HHernandez_DATA621_Discussion09

ELMR 3.2

library(ggplot2)
require("faraway")
data(turtle)
t <- turtle
head(turtle)

##   temp male female
## 1 27.2    1      9
## 2 27.2    0      8
## 3 27.2    1      8
## 4 27.7    7      3
## 5 27.7    4      2
## 6 27.7    6      2

plot(t$male  ~ t$temp)

plot(t$female ~ t$temp)

#Using Poisson regression as the target variable is a count of males
logm <- glm(formula = male ~ temp, family= "poisson", data=t)
summary(logm)

## 
## Call:
## glm(formula = male ~ temp, family = "poisson", data = t)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.7089  -0.6825  -0.1991   0.4930   2.6332  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -9.4281     3.0516  -3.090  0.00200 ** 
## temp          0.3944     0.1064   3.706  0.00021 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 36.608  on 14  degrees of freedom
## Residual deviance: 23.369  on 13  degrees of freedom
## AIC: 77.225
## 
## Number of Fisher Scoring iterations: 5

# Residuals vs Fitted values
plot(logm$fitted.values, logm$residuals)

# Adding a quadratic term in temp
logm2 <- glm(formula = male ~ poly(temp,2), family= "poisson", data=t)
summary(logm2)

## 
## Call:
## glm(formula = male ~ poly(temp, 2), family = "poisson", data = t)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.7887  -0.5097  -0.2783   0.2461   1.7273  
## 
## Coefficients:
##                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      1.6307     0.1280  12.738  < 2e-16 ***
## poly(temp, 2)1   2.0232     0.5090   3.975 7.04e-05 ***
## poly(temp, 2)2  -1.5356     0.4996  -3.074  0.00211 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 36.608  on 14  degrees of freedom
## Residual deviance: 12.763  on 12  degrees of freedom
## AIC: 68.619
## 
## Number of Fisher Scoring iterations: 5

# Residuals vs Fitted values
plot(logm2$fitted.values, logm2$residuals)