gistfile1.r

#Solving for the values of SSR,SSE, and SST using matrix in R.
#Codes:

#Lets input first everything we need in the computations.
#Inputting the given for the dependent and independent value.
IndependentVar <-c(1,93,1,104,1,104,1,126,1,98,1,99,1,94,1,96,
[17] 1,124,1,73,1,110,1,90,1,104,1,81,1,106,1,113,1,129,1,97,1,
[37] 101,1,91,1,100,1,123,1,88,1,117,1,107,1,105,1,86,1,131,1,
[58] 95,1,98)
 
DependentVar <- c(1769,1740,1941,2367,2467,1640,1756,1706,
[9] 1767,1200,1706,1985,1555,1749,2056,1729,2186,1858,1819,
[20] 1350,2030,2550,1544,1766, 1937,1691,1623,1791,2001,1874)
 
#Next we put them in a matrix
 
X <- matrix(IndependentVar, ncol = 2, byrow = T)
 
Y <- matrix(DependentVar, ncol = 1, byrow = T)
 
#This time lets solve for the X’ and Y’.
 
XPrime <- t(X) #transposing X
YPrime <- t(Y) #transposing Y
 
#Now, lets make an Identity matrix
 
n <- c(30)  #here we assign our n equal to 30
I <- matrix(0, nrow = n, ncol = n)  #we define an n by n 
                        #matrix here that has an entries of 0.
I[row(I) == col(I)] <- 1  #here we assign a value 1 if the ith 
                          #rows is equal to the jth columns.
 
#Since we have our Identity matrix now, it’s easy for us then 
#to make a J matrix that consist of entries 1.
 
J <- matrix(1, nrow = n, ncol = n)
 
#We are almost ready for computation, but before that we need 
#to define first our H. To do that lets define the inverse 
#first.

XXPrime <- XPrime%*%X       #here we define X’X
Inverse <- solve(XXPrime)   #here we have (X’X)^(-1)
H <- X%*%Inverse%*%XPrime

#Ok we’re done with all the variables we need in our
#computation, this time lets compute for SSR.
 
SSRCen <- H – J/30  #here we define (H – J/n)
SSR <- YPrime%*%SSRCen%*%Y
SSR
        [,1]
[1,]  640267.6
 
#Next, we compute for SSE
 
SSECen <- I – H  #here we define (I – H)
SSE <- YPrime%*%SSECen%*%Y
SSR
        [,1]
[1,]  1825214
 
#Time to smile, we are approaching to the finish line. Lets 
#make it fast and solve for SST :)

SSTCen <- I – J/30  #here we define (I – J/n)
SST <- YPrime%*%SSTCen%*%Y
SST
        [,1]
[1,]  2465481
#Ok there you go, we got the values of SSR, SSE, and SST. You 
#can confirm that in SPSS (we did it actually).
 
#Moreover, you can also confirm SSR by using SSR = SST – SSE
SSR <- SST – SSE
SSR
        [,1]
[1,]  640267.6
 
#In addition, we can also solve for matrix beta’s, i.e. the 
#beta null and beta one.
Beta <- Inverse%*%XPrime%*%Y
Beta
        [,1]
[1,]  761.04720
[2,]   10.48381
 
#There you go, everything is done, and we’re ready to submit 
#it. :)