diff --git a/tests/testthat/test-sgd_lm.R b/tests/testthat/test-sgd_lm.R
index 8827df3..fc63d9b 100644
--- a/tests/testthat/test-sgd_lm.R
+++ b/tests/testthat/test-sgd_lm.R
@@ -88,6 +88,7 @@ test_that("sgd_lm burn matters 2", {
   check = max(abs(out1$coefficients - out2$coefficients))
   expect_false(check==0)
 })
+
 test_that("sgd_lm with scalar X", {
   n = 1e05
   p = 2
@@ -100,3 +101,16 @@ test_that("sgd_lm with scalar X", {
   check = max(abs(out1$coefficients - out2$coefficients))
   expect_false(check==0)
 })
+
+test_that("sgd_lm with scalar X with/out intercept", {
+  n = 1e05
+  p = 2
+  bt0 = c(0,5)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_lm(y~., data=my.dat, intercept=TRUE)
+  out2 = sgd_lm(y~., data=my.dat, intercept=FALSE)
+  check = max(abs(out1$coefficients[-1] - out2$coefficients))
+  expect_false(check==0)
+})
diff --git a/tests/testthat/test-sgd_qr.R b/tests/testthat/test-sgd_qr.R
new file mode 100644
index 0000000..27a5552
--- /dev/null
+++ b/tests/testthat/test-sgd_qr.R
@@ -0,0 +1,116 @@
+test_that("sgd_qr studentize matters", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat, studentize=TRUE)
+  out2 = sgd_qr(y~., data=my.dat, studentize=FALSE)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgd_qr no_studentize matters", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat)
+  out2 = sgd_qr(y~., data=my.dat, no_studentize=1e06)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgd_qr intercept matters 1", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat)
+  out2 = sgd_qr(y~., data=my.dat, intercept=FALSE)
+  check = max(abs(out1$coefficients[-1] - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgd_qr intercept matters 2", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat, studentize=FALSE)
+  out2 = sgd_qr(y~., data=my.dat, studentize=FALSE, intercept=FALSE)
+  check = max(abs(out1$coefficients[-1] - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgd_qr bt_start matters", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat)
+  out2 = sgd_qr(y~., data=my.dat, bt_start=bt0)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgd_qr burn matters 1", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat)
+  out2 = sgd_qr(y~., data=my.dat, burn=100)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgd_qr burn matters 2", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat, studentize=FALSE)
+  out2 = sgd_qr(y~., data=my.dat, burn=100, studentize=FALSE)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgd_qr with scalar X", {
+  n = 1e05
+  p = 2
+  bt0 = rep(5,2)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat, studentize=TRUE)
+  out2 = sgd_qr(y~., data=my.dat, studentize=FALSE)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgd_qr with scalar X with/out intercept", {
+  n = 1e05
+  p = 2
+  bt0 = c(0,5)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgd_qr(y~., data=my.dat, intercept=TRUE)
+  out2 = sgd_qr(y~., data=my.dat, intercept=FALSE)
+  check = max(abs(out1$coefficients[-1] - out2$coefficients))
+  expect_false(check==0)
+})
diff --git a/tests/testthat/test-sgdi_lm.R b/tests/testthat/test-sgdi_lm.R
index 53e418b..e266fc4 100644
--- a/tests/testthat/test-sgdi_lm.R
+++ b/tests/testthat/test-sgdi_lm.R
@@ -50,3 +50,42 @@ test_that("Run the code with an option studentize=F",
             expect_true(check<1e-2)
           }
 )
+
+test_that("sgdi_lm no_studentize matters", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_lm(y~., data=my.dat)
+  out2 = sgdi_lm(y~., data=my.dat, no_studentize=1e06)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgdi_lm with scalar X", {
+  n = 1e05
+  p = 2
+  bt0 = rep(5,2)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_lm(y~., data=my.dat, studentize=TRUE)
+  out2 = sgdi_lm(y~., data=my.dat, studentize=FALSE)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgdi_lm with scalar X with/out intercept", {
+  n = 1e05
+  p = 2
+  bt0 = c(0,5)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_lm(y~., data=my.dat, intercept=TRUE)
+  out2 = sgdi_lm(y~., data=my.dat, intercept=FALSE)
+  check = max(abs(out1$coefficients[-1] - out2$coefficients))
+  expect_false(check==0)
+})
diff --git a/tests/testthat/test-sgdi_qr.R b/tests/testthat/test-sgdi_qr.R
index 796fb92..cd58f1f 100644
--- a/tests/testthat/test-sgdi_qr.R
+++ b/tests/testthat/test-sgdi_qr.R
@@ -65,3 +65,82 @@ test_that("Different significance levels",
             expect_true(check>0)
           }
 )
+
+test_that("sgdi_qr no_studentize matters", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_qr(y~., data=my.dat)
+  out2 = sgdi_qr(y~., data=my.dat, no_studentize=1e06)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgdi_qr with scalar X", {
+  n = 1e05
+  p = 2
+  bt0 = rep(5,2)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_qr(y~., data=my.dat, studentize=TRUE)
+  out2 = sgdi_qr(y~., data=my.dat, studentize=FALSE)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgdi_qr with scalar X with/out intercept", {
+  n = 1e05
+  p = 2
+  bt0 = c(0,5)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_qr(y~., data=my.dat, intercept=TRUE)
+  out2 = sgdi_qr(y~., data=my.dat, intercept=FALSE)
+  check = max(abs(out1$coefficients[-1] - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgdi_qr burn matters 1", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_qr(y~., data=my.dat)
+  out2 = sgdi_qr(y~., data=my.dat, burn=100)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+test_that("sgdi_qr burn matters 2", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = 2*matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_qr(y~., data=my.dat, studentize=FALSE)
+  out2 = sgdi_qr(y~., data=my.dat, burn=100, studentize=FALSE)
+  check = max(abs(out1$coefficients - out2$coefficients))
+  expect_false(check==0)
+})
+
+
+test_that("sgdi_qr path_index matters", {
+  n = 1e05
+  p = 5
+  bt0 = rep(5,p)
+  x = matrix(rnorm(n*(p-1)), n, (p-1))
+  y = cbind(1,x) %*% bt0 + rnorm(n)
+  my.dat = data.frame(y=y, x=x)
+  out1 = sgdi_qr(y~., data=my.dat, path=TRUE, path_index=1)
+  out2 = sgdi_qr(y~., data=my.dat, path=TRUE, path_index=2)
+  check = max(abs(out1$beta_hat_path[100] - out2$beta_hat_path[100]))
+  expect_false(check==0)
+})
\ No newline at end of file