Question

5.
a. Analyze the Bread variable in the SandwichAnts dataset using aov() in R and
interpret your results.
The data may be found here:
install.packages("Lock5Data")
library(Lock5Data)
data(SandwichAnts,package="Lock5Data")
attach(SandwichAnts)
b. State the linear model for this problem. Define all notation and model terms.
c. Create the design matrix for this problem.
d. Estimate model parameters for this problem using ? = (?^T?)^-1?^T?
e. Interpret the meaning of the estimates from part d.
f. Rerun this problem using lm()in R. Interpret the coefficients in the output.
g. Rewrite the model in as a linear regression using dummy variables. Confirm the
results from part f. agree with the results from part g.
h. Perform a one-way ANOVA of Bread using a randomization test on the
SandwichAnts dataset.

Answer 1

(a)

You did not mention the dependent variable. I suppose it is the Ants variable in SandwichAnts data If it is not then you can ask me in comments.

[ I am giving the R codes for the first 4 Questions.]

library(Lock5Data)
data(SandwichAnts,package="Lock5Data")
attach(SandwichAnts)
summary(SandwichAnts)

# (b)
# Here Ants is discrete variable order iscontinuous variable and the others are catagorical variable.
# Let us build the linear model for this
# y=b1+x1+x2+e where y:- Ants, b1:- constant term, X1:-Effect of Bread, X2:-Effect of Filling, e:- Error(follows independently Normal with mean zero and unknownvarince)

#(c)
# the design matrix is X = [1,x11,x12,x13,x14,x21,x22,x23]
# where 1 is the vector of ones X1 is divided into 4 catagories and X2 is divided into 3 catagories
# X11,x12,...,X14 are 4 dummy variables denoting four catagories of X1 and X21,x22,x23 are the three dummy variables denoting three catagories of x2

x11=as.numeric(Bread=="Multigrain") ; x12=as.numeric(Bread=="Rye")
x13=as.numeric(Bread=="White") ; x14=as.numeric(Bread=="Wholemeal")

x21=as.numeric(Filling=="Ham & Pickles") ; x22=as.numeric(Filling=="Peanut Butter") ;x23=as.numeric(Filling=="Vegemite")

X=cbind(rep(1,24),x11,x12,x13,x14,x21,x22,x23)

#(d)
library(matlib)
b=Ginv(t(X)%*%X)%*%(t(X)%*%Ants) # estimated parameters b=((X'x)^-1)X'y

[ If you have any confusion regarding anything let me know]