Я пытаюсь вручную рассчитать коэффициенты регрессии, а не использовать данные по умолчанию http://people.sc.fsu.edu/~jburkardt/datasets/regression/x31.txt
Вот мой код, который правильно создает Q&R, удовлетворяющий A=QR. Но я не могу найти коэффициенты как измерения вопросов и ответов, создающих проблемы. Могут ли мне здесь помочь специалисты? Когда у меня есть правильные вопросы и ответы, как поиск коэффициентов может пойти не так?
library(xlsx)
data.df<-read.xlsx("regression.xlsx",2,header = F)
#Remove unneccesary Index position
data.df<-data.df[2:5]
#Decomposing
#coefficients [b]=inv(t(X)(Matrix Multiplication)(X))(Matrix Multiplication)t(X)(Matrix Multiplication)y
Y<-as.matrix(data.df[4])
#But note that if you need to express Y=Xb, the coefficient of b_0 must be X_0
#which is 1
X_0<-as.data.frame(c(1,1,1,1,1,1,1,1,1,1))
X<-(cbind(X_0,data.df[1:3]))
names(X)<-c("X1","X2","X3","X4")
X<-as.matrix(X)
#Create copy for final evaluvations
A<-X
x1<-as.matrix(X[,1])
deter_x<-sqrt(sum(x1^2))
n=dim(x1)[1]
deter_e1<-as.matrix(c(deter_x,rep(0,n-1)))
v1=x1+deter_e1
#c_i=2/(transpose(v_i)%*%(v_i))
c1<-as.numeric(2/(t(v1)%*%v1))
#H_i = I - c_i*v_i%*%transpose(v_i)
I<-diag(n)
H1<-I-c1*(v1%*%t(v1))
R1<-H1%*%X
#Check R1 and see if it is Upper Triangle Matrix
R1
#We will take rest of the interesting portion of matrix R1.
n=dim(R1)[1]
X<-as.matrix(as.data.frame(cbind(R1[2:n,2],R1[2:n,3],R1[2:n,4])))
x1<-as.matrix(X[,1])
deter_x<-sqrt(sum(x1^2))
n=dim(x1)[1]
deter_e1<-as.matrix(c(deter_x,rep(0,n-1)))
v1=x1-deter_e1
#c_i=2/(transpose(v_i)%*%(v_i))
c1<-as.numeric(2/(t(v1)%*%v1))
#H_i = I - c_i*v_i%*%transpose(v_i)
I<-diag(n)
H2<-I-c1*(v1%*%t(v1))
R2<-H2%*%X
#Check R2 and see if it is Upper Triangle Matrix, if no go for R3
n=dim(R2)[1]
X<-as.matrix(as.data.frame(cbind(R2[2:n,2],R2[2:n,3])))
x1<-as.matrix(X[,1])
deter_x<-sqrt(sum(x1^2))
n=dim(x1)[1]
deter_e1<-as.matrix(c(deter_x,rep(0,n-1)))
v1=x1+deter_e1
#c_i=2/(transpose(v_i)%*%(v_i))
c1<-as.numeric(2/(t(v1)%*%v1))
#H_i = I - c_i*v_i%*%transpose(v_i)
I<-diag(n)
H3<-I-c1*(v1%*%t(v1))
R3<-H3%*%X
R3
#Check R3 and see if it is Upper Triangle Matrix, if no go for R4
n=dim(R3)[1]
X<-as.matrix(as.data.frame(cbind(R3[2:n,2])))
x1<-as.matrix(X[,1])
deter_x<-sqrt(sum(x1^2))
n=dim(x1)[1]
deter_e1<-as.matrix(c(deter_x,rep(0,n-1)))
v1=x1-deter_e1
#c_i=2/(transpose(v_i)%*%(v_i))
c1<-as.numeric(2/(t(v1)%*%v1))
#H_i = I - c_i*v_i%*%transpose(v_i)
I<-diag(n)
H4<-I-c1*(v1%*%t(v1))
R4<-H4%*%X
R4
#As we can see R4 has all values except first element as zero
#Let us replace Matrices iteratively in R1 from R2 to R4 and round it of
R1[2:10,2:4]<-R2
R1[3:10,3:4]<-R3
R1[4:10,4]<-R4
R<-round(R1,5)
R
#Find Complete H1
#Q=H1%*%H2%*%H3%*%H4
H1_COM<-H1
#
H_temp<-diag(10)
n=dim(H_temp)[1]
dim(H_temp[2:n,2:n])
dim(H2)
H_temp[2:n,2:n]<-H2
H2_COM<-H_temp
H2_COM
H_temp<-diag(10)
n=dim(H_temp)[1]
dim(H_temp[3:n,3:n])
dim(H3)
H_temp[3:n,3:n]<-H3
H3_COM<-H_temp
H3_COM
H_temp<-diag(10)
n=dim(H_temp)[1]
dim(H_temp[4:n,4:n])
dim(H4)
H_temp[4:n,4:n]<-H4
H4_COM<-H_temp
Q=H1_COM%*%H2_COM%*%H3_COM%*%H4_COM
# The following code properly reconstructs A Matrix proving proper Q & R
A=round(Q%*%R)
# When you try to find coefficients using Q&R you will end up in error.
solve(R)%*%t(Q)%*%Y
#Error in solve.default(R) : 'a' (10 x 4) must be square
#So trying to get matrix R without all 0 rows R[1:4,1:4]
solve(R[1:4,1:4])%*%t(Q)%*%Y
#Error in solve(R[1:4, 1:4]) %*% t(Q) : non-conformable arguments
dim(solve(R[1:4,1:4]))
dim(solve(R[1:4,1:4]))
#4 4
dim(t(Q))
#[1] 10 10
dim(Y)
#10 1
