# STAT_516_Lec_11_inclass


vo2max <- data.frame(chg = c(17.05,4.96,10.40,11.05,0.26,2.51,
                             -0.87,-10.74,-3.27,-1.97,7.50,-7.25),
                     grp = as.factor(c(rep("aerobic",6),rep("running",6))),
                     age = c(31,23,27,28,22,24,23,22,22,25,27,20))
vo2max


boxplot(chg ~ grp, data = vo2max)

boxplot(age ~ grp, data = vo2max)

plot(chg ~ age, data = vo2max, pch = ifelse(grp == "running",19,1))

lm_vo2max <- lm(chg ~ grp + age, data = vo2max)
summary(lm_vo2max)

parms <- coef(lm_vo2max)

abline(parms[1],parms[3],lty = 2)
abline(parms[1] + parms[2],parms[3])

# do not use sequential SS, which is what you get from the anova() function
# instead use Anova() from that R package car

library(car)
Anova(lm_vo2max,type="III")


mean(vo2max$chg[vo2max$grp == "running"])
mean(vo2max$chg[vo2max$grp == "aerobic"])

# soybean data
soybean <- data.frame(yield = c(12.2,12.1,12.3,16.6,15.6,15.0,9.5,9.8,8.6,
                                12.4,13.1,12.3,15.8,15.8,16.2,9.5,9.1,10.4,
                                11.9,12.7,12.6,16.5,15.8,16.7,9.6,10.3,9.4,
                                11.3,12.4,13.2,15.0,16.0,15.8,8.8,9.5,10.2,
                                11.8,11.4,12.3,15.4,15.8,15.9,9.5,8.5,9.3),
                      trt = as.factor(rep(c(rep("C",3),rep("SL",3),rep("PS",3)),5)),
                      height = c(45,48,48,63,45,35,52,62,41,
                                 52,60,51,50,50,50,54,52,67,
                                 42,61,56,63,48,62,58,67,55,
                                 35,50,65,33,50,49,45,55,66,
                                 40,33,51,38,49,52,57,40,56))
head(soybean,n = 12)

boxplot(yield ~ trt, data = soybean)
boxplot(height ~ trt, data = soybean)

plot(yield ~ height, data = soybean, pch = as.character(trt))

lm_soybean <- lm(yield ~ trt + height + trt:height, data = soybean)
summary(lm_soybean)