eleph <- read.csv("http://cknudson.com/data/elephant.csv")
attach(eleph)
hist(MATINGS)
modE <- lm(MATINGS ~ AGE)
resE <- residuals(modE)
plot(AGE , MATINGS)
abline(modE)
residuals(MATINGS ~ AGE)
## NULL
plot(resE)
agemat<-c(mean(subset(eleph, AGE==27)$MATINGS),mean(subset(eleph, AGE==28)$MATINGS),mean(subset(eleph, AGE==29)$MATINGS),mean(subset(eleph, AGE==30)$MATINGS),mean(subset(eleph, AGE==32)$MATINGS),mean(subset(eleph, AGE==33)$MATINGS),mean(subset(eleph, AGE==34)$MATINGS),mean(subset(eleph, AGE==36)$MATINGS),mean(subset(eleph, AGE==37)$MATINGS),mean(subset(eleph, AGE==38)$MATINGS),mean(subset(eleph, AGE==39)$MATINGS),mean(subset(eleph, AGE==41)$MATINGS),mean(subset(eleph, AGE==42)$MATINGS),mean(subset(eleph, AGE==43)$MATINGS),mean(subset(eleph, AGE==44)$MATINGS),mean(subset(eleph, AGE==45)$MATINGS),mean(subset(eleph, AGE==47)$MATINGS),mean(subset(eleph, AGE==48)$MATINGS),mean(subset(eleph, AGE==52)$MATINGS))
agemat
## [1] 0.000000 1.500000 1.000000 1.000000 2.000000 3.000000 1.750000
## [8] 5.500000 2.666667 2.000000 1.000000 3.000000 4.000000 3.600000
## [15] 3.000000 5.000000 7.000000 2.000000 9.000000
a2<-log(agemat)
plot(a2)
ages<-c(27,28,29,30,32,33,34,36,37,38,39,41,42,43,44,45,47,48,52)
plot(ages, a2)
#log of matings is a better determiner of age than just age, and as age goes up so does matings
#No evidence for quadratic, looks more linear
attach(eleph)
## The following objects are masked from eleph (pos = 3):
##
## AGE, MATINGS
AGEexp <- exp(AGE)
AGEsq <- AGE^2
modE2 <- glm(MATINGS ~ AGE, family = "poisson")
modE3 <- glm(MATINGS ~ AGEsq, family = "poisson")
modE4 <- glm(MATINGS ~ AGEexp, family = "poisson")
modE5 <- glm(MATINGS ~ 1, family = "poisson")
modE6 <- glm(MATINGS ~ AGEexp + AGE, family = "poisson")
summary(modE6)
##
## Call:
## glm(formula = MATINGS ~ AGEexp + AGE, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.74369 -0.87056 -0.09645 0.55428 2.28465
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.373e+00 6.147e-01 -2.234 0.0255 *
## AGEexp 7.886e-24 1.091e-23 0.723 0.4696
## AGE 6.276e-02 1.604e-02 3.914 9.09e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 75.372 on 40 degrees of freedom
## Residual deviance: 50.509 on 38 degrees of freedom
## AIC: 157.95
##
## Number of Fisher Scoring iterations: 5
summary(modE2)
##
## Call:
## glm(formula = MATINGS ~ AGE, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.80798 -0.86137 -0.08629 0.60087 2.17777
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.58201 0.54462 -2.905 0.00368 **
## AGE 0.06869 0.01375 4.997 5.81e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 75.372 on 40 degrees of freedom
## Residual deviance: 51.012 on 39 degrees of freedom
## AIC: 156.46
##
## Number of Fisher Scoring iterations: 5
summary(modE3)
##
## Call:
## glm(formula = MATINGS ~ AGEsq, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.76066 -0.84290 -0.06587 0.58710 2.25632
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.2588755 0.2847181 -0.909 0.363
## AGEsq 0.0008635 0.0001711 5.047 4.5e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 75.372 on 40 degrees of freedom
## Residual deviance: 51.590 on 39 degrees of freedom
## AIC: 157.04
##
## Number of Fisher Scoring iterations: 5
summary(modE4)
##
## Call:
## glm(formula = MATINGS ~ AGEexp, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.2462 -1.0928 -0.3413 0.2920 3.1527
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 9.252e-01 9.958e-02 9.290 < 2e-16 ***
## AGEexp 3.327e-23 9.076e-24 3.666 0.000247 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 75.372 on 40 degrees of freedom
## Residual deviance: 65.782 on 39 degrees of freedom
## AIC: 171.23
##
## Number of Fisher Scoring iterations: 5
summary(modE5)
##
## Call:
## glm(formula = MATINGS ~ 1, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3164 -1.1799 -0.4368 0.1899 3.0252
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.98691 0.09535 10.35 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 75.372 on 40 degrees of freedom
## Residual deviance: 75.372 on 40 degrees of freedom
## AIC: 178.82
##
## Number of Fisher Scoring iterations: 5
sqrt(AGE^2)
## [1] 27 28 28 28 28 29 29 29 29 29 29 30 32 33 33 33 33 33 34 34 34 34 36
## [24] 36 37 37 37 38 39 41 42 43 43 43 43 43 44 45 47 48 52
#and increase in 1 for age leads to an incrase in 1.03 matings
modE2 <- glm(MATINGS ~ AGE, family = "poisson")
confint(modE4, parm="AGEexp",level = .95)
## Waiting for profiling to be done...
## 2.5 % 97.5 %
## 1.356193e-23 4.956250e-23
teststat<-deviance(modE2)-deviance(modE5)
pchisq(teststat,df=1,lower.tail=FALSE)
## [1] 1
attach(eleph)
## The following objects are masked from eleph (pos = 3):
##
## AGE, MATINGS
## The following objects are masked from eleph (pos = 4):
##
## AGE, MATINGS
modE7 <- glm(MATINGS ~ AGE , family = "poisson")
modE8 <- glm(MATINGS ~ AGEsq, family = "poisson")
modE9 <- glm(MATINGS ~ AGEsq + AGE, family = "poisson")
summary(modE7)
##
## Call:
## glm(formula = MATINGS ~ AGE, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.80798 -0.86137 -0.08629 0.60087 2.17777
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.58201 0.54462 -2.905 0.00368 **
## AGE 0.06869 0.01375 4.997 5.81e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 75.372 on 40 degrees of freedom
## Residual deviance: 51.012 on 39 degrees of freedom
## AIC: 156.46
##
## Number of Fisher Scoring iterations: 5
summary(modE8)
##
## Call:
## glm(formula = MATINGS ~ AGEsq, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.76066 -0.84290 -0.06587 0.58710 2.25632
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.2588755 0.2847181 -0.909 0.363
## AGEsq 0.0008635 0.0001711 5.047 4.5e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 75.372 on 40 degrees of freedom
## Residual deviance: 51.590 on 39 degrees of freedom
## AIC: 157.04
##
## Number of Fisher Scoring iterations: 5
teststat2 <-deviance(modE9)-deviance(modE7)
pchisq(teststat2 ,df=1, lower.tail=FALSE)
## [1] 1