diff --git a/Cargo.lock b/Cargo.lock
index f15e363bfd6ae..c974e9d13a6b9 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -771,6 +771,12 @@ version = "0.3.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e3b5ca7a04898ad4bcd41c90c5285445ff5b791899bb1b0abdd2a2aa791211d7"
 
+[[package]]
+name = "bytemuck"
+version = "1.13.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "17febce684fd15d89027105661fec94afb475cb995fbc59d2865198446ba2eea"
+
 [[package]]
 name = "byteorder"
 version = "1.3.4"
@@ -3906,12 +3912,11 @@ dependencies = [
 
 [[package]]
 name = "linregress"
-version = "0.4.3"
+version = "0.5.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1e6e407dadb4ca4b31bc69c27aff00e7ca4534fdcee855159b039a7cebb5f395"
+checksum = "4de04dcecc58d366391f9920245b85ffa684558a5ef6e7736e754347c3aea9c2"
 dependencies = [
  "nalgebra",
- "statrs",
 ]
 
 [[package]]
@@ -4327,9 +4332,9 @@ dependencies = [
 
 [[package]]
 name = "nalgebra"
-version = "0.27.1"
+version = "0.32.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "462fffe4002f4f2e1f6a9dcf12cc1a6fc0e15989014efc02a941d3e0f5dc2120"
+checksum = "307ed9b18cc2423f29e83f84fd23a8e73628727990181f18641a8b5dc2ab1caa"
 dependencies = [
  "approx",
  "matrixmultiply",
@@ -4337,17 +4342,15 @@ 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 = "0.2.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "01fcc0b8149b4632adc89ac3b7b31a12fb6099a0317a4eb2ebff574ef7de7218"
+checksum = "91761aed67d03ad966ef783ae962ef9bbaca728d2dd7ceb7939ec110fffad998"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -4928,7 +4931,6 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9a64b1ec5cda2586e284722486d802acf1f7dbdc623e2bfc57e65ca1cd099290"
 dependencies = [
  "autocfg 1.0.1",
- "libm",
 ]
 
 [[package]]
@@ -6964,16 +6966,6 @@ dependencies = [
  "getrandom 0.2.3",
 ]
 
-[[package]]
-name = "rand_distr"
-version = "0.4.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "051b398806e42b9cd04ad9ec8f81e355d0a382c543ac6672c62f5a5b452ef142"
-dependencies = [
- "num-traits",
- "rand 0.8.4",
-]
-
 [[package]]
 name = "rand_hc"
 version = "0.1.0"
@@ -7370,6 +7362,15 @@ dependencies = [
  "rustc_version 0.2.3",
 ]
 
+[[package]]
+name = "safe_arch"
+version = "0.7.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f398075ce1e6a179b46f51bd88d0598b92b00d3551f1a2d4ac49e771b56ac354"
+dependencies = [
+ "bytemuck",
+]
+
 [[package]]
 name = "safemem"
 version = "0.3.3"
@@ -8865,14 +8866,15 @@ checksum = "0f0242b8e50dd9accdd56170e94ca1ebd223b098eb9c83539a6e367d0f36ae68"
 
 [[package]]
 name = "simba"
-version = "0.5.1"
+version = "0.8.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8e82063457853d00243beda9952e910b82593e4b07ae9f721b9278a99a0d3d5c"
+checksum = "061507c94fc6ab4ba1c9a0305018408e312e17c041eb63bef8aa726fa33aceae"
 dependencies = [
  "approx",
  "num-complex",
  "num-traits",
  "paste 1.0.4",
+ "wide",
 ]
 
 [[package]]
@@ -9793,19 +9795,6 @@ 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 = "0.8.0"
@@ -11645,6 +11634,16 @@ dependencies = [
  "thiserror",
 ]
 
+[[package]]
+name = "wide"
+version = "0.7.11"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "aa469ffa65ef7e0ba0f164183697b89b854253fd31aeb92358b7b6155177d62f"
+dependencies = [
+ "bytemuck",
+ "safe_arch",
+]
+
 [[package]]
 name = "widestring"
 version = "0.4.3"
diff --git a/frame/benchmarking/Cargo.toml b/frame/benchmarking/Cargo.toml
index 0600b934d44e2..61c542442530f 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 = "0.4.3", optional = true }
+linregress = { version = "0.5.3", optional = true }
 paste = "1.0"
 codec = { package = "parity-scale-codec", version = "2.0.0", default-features = false }
 scale-info = { version = "1.0", default-features = false, features = ["derive"] }