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

Y_p = β₀ + β₁x₁ + ... + β_kx_k + σΦ^-1(p)

Prediction (Y_p): log failure time (Weibull, exponential, lognormal, and loglogistic models) or failure time (normal, extreme value, and logistic models).
Predictors (x₁, x₂ ... x_k): the predictor variables, which can be either continuous or categorical.
Constant (β₀): the value of Y_p (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,... , β_k): 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 p^th 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 Error			95.0% Normal CI
Predictor	Coef	Standard 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(Y_p) = 6.8731 – 0.0565899(Weight) + (1.0/5.79286)Φ^-1(p)

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

Where:

Y_p: the failure time for the compressor case failures
Weight: weight of the projectile thrown at the engine
Φ^-1(p): the pth quantile from the standardized extreme value distribution (for more information, go Methods and formulas for equations in Regression with Life Data and click "Quantile function").