y= succes/fail (%)

x= Var1 : Temperature data

m1<-glm(cbind(succes,fail)~Var1, data=data, family = binomial(logit))

HTML:

```
Call:
glm(formula = cbind(succes, fail) ~ Var1, family = binomial(logit),
data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-14.2244 -0.1595 1.8024 1.9983 6.9403
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.196658 0.098642 12.13 <2e-16 ***
Var1 0.104118 0.004219 24.68 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 2195.8 on 224 degrees of freedom
Residual deviance: 1769.5 on 223 degrees of freedom
AIC: 2008.8
Number of Fisher Scoring iterations: 6
```

I found a possible way to correct for the overdispersion:

HTML:

```
sigma2<-sum(residuals(m1,type = "pearson")^2)/222
summary(m1, dispersion=sigma2)
Call:
glm(formula = cbind(succes, fail) ~ Var1, family = binomial(logit),
data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-14.2244 -0.1595 1.8024 1.9983 6.9403
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.19666 0.41038 2.916 0.00355 **
Var1 0.10412 0.01755 5.932 3e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 17.30784)
Null deviance: 2195.8 on 224 degrees of freedom
Residual deviance: 1769.5 on 223 degrees of freedom
AIC: 2008.8
Number of Fisher Scoring iterations: 6
```