#ELMR 3.4
require(ISLR)
require(leaps)
library("faraway")
data(africa, package="faraway")
names(africa)
## [1] "miltcoup" "oligarchy" "pollib" "parties" "pctvote" "popn"
## [7] "size" "numelec" "numregim"
head(africa)
## miltcoup oligarchy pollib parties pctvote popn size numelec
## Angola 0 0 2 38 NA 9.7 1247 0
## Benin 5 7 1 34 45.68 4.6 113 8
## Botswana 0 0 NA 7 20.30 1.2 582 5
## Burkina 6 13 2 62 17.50 8.8 274 5
## Burundi 2 13 2 10 34.39 5.3 28 3
## Cameroon 0 0 2 34 30.30 11.6 475 14
## numregim
## Angola 1
## Benin 3
## Botswana 1
## Burkina 3
## Burundi 3
## Cameroon 3
LM shows oligarch, pollib and parties as being significant. Plot shows a trend and not spread of data.
lmod<-lm(miltcoup ~., africa)
plot(predict(lmod),residuals(lmod),xlab="Fitted",ylab="Residuals")
summary(lmod)
##
## Call:
## lm(formula = miltcoup ~ ., data = africa)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.89967 -0.90106 0.00466 0.77182 2.60931
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.8360534 1.0887267 1.686 0.10324
## oligarchy 0.1325624 0.0578618 2.291 0.02999 *
## pollib -1.2275514 0.4191202 -2.929 0.00684 **
## parties 0.0627987 0.0234284 2.680 0.01238 *
## pctvote 0.0205813 0.0144650 1.423 0.16624
## popn 0.0240960 0.0137765 1.749 0.09164 .
## size -0.0005773 0.0004559 -1.266 0.21631
## numelec -0.0502585 0.0878190 -0.572 0.57186
## numregim -0.1193285 0.3054271 -0.391 0.69909
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.264 on 27 degrees of freedom
## (11 observations deleted due to missingness)
## Multiple R-squared: 0.6036, Adjusted R-squared: 0.4861
## F-statistic: 5.138 on 8 and 27 DF, p-value: 0.0005869
Stripchart shows some outliers on the size variable
stripchart(africa)
Set linear model with sqrt of response variable while adding log to predictor variable size. Parties variable is no longer signficant
lmod<-lm(sqrt(miltcoup) ~.-size+log(size), family=poisson, africa)
plot(predict(lmod),residuals(lmod),xlab="Fitted",ylab="Residuals")
summary(lmod)
##
## Call:
## lm(formula = sqrt(miltcoup) ~ . - size + log(size), data = africa,
## family = poisson)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.71223 -0.35268 -0.05894 0.28168 0.92559
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.040669 0.455156 2.286 0.03030 *
## oligarchy 0.071439 0.023298 3.066 0.00488 **
## pollib -0.409679 0.170740 -2.399 0.02359 *
## parties 0.022552 0.009549 2.362 0.02565 *
## pctvote 0.011945 0.005872 2.034 0.05187 .
## popn 0.008310 0.005673 1.465 0.15452
## numelec -0.004258 0.036190 -0.118 0.90721
## numregim 0.071176 0.122296 0.582 0.56539
## log(size) -0.151683 0.055425 -2.737 0.01084 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5122 on 27 degrees of freedom
## (11 observations deleted due to missingness)
## Multiple R-squared: 0.6581, Adjusted R-squared: 0.5568
## F-statistic: 6.495 on 8 and 27 DF, p-value: 0.0001003
Persons F-test shows pollit and parties with higher AIC values
lmod<-glm(miltcoup ~oligarchy+pollib+parties, family=poisson, africa)
summary(lmod)
##
## Call:
## glm(formula = miltcoup ~ oligarchy + pollib + parties, family = poisson,
## data = africa)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.4495 -1.0868 -0.3699 0.5723 1.7526
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.27416 0.36432 0.753 0.45172
## oligarchy 0.09892 0.02012 4.916 8.82e-07 ***
## pollib -0.51592 0.19511 -2.644 0.00819 **
## parties 0.01641 0.00865 1.897 0.05778 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 79.124 on 41 degrees of freedom
## Residual deviance: 42.242 on 38 degrees of freedom
## (5 observations deleted due to missingness)
## AIC: 123.92
##
## Number of Fisher Scoring iterations: 5
plot(predict(lmod),residuals(lmod),xlab="Fitted",ylab="Residuals")
halfnorm(residuals(lmod))
GLM with oligarch and polib
lmod<-glm(miltcoup ~oligarchy+pollib, family=poisson, africa)
summary(lmod)
##
## Call:
## glm(formula = miltcoup ~ oligarchy + pollib, family = poisson,
## data = africa)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.4078 -1.1368 -0.3286 0.4070 1.9516
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.41840 0.36544 1.145 0.2522
## oligarchy 0.10079 0.01974 5.107 3.28e-07 ***
## pollib -0.42752 0.19134 -2.234 0.0255 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 79.124 on 41 degrees of freedom
## Residual deviance: 45.498 on 39 degrees of freedom
## (5 observations deleted due to missingness)
## AIC: 125.18
##
## Number of Fisher Scoring iterations: 5
plot(predict(lmod),residuals(lmod),xlab="Fitted",ylab="Residuals")
halfnorm(residuals(lmod))
GLM with Parties and polib
lmod<-glm(miltcoup ~pollib+parties, family=poisson, africa)
summary(lmod)
##
## Call:
## glm(formula = miltcoup ~ pollib + parties, family = poisson,
## data = africa)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9418 -1.4580 -0.1855 0.8156 2.6868
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.034517 0.305296 3.389 0.000703 ***
## pollib -0.627335 0.182239 -3.442 0.000577 ***
## parties 0.022481 0.009247 2.431 0.015052 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 79.124 on 41 degrees of freedom
## Residual deviance: 65.847 on 39 degrees of freedom
## (5 observations deleted due to missingness)
## AIC: 145.53
##
## Number of Fisher Scoring iterations: 5
plot(predict(lmod),residuals(lmod),xlab="Fitted",ylab="Residuals")
halfnorm(residuals(lmod))
