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3. for expert using r i solve it but i...

# Question: for expert using r i solve it but i...

###### Question details
For expert using R , I solve it but i need to figure out what I got is correct or wrong. Thank you
# Simple Linear Regression and Polynomial Regression
# HW 2
#

# Read data from csv file
str(data)

# scatterplot of independent and dependent variables
plot(data$pectin,data$firmness,xlab="Pectin, %",ylab="Firmness")

par(mfrow = c(2, 2)) # Split the plotting panel into a 2 x 2 grid

model <- lm(firmness ~ pectin , data=data)
summary(model)
anova(model)
plot(model)
shapiro.test(resid(model))
# examine histogram and boxplot of residuals
par(mfrow = c(1, 1))
hist(resid(model))
boxplot(resid(model))

# predict dependent variable for specified value of independent variable
predict(model, data.frame(pectin = 1.5))

# Estimated regression line and scatterplot of data
plot(data$pectin,data$firmness,xlab="Pectin, %", ylab="Firmness",
ylim=c(45,75),xlim=c(0,3),main="Simple Linear Regression",
pch=19,cex=1.5)
lines(sort(data$pectin),fitted(model)[order(data$pectin)], col="blue", type="l")

par(mfrow = c(2, 2))
# fit a second degree polynomial
# create quadratic term for pectin
data$pectinSq <- data$pectin^2
model2 <- lm(firmness ~ pectin + pectinSq , data=data)
summary(model2)
anova(model2)
plot(model2)
shapiro.test(resid(model2))
par(mfrow = c(1, 1))
hist(resid(model2))
boxplot(resid(model2))

# predict dependent variable for specified value of independent variable
predict(model2, data.frame(pectin = 1.5, pectinSq=2.25))

# Estimated regression line and scatterplot of data
plot(data$pectin,data$firmness,xlab="Pectin, %", ylab="Firmness",
ylim=c(45,75),xlim=c(0,3),main="Simple Linear Regression",
pch=19,cex=1.5)
lines(sort(data$pectin),fitted(model2)[order(data$pectin)], col="blue", type="l")