FA6

Do problem 3.12 in the book without using the LM function in R.  The corresponding data file is data-table-B8.csv is attached. Specifically, the problem is regressing clathrate formation (y - mass%) on the amount of surfactant (x1 - mass %) and time (x2 - min). 

library(MASS)

## Warning: package 'MASS' was built under R version 4.2.2

data<- read.csv("C:\\Users\\abdal\\Downloads\\data-table-B8(2).csv")
X1<-data$x1
X2<-data$x2
y<-data$y
d<- t(y)
Y<-t(d)
ones<-rep(1,36)
X<-cbind(ones,X1,X2)
Beta<-ginv(t(X)%*%X)%*%t(X)%*%y

A

A.Write the model equation of clathrate formation regressed on both surfactant and time. 

codebook:
Y: Clathrate Formation
x1: Surfactant
x2: Time

\(Y=\beta_0+\beta_1x_1+\beta_2x_2+\epsilon\)

B

B.Fit the model in R without using the LM function. What is the dimensionality of Y? What is the dimensionality of X?

Beta<-ginv(t(X)%*%X)%*%t(X)%*%y

Dimension of Y is 36X1

dim(Y)

## [1] 36  1

Dimension of X is 36X3

dim(X)

## [1] 36  3

C

C.What are the least squares estimates of the regression parameters in the model?

Beta

##             [,1]
## [1,]  11.0869804
## [2,] 350.1192457
## [3,]   0.1089344

\[ \beta_0=11.0869 \\ \beta_1=350.1192457\\ \beta_2=0.1089344 \]