R Manually implementing Regression Likelihood Ratio Test

I'm trying to implement my own linear regression likelihood ratio test.

The test is where you take the sum of squares of a reduced model and the sum of squares of a full model and compare it to the F statistic.

However, I am having some trouble implementing the function, especially when dealing with dummy variables.

This is the dataset I am working with and testing the function on.

Here is the code so far: The function inputs are the setup matrix mat, the response matrix which has just one column, the indices (variables) being test, and the alpha value the test is at.

linear_regression_likelihood <- function(mat, response, indices, alpha) {
  mat <- as.matrix(mat)
  reduced <- mat[,c(1, indices)]

  q <- 1 #set q = 1 just to test on data

  p <- dim(mat)[2]
  n <- dim(mat)[1]

  f_stat <- qf(1-alpha, df1 = p-q, df2 = n-(p+1))
  beta_hat_full <- qr.solve(t(mat)%*%mat)%*%t(mat)%*%response
  y_hat_full <- mat%*%beta_hat_full
  SSRes_full <- t(response - y_hat_full)%*%(response-y_hat_full)


  beta_hat_red <- qr.solve(t(reduced)%*%reduced)%*%t(reduced)%*%response
  y_hat_red <- reduced%*%beta_hat_red
  SSRes_red <- t(response - y_hat_red)%*%(response-y_hat_red)



  s_2 <- (t(response - mat%*%beta_hat_full)%*%(response - mat%*%beta_hat_full))/(n-p+1)

  critical_value <- ((SSRes_red - SSRes_full)/(p-q))/s_2
  print(critical_value)
  if (critical_value > f_stat) {
    return ("Reject H0")
  }
  else {
    return ("Fail to Reject H0")
  }
}

Here is the setup code, where I setup the matrix in the correct format. Data is the read in csv file.

data <- data[, 2:5]

mat <- data[, 2:4]


response <- data[, 1]


library(ade4)
df <-data.frame(mat$x3)
dummy <- acm.disjonctif(df)
dummy
mat <- cbind(1, mat[1:2], dummy)

linear_regression_likelihood(mat, response, 2:3, 0.05)

This is the error I keep getting.

Error in solve.default(as.matrix(c)) : system is computationally singular: reciprocal condition number = 1.63035e-18

I know it has to do with taking the inverse of the matrix after it is multiplied, but the function is unable to do so. I thought it may be due to the dummy variables having too small of values, but I am not sure of any other way to include the dummy variables.

The test I am doing is to check whether the factor variable x3 has any affect on the response y. The actual answer which I verified using the built in functions states that we fail to reject the null hypothesis.

Any advice is appreciated. Please let me know if you require anymore information.

Thank you for reading