library("readxl")

my_data = read_excel("ex11-54cheese.xls")

# 11.53

taste = my_data[[2]]

print("Taste")
print(paste("Mean: ", toString(mean(taste))))
print(paste("Median: ", toString(median(taste))))
print(paste("Standard Deviation: ", toString(sd(taste))))
print(paste("Inter Quartile Range: ", toString(IQR(taste))))
stem(taste)
qqnorm(taste, main = "Normal Q-Q Plot of Taste")
qqline(taste)
cat("\n")

acetic = my_data[[3]]

print("Acetic")
print(paste("Mean: ", toString(mean(acetic))))
print(paste("Median: ", toString(median(acetic))))
print(paste("Standard Deviation: ", toString(sd(acetic))))
print(paste("Inter Quartile Range: ", toString(IQR(acetic))))
stem(acetic)
qqnorm(acetic, main = "Normal Q-Q Plot of Acetic")
qqline(acetic)
cat("\n")

h2s = my_data[[4]]

print("H2S")
print(paste("Mean: ", toString(mean(h2s))))
print(paste("Median: ", toString(median(h2s))))
print(paste("Standard Deviation: ", toString(sd(h2s))))
print(paste("Inter Quartile Range: ", toString(IQR(h2s))))
stem(h2s)
qqnorm(h2s, main = "Normal Q-Q Plot of H2S")
qqline(h2s)
cat("\n")

lactic = my_data[[5]]

print("Lactic")
print(paste("Mean: ", toString(mean(lactic))))
print(paste("Median: ", toString(median(lactic))))
print(paste("Standard Deviation: ", toString(sd(lactic))))
print(paste("Inter Quartile Range: ", toString(IQR(lactic))))
stem(lactic)
qqnorm(lactic, main = "Normal Q-Q Plot of Lactic")
qqline(lactic)
cat("\n")

#11.54

plot(acetic, lactic, main = "Lactic vs Acetic", xlab = "Acetic", ylab = "Lactic")
co = cor(acetic, lactic)
print(paste("Correlation between Acetic and Lactic: ", toString(co)))
t = sqrt(length(acetic) - 2) * co / sqrt(1-co^2)
print(paste("P(|T|>", toString(t), ")=", toString(2 * (1-pt(abs(t), length(acetic) - 2)))))
cat("\n")

plot(acetic, taste, main = "Taste vs Acetic", xlab = "Acetic", ylab = "Taste")
co = cor(acetic, taste)
print(paste("Correlation between Acetic and Taste: ", toString(co)))
t = sqrt(length(acetic) - 2) * co / sqrt(1-co^2)
print(paste("P(|T|>", toString(t), ")=", toString(2 * (1-pt(abs(t), length(acetic) - 2)))))
cat("\n")

plot(acetic, h2s, main = "H2S vs Acetic", xlab = "Acetic", ylab = "H2S")
co = cor(acetic, h2s)
print(paste("Correlation between Acetic and H2S: ", toString(co)))
t = sqrt(length(acetic) - 2) * co / sqrt(1-co^2)
print(paste("P(|T|>", toString(t), ")=", toString(2 * (1-pt(abs(t), length(acetic) - 2)))))
cat("\n")

plot(lactic, taste, main = "Taste vs Lactic", xlab = "Lactic", ylab = "Taste")
co = cor(lactic, taste)
print(paste("Correlation between Lactic and Taste: ", toString(co)))
t = sqrt(length(acetic) - 2) * co / sqrt(1-co^2)
print(paste("P(|T|>", toString(t), ")=", toString(2 * (1-pt(abs(t), length(acetic) - 2)))))
cat("\n")

plot(lactic, h2s, main = "H2S vs Lactic", xlab = "Lactic", ylab = "H2S")
co = cor(lactic, h2s)
print(paste("Correlation between Lactic and H2S: ", toString(co)))
t = sqrt(length(acetic) - 2) * co / sqrt(1-co^2)
print(paste("P(|T|>", toString(t), ")=", toString(2 * (1-pt(abs(t), length(acetic) - 2)))))
cat("\n")

plot(taste, h2s, main = "H2S vs Taste", xlab = "Taste", ylab = "H2S")
co = cor(taste, h2s)
print(paste("Correlation between Taste and H2S: ", toString(co)))
t = sqrt(length(acetic) - 2) * co / sqrt(1-co^2)
print(paste("P(|T|>", toString(t), ")=", toString(2 * (1-pt(abs(t), length(acetic) - 2)))))
cat("\n")


#11.55
pred = lm(taste ~ acetic, data = data.frame(taste, acetic))
plot(taste ~ acetic, data = data.frame(taste, acetic), main = "Taste vs Acetic", ylab = "Taste", xlab = "Acetic")
abline(pred)
res = resid(pred)
plot(acetic, res, main = "Taste Residuals vs Acetic", xlab = "Acetic", ylab = "Residual")
abline(0, 0)
print(paste("Taste = ", toString(as.numeric(pred$coef[1])), "+", toString(as.numeric(pred$coef[2])), "* Acetic"))
SSM = sum((predict(pred) - mean(taste)) ^ 2)
SSE = (sum((taste - predict(pred))^2))
f = SSM * (length(taste) - 2) / SSE
print(paste("P(F >", toString(f), " )=", toString(1-pf(f, 1, length(taste)-2))))
print(paste("R^2 = ",  toString(SSM / (SSM + SSE))))
print(paste("S = ", toString(sqrt(SSE / (length(taste)-2)))))
cat("\n")

#11.56
pred = lm(taste ~ h2s, data = data.frame(taste, h2s))
plot(taste ~ h2s, data = data.frame(taste, h2s), main = "Taste vs H2S", ylab = "Taste", xlab = "H2S")
abline(pred)
res = resid(pred)
plot(acetic, res, main = "Taste Residuals vs H2S", xlab = "H2S", ylab = "Residual")
abline(0, 0)
print(paste("Taste = ", toString(as.numeric(pred$coef[1])), "+", toString(as.numeric(pred$coef[2])), "* H2S"))
SSM = sum((predict(pred) - mean(taste)) ^ 2)
SSE = (sum((taste - predict(pred))^2))
f = SSM * (length(taste) - 2) / SSE
print(paste("P(F >", toString(f), " )=", toString(1-pf(f, 1, length(taste)-2))))
print(paste("R^2 = ",  toString(SSM / (SSM + SSE))))
print(paste("S = ", toString(sqrt(SSE / (length(taste)-2)))))
cat("\n")

#11.57
pred = lm(taste ~ lactic, data = data.frame(taste, lactic))
plot(taste ~ lactic, data = data.frame(taste, lactic), main = "Taste vs Lactic", ylab = "Taste", xlab = "Lactic")
abline(pred)
res = resid(pred)
plot(acetic, res, main = "Taste Residuals vs Lactic", xlab = "Lactic", ylab = "Residual")
abline(0, 0)
print(paste("Taste = ", toString(as.numeric(pred$coef[1])), "+", toString(as.numeric(pred$coef[2])), "* Lactic"))
SSM = sum((predict(pred) - mean(taste)) ^ 2)
SSE = (sum((taste - predict(pred))^2))
f = SSM * (length(taste) - 2) / SSE
print(paste("P(F >", toString(f), " )=", toString(1-pf(f, 1, length(taste)-2))))
print(paste("R^2 = ",  toString(SSM / (SSM + SSE))))
print(paste("S = ", toString(sqrt(SSE / (length(taste)-2)))))
cat("\n")

#11.58 mixed with 11.55 - 11.57

#11.59

tah = lm(taste ~ (acetic + h2s), data.frame(taste, acetic, h2s))
summary(tah)

#11.60

tah = lm(taste ~ (lactic + h2s), data.frame(taste, lactic, h2s))
summary(tah)

#11.61

tah = lm(taste ~ (lactic + h2s + acetic), data.frame(taste, lactic, h2s, acetic))
summary(tah)