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actually other expert help me with a solution for hw1 (thanks a lot for him). so , if you look just the question that I post you can see it or just write the first line of the question , thank you for your interest in my question . I post the code that I used at first homework

# Set directory to data folder

setwd("C:data")

# getwd()

# Read data from csv file

data <- read.csv("SweetPotatoFirmness.csv",header=TRUE, sep=",")

head(data)

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)

plot(model)

par(mfrow=c(1,1))

# Residual Plot

data$residuals <- resid(model)

data$predict <- predict(model)

plot(data$predict,data$residuals,xlab="Fitted Values",ylab="Residuals")

# 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")

A food processor was receiving complaints from its customers about the firmness of its canned sweet potatoes. The firm's research scientist decided to gather data on their product to determine if adding pectin to the sweet potatoes might result in a product with a more desirable firmness. The scientist measured firmness on canned sweet potatoes at various pectin concentrations. Before testing, the cans were sealed and placed in a 25 environment for 30 days. Pectin Concentration Fimness Reading 0% 1% 2% 3% 6.90, 50.20, 51.3056.48, 59.34, 62.9767.91, 70.78, 73.6768.13. 70.85, 72.34 Let denote the pectin concentration of the sweet potatoes in a can and denote the firmness reading following the 30 days of storage at 25. Question 1: Simple Linear Regression (continued from HW1) (a)Interpret the slope parameter estimated in HW 1 (b)Perform regression diagnostics and comment on the validity of each assumption. This includes the four diagnostic plots and the Shapiro-Wilk test. For Shapiro-Wilk, give hypotheses, result from R, use to make a decision about the null hypothesis, and give a conclusion.

(b) Perform regression diagnostics and comment on the validity of each assumption. This includes the four diagnostic plots and the Shapiro-Wilk test. For Shapiro-Wilk, give hypotheses, result from R use a0.01 to make a decision about the null hypothesis, and give a conclusion. (c) Complete the following analysis of variance table for this model. Source df SumSq Mean SqF value PrF Total

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