# How can I tell Julia what are the parameters in a linear model?

**URL:** https://discourse.julialang.org/t/how-can-i-tell-julia-what-are-the-parameters-in-a-linear-model/87692
**Category:** Statistics
**Tags:** regression, fit, curve-fitting, glm, linear-regression
**Created:** [September 23, 2022, 11:27am UTC](https://discourse.julialang.org/t/how-can-i-tell-julia-what-are-the-parameters-in-a-linear-model/87692 "2022-09-23T11:27:06Z")
**Posts on this page:** 1
**Showing post:** 12

<div class="post-metadata">

### Author: ![ayushpatnaikgit](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ayushpatnaikgit/32/25229_2.png) [@ayushpatnaikgit](https://discourse.julialang.org/u/ayushpatnaikgit)
#### Post date: [September 26, 2022, 1:53pm UTC](https://discourse.julialang.org/t/how-can-i-tell-julia-what-are-the-parameters-in-a-linear-model/87692/12 "2022-09-26T13:53:24Z")

</div>

I have made minor changes, please have a look:

```julia
using DataFrames
using Optim

x = range(-50, 50, length=101);
y = range(-70, 50, length=51);
domain = Iterators.product(x,y) |> collect
β = [1.0, 2.0, 10.0, 20.0]
f((x,y)) = (x, y, (β[1]*(x - β[3])^2 + β[2] * (y - β[4])^2 + 10*randn()))
points = vec(map(f, domain))

df = DataFrame(NamedTuple{(:x, :y, :z)}.(points))

function g(β) # since f is already used. 
    z = df.z; x = df.x; y = df.y
    x₀ = β[3]; y₀ = β[4]
    ẑ = β[1]*(x .- x₀).^2 + β[2]*(y .- y₀).^2 
    return sum((z - ẑ).^2)
end

result = optimize(g, [1.0, 2.0, 10.0, 20.0]) # Actual initial conditions
coefficients = Optim.minimizer(result) # looks like it's the right answer. 

result = optimize(g, [1.6, 20.0, 0.0, 0.0]) # Some random initial conditions. 
coefficients = Optim.minimizer(result) # Still the correct answer. 

```

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