# Display equation to predict z-scores

##### New Member
I am trying to formulate prediction equations for normal lung function. The most suitable model has BCPE distribution As shown below
summary(bcpe)
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Family: c("BCPE", "Box-Cox Power Exponential")

Call: gamlss(formula = fevfvc ~ log(height) + pb(log(age)), sigma.formula = ~pb(log(age)), nu.formula = ~log(age),
tau.formula = ~log(age), family = BCPE(mu.link = "log"), data = mm, method = CG())

Fitting method: CG()

------------------------------------------------------------------
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.477818 0.033650 162.790 < 2e-16 ***
log(height) -0.162232 0.007574 -21.419 < 2e-16 ***
pb(log(age)) -0.046870 0.006363 -7.366 3.55e-13 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

------------------------------------------------------------------
Sigma Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.30559 0.21462 -15.402 < 2e-16 ***
pb(log(age)) 0.19503 0.06008 3.246 0.00121 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

------------------------------------------------------------------
Nu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 14.6804 3.2844 4.470 8.68e-06 ***
log(age) -2.8624 0.9155 -3.127 0.00182 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

------------------------------------------------------------------
Tau Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.739 1.241 4.623 4.25e-06 ***
log(age) -1.238 0.340 -3.640 0.000285 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

------------------------------------------------------------------
NOTE: Additive smoothing terms exist in the formulas:
i) Std. Error for smoothers are for the linear effect only.
ii) Std. Error for the linear terms maybe are not accurate.
------------------------------------------------------------------
No. of observations in the fit: 1061
Degrees of Freedom for the fit: 10.44159
Residual Deg. of Freedom: 1050.558
at cycle: 16

Global Deviance: 7044.917
AIC: 7065.801
SBC: 7117.664
******************************************************************
I am trying to identify the equation used in
mm\$zCG <- resid(bcpe)
I tried to find the equation in the literature but I did not find what I am looking for
Any help is highly appreciated