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# 2
forbes500 <- read.table("Forbes500.csv",header=TRUE,sep=",")
dim(forbes500)
names(forbes500)
# [1] "Company"      "Assets"       "Sales"       "Market_Value" "Profits"      "Cash_Flow"    "Employees"   
# [8] "sector"

#View(forbes500)
attach(forbes500)
# (a)
plot( log(Assets), log(Sales), pch=as.numeric(sector), col=as.numeric(sector))
legend(5.5, 11, levels(sector), pch=1:8, col=1:8)

# (b)
# i)
detach(forbes500)
fit.1 <- lm( log(Sales) ~ log(Assets)*sector, data=forbes500)

# ii)
fit.2 <- lm( log(Sales) ~ log(Assets) + sector, data=forbes500)

# iii)
anova(fit.1, fit.2)
# Analysis of Variance Table
#
# Model 1: log(Sales) ~ log(Assets) * sector
# Model 2: log(Sales) ~ log(Assets) + sector
#   Res.Df    RSS Df Sum of Sq      F Pr(>F)
# 1    61 15.704                           
# 2    68 16.681 -7 -0.97687 0.5421 0.7992

# The null hypothesis is that the additional terms: interaction terms have jointly no impact on
# log(sales), and the alternative is that at least one of them has some impact.
# The F-test shows a very low F-statistic and very high p-value, and therefore, we failed
# to reject the null....

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