, which can be either continuous or categorical.
  • Constant (β0): the value of Yp (failure time or log failure time) when all of the explanatory variables are equal to zero and the percentile of the quantile function is 0.
  • Coefficient (β1, β2,... , βk): the amount by which Y changes when the corresponding explanatory variable (x) increases by one unit and all other explanatory variables are held constant.
  • Scale (σ): the scale parameter. For Weibull and exponential, scale = 1.0/shape.
  • Quantile function (Φ-1(p): the pth quantile of the standardized life distribution.

This model might not provide a good fit to the data. To assess model fit, check the assumptions of the model by using the probability plot of the standardized residuals and the Cox-Snell residuals.

Example output

Regression Table Standard 95.0% Normal CI Predictor Coef Error Z P Lower Upper Intercept 6.68731 0.193766 34.51 0.000 6.30754 7.06709 Design Standard -0.705643 0.0725597 -9.72 0.000 -0.847857 -0.563428 Weight -0.0565899 0.0212396 -2.66 0.008 -0.0982187 -0.0149611 Shape 5.79286 1.07980 4.02001 8.34755 Log-Likelihood = -88.282

Interpretation

The estimated model for the new compressor cases is: log(Yp) = 6.8731 – 0.0565899(Weight) + (1.0/5.79286)Φ-1(p)

The estimated model for the standard compressor cases is: log(Yp) = (6.8731 – 0.705643) – 0.0565899(Weight) + (1.0/5.79286)Φ-1(p)

Where:
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