head(puffin)
dim(puffin)
summary(puffin)
pairs(puffin)
puffin$sqrtfreq <- sqrt(puffin$Nesting_Frequency)
puff.sqlm <- lm(sqrtfreq~ Grass_Cover + Mean_Soil_Depth + Slope_Angle
+Distance_from_Edge, data=puffin)
old.par <- par(no.readonly = TRUE)
par(mfrow=c(2,1))
qqnorm(puff.sqlm$res,main="Normal probability plot", col=2)
qqline(puff.sqlm$res, col="blue")
plot(puff.sqlm$fit, puff.sqlm$res,xlab="Fitted values",ylab="Residuals",
main="Anscombe plot")
abline(h=0)
summary(puff.sqlm)
par(old.par)
#####################################
# F test for two betas at the same time:
######################################
puff.sqlm2 <- lm(sqrtfreq~ Mean_Soil_Depth + Distance_from_Edge, data=puffin)
anova(puff.sqlm)
anova(puff.sqlm2)
fval <- 1/2*(14.245-12.756)/0.387 # 1.924
qf(0.95, 2, 33) # 3.28
1-pf(fval, 2, 33) # 0.162
anova(puff.sqlm2, puff.sqlm)
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