# Fit, AIC and deviation of my generalized linear model (poisson)

I need to fit a GLM (generalized linear model) in R, something like

model <- glm(Daily.Results ~ sqrt.of.Clicks + Days + log.of.Clicks * sqrt.of.Days, family = poisson)


which relates

Daily.Results = variable that I need to count (and predict)

Clicks = counts clicks in a link (which drives a person to be a potencial buyer)

sqrt.of.Clicks = square root of Clicks

log.of.Clicks = natural logarithm of Clicks

Days = 1, 2, 3... sqrt.of.Days = square root of 1, 2, 3...

in a dataset with 14 rows/observations

and family = poisson because Daily.Results are non negative integers, with log link-function

The results of summary(model) are:

Call:
glm(formula = Daily.Results ~ sqrt.of.Clicks + Days + log.of.Clicks *
sqrt.of.Days, family = "poisson")

Deviance Residuals:
Min        1Q    Median        3Q       Max
-2.24096  -0.61927  -0.09041   0.81640   2.45392

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                120.88890   22.33723   5.412 6.23e-08 ***
sqrt.of.Clicks               0.27487    0.07698   3.571 0.000356 ***
Days                         0.35892    0.09334   3.845 0.000120 ***
log.of.Clicks              -15.84863    3.20527  -4.945 7.63e-07 ***
sqrt.of.Days               -23.43680    4.22029  -5.553 2.80e-08 ***
log.of.Clicks:sqrt.of.Days   2.66063    0.47141   5.644 1.66e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 499.316  on 13  degrees of freedom
Residual deviance:  23.706  on  8  degrees of freedom
AIC: 141.81

Number of Fisher Scoring iterations: 4


The model above is the one which have the minimal AIC and Residual deviance (after some data transformation tentatives / log and sqrt of the data)

1. I do not know very well how good or bad can be this model. By now, I often read people saying here that lower AIC and residual deviance means better fit. Is this correct and enough?
2. Also, would be nice to know which value can be considered lower enough (R squared is so far more friendly). Can you help me with that?
3. A really good fit can lead to bad predictions? Can you give some example?
4. The diagnostic plots of my regression (plot(model)) follows, and I could not tell if some visual information can be found there. Perhaps, evidence of errors that I don't realized.

Residuals vs Fitted

Normal Q-Q

Scale-Location

Residuals vs Leverage

Cook's distance

Cook's distance vs Leverage