# Efficient way of doing linear regression

**URL:** https://discourse.julialang.org/t/efficient-way-of-doing-linear-regression/31232
**Category:** Performance
**Tags:** regression
**Created:** [November 18, 2019, 5:21pm UTC](https://discourse.julialang.org/t/efficient-way-of-doing-linear-regression/31232 "2019-11-18T17:21:15Z")
**Posts on this page:** 1
**Showing post:** 27

<div class="post-metadata">

### Author: ![markushhh](https://avatars.discourse-cdn.com/v4/letter/m/f1d935/32.png) [@markushhh](https://discourse.julialang.org/u/markushhh)
#### Post date: [November 25, 2019, 8:50am UTC](https://discourse.julialang.org/t/efficient-way-of-doing-linear-regression/31232/27 "2019-11-25T08:50:11Z")

</div>

what about?

```julia
using Random

N = 10000
x = rand(N)
X = [ones(N) x]
y = 10 .+ x .* 0.3

function linreg1(y, X)
    β_hat = (X' * X) \ X' * y
    return(β_hat)
end

function linreg2(y, X)
    β_hat = X \ y
    return(β_hat)
end

using GLM
GLM.fit(LinearModel, X, y, true)

using DataFrames, GLM
data = DataFrame(X = x, Y = y)
lm(@formula(Y ~ X), data)

using BenchmarkTools
@benchmark linreg1(y, X)
@benchmark linreg2(y, X)
@benchmark GLM.fit(LinearModel, X, y, true)
@benchmark lm(@formula(Y ~ X), data)

```

and the results are

lingerg1:

```julia
BenchmarkTools.Trial: 
  memory estimate: 156.78 KiB
  allocs estimate: 8
  --------------
  minimum time: 213.900 μs (0.00% GC)
  median time: 289.351 μs (0.00% GC)
  mean time: 552.780 μs (4.66% GC)
  maximum time: 76.192 ms (0.00% GC)
  --------------
  samples: 8836
  evals/sample: 1

```

linreg2:

```julia
BenchmarkTools.Trial: 
  memory estimate: 303.69 KiB
  allocs estimate: 45
  --------------
  minimum time: 118.300 μs (0.00% GC)
  median time: 170.300 μs (0.00% GC)
  mean time: 344.598 μs (17.20% GC)
  maximum time: 57.911 ms (0.00% GC)
  --------------
  samples: 10000
  evals/sample: 1

```

fit():

```julia
BenchmarkTools.Trial: 
  memory estimate: 470.45 KiB
  allocs estimate: 26
  --------------
  minimum time: 133.700 μs (0.00% GC)
  median time: 189.299 μs (0.00% GC)
  mean time: 428.768 μs (17.15% GC)
  maximum time: 45.171 ms (0.00% GC)
  --------------
  samples: 10000
  evals/sample: 1

```

lm():

```julia
BenchmarkTools.Trial: 
  memory estimate: 1.08 MiB
  allocs estimate: 186
  --------------
  minimum time: 546.600 μs (0.00% GC)
  median time: 839.500 μs (0.00% GC)
  mean time: 1.917 ms (10.94% GC)
  maximum time: 127.190 ms (0.00% GC)
  --------------
  samples: 2588
  evals/sample: 1

```

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