# How to interpret the hurdle or zero-inflated model

I have 137 data points that are inspection and I'm trying to find the hurdle negative binomial distribution that fits. Here is how the data looks

I have the following code

modelhurdNB<-hurdle(Count ~ Start, data=inspData,
dist = "negbin", zero.dist = "binomial", link = "logit",
model = TRUE, y = TRUE, x = FALSE)
AICHurdNB=AIC(modelhurdNB)


summary of the model is

Call:
hurdle(formula = Count ~ Start, data = inspData, dist = "negbin",
zero.dist = "binomial", link = "logit", model = TRUE, y = TRUE,
x = FALSE)

Pearson residuals:
Min        1Q    Median        3Q       Max
-0.627069 -0.524570 -0.488098  0.007419  5.510233

Count model coefficients (truncated negbin with log link):
Estimate Std. Error z value Pr(>|z|)
(Intercept)  1.530519   0.671367   2.280   0.0226 *
Start       -0.002971   0.002211  -1.344   0.1791
Log(theta)  -0.645959   0.899062  -0.718   0.4725
Zero hurdle model coefficients (binomial with logit link):
Estimate Std. Error z value Pr(>|z|)
(Intercept)  0.515575   0.683851   0.754    0.451
Start       -0.003274   0.002714  -1.206    0.228
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Theta: count = 0.5242
Number of iterations in BFGS optimization: 13
Log-likelihood: -125.3 on 5 Df


This is the model that has the lowest AIC. However, The start time of the inspection has a p value higher than 0.05. The binomial part is also statistically insignificant. Hence,

1) How good of a model is this?

2) How do I obtain the parameter of the binomial? (Is it the statistically insignificant coefficient?)

$$\operatorname{logit}(p) = \hat{\beta}_0 + \hat{\beta}_1\operatorname{Start}$$
With $$\hat{\beta}_0 = 0.51$$ and $$\hat{\beta}_1 \approx 0$$. To obtain the binomial probability, invert the logit using
$$p = \dfrac{1}{1+\exp(-(\hat{\beta}_0 + \hat{\beta}_1\operatorname{Start}))}$$