diff --git a/Cargo.lock b/Cargo.lock
index 59ff43598faed..e89a03d40adb3 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -784,6 +784,12 @@ version = "0.3.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e3b5ca7a04898ad4bcd41c90c5285445ff5b791899bb1b0abdd2a2aa791211d7"
 
+[[package]]
+name = "bytemuck"
+version = "1.13.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c041d3eab048880cb0b86b256447da3f18859a163c3b8d8893f4e6368abe6393"
+
 [[package]]
 name = "byteorder"
 version = "1.3.4"
@@ -4225,12 +4231,11 @@ dependencies = [
 
 [[package]]
 name = "linregress"
-version = "0.4.4"
+version = "0.5.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d6c601a85f5ecd1aba625247bca0031585fb1c446461b142878a16f8245ddeb8"
+checksum = "475015a7f8f017edb28d2e69813be23500ad4b32cfe3421c4148efc97324ee52"
 dependencies = [
  "nalgebra",
- "statrs",
 ]
 
 [[package]]
@@ -4656,9 +4661,9 @@ dependencies = [
 
 [[package]]
 name = "nalgebra"
-version = "0.27.1"
+version = "0.32.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "462fffe4002f4f2e1f6a9dcf12cc1a6fc0e15989014efc02a941d3e0f5dc2120"
+checksum = "f6515c882ebfddccaa73ead7320ca28036c4bc84c9bcca3cc0cbba8efe89223a"
 dependencies = [
  "approx",
  "matrixmultiply",
@@ -4666,17 +4671,15 @@ dependencies = [
  "num-complex",
  "num-rational 0.4.0",
  "num-traits",
- "rand 0.8.4",
- "rand_distr",
  "simba",
  "typenum",
 ]
 
 [[package]]
 name = "nalgebra-macros"
-version = "0.1.0"
+version = "0.2.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "01fcc0b8149b4632adc89ac3b7b31a12fb6099a0317a4eb2ebff574ef7de7218"
+checksum = "d232c68884c0c99810a5a4d333ef7e47689cfd0edc85efc9e54e1e6bf5212766"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -5262,7 +5265,6 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9a64b1ec5cda2586e284722486d802acf1f7dbdc623e2bfc57e65ca1cd099290"
 dependencies = [
  "autocfg 1.0.1",
- "libm",
 ]
 
 [[package]]
@@ -7447,16 +7449,6 @@ dependencies = [
  "getrandom 0.2.3",
 ]
 
-[[package]]
-name = "rand_distr"
-version = "0.4.3"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "32cb0b9bc82b0a0876c2dd994a7e7a2683d3e7390ca40e6886785ef0c7e3ee31"
-dependencies = [
- "num-traits",
- "rand 0.8.4",
-]
-
 [[package]]
 name = "rand_hc"
 version = "0.1.0"
@@ -7920,6 +7912,15 @@ dependencies = [
  "rustc_version 0.2.3",
 ]
 
+[[package]]
+name = "safe_arch"
+version = "0.6.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "794821e4ccb0d9f979512f9c1973480123f9bd62a90d74ab0f9426fcf8f4a529"
+dependencies = [
+ "bytemuck",
+]
+
 [[package]]
 name = "safemem"
 version = "0.3.3"
@@ -9476,14 +9477,15 @@ dependencies = [
 
 [[package]]
 name = "simba"
-version = "0.5.1"
+version = "0.8.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8e82063457853d00243beda9952e910b82593e4b07ae9f721b9278a99a0d3d5c"
+checksum = "50582927ed6f77e4ac020c057f37a268fc6aebc29225050365aacbb9deeeddc4"
 dependencies = [
  "approx",
  "num-complex",
  "num-traits",
  "paste 1.0.6",
+ "wide",
 ]
 
 [[package]]
@@ -10449,19 +10451,6 @@ version = "1.1.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a2eb9349b6444b326872e140eb1cf5e7c522154d69e7a0ffb0fb81c06b37543f"
 
-[[package]]
-name = "statrs"
-version = "0.15.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "05bdbb8e4e78216a85785a85d3ec3183144f98d0097b9281802c019bb07a6f05"
-dependencies = [
- "approx",
- "lazy_static",
- "nalgebra",
- "num-traits",
- "rand 0.8.4",
-]
-
 [[package]]
 name = "strsim"
 version = "0.10.0"
@@ -12234,6 +12223,16 @@ dependencies = [
  "thiserror",
 ]
 
+[[package]]
+name = "wide"
+version = "0.7.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "feff0a412894d67223777b6cc8d68c0dab06d52d95e9890d5f2d47f10dd9366c"
+dependencies = [
+ "bytemuck",
+ "safe_arch",
+]
+
 [[package]]
 name = "widestring"
 version = "0.4.3"
diff --git a/frame/benchmarking/Cargo.toml b/frame/benchmarking/Cargo.toml
index 37259f351e9f1..9b67a8cf4ef89 100644
--- a/frame/benchmarking/Cargo.toml
+++ b/frame/benchmarking/Cargo.toml
@@ -13,7 +13,7 @@ readme = "README.md"
 targets = ["x86_64-unknown-linux-gnu"]
 
 [dependencies]
-linregress = { version = "0.4.4", optional = true }
+linregress = { version = "0.5.1", optional = true }
 paste = "1.0"
 codec = { package = "parity-scale-codec", version = "3.0.0", default-features = false }
 scale-info = { version = "2.0.0", default-features = false, features = ["derive"] }