# How do I force GLM to pass through a certain y intercept?

**URL:** <https://discourse.julialang.org/t/how-do-i-force-glm-to-pass-through-a-certain-y-intercept/59500>\
**Category:** General Usage\
**Tags:** question, package, regression, glm\
**Created:** [April 17, 2021, 8:53pm UTC](https://discourse.julialang.org/t/how-do-i-force-glm-to-pass-through-a-certain-y-intercept/59500 "2021-04-17T20:53:04Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![cocoa1231](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cocoa1231/32/22215_2.png) [@cocoa1231](https://discourse.julialang.org/u/cocoa1231)\
**Post date:** [April 17, 2021, 8:53pm UTC](https://discourse.julialang.org/t/how-do-i-force-glm-to-pass-through-a-certain-y-intercept/59500/1 "2021-04-17T20:53:04Z")

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Hello all!

So I am using GLM to fit a graph of resistance vs. temperature, and I need the regression line to have an intercept of 100 Ohms at 0 degrees Centigrade. My code is -

```julia
	xdata = temp_calib_data[:Pt100][:, 1] |> Vector{Float64}
	ydata = temp_calib_data[:Pt100][:, 2] |> Vector{Float64}
	
	data = DataFrame(:X => xdata, :Y=> ydata)
	Pt100_fit = lm(@formula(Y~X), data)
	b, m = round.(coef(Pt100_fit), digits=3)
	scatter(xdata, ydata, label="Data", legend=:topleft, xlabel="Temperature (Hg)", ylabel = "Resistance Ω")
	plot!(xdata, predict(Pt100_fit), ls=:dash, label="m = $m, b=$b")

```

I tried using `@formula(Y~100+X)` however that threw an error. How can I force a certain intercept?

Thank you for the help!

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<div class="post-metadata">

**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [April 17, 2021, 10:18pm UTC](https://discourse.julialang.org/t/how-do-i-force-glm-to-pass-through-a-certain-y-intercept/59500/2 "2021-04-17T22:18:16Z")

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Do not know the proper way, but the quick and dirty way should “work” by adding a lot of points very close to 0 with desired intercept value of 100:

```julia
N = length(xdata)
x0 = -2N*eps():eps():2N*eps()
y0 = 100 .+ 0*x0
Xd = [x0; xdata]
Yd = [y0; ydata]
data = DataFrame(:X => Xd, :Y=> Yd)
...

```

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<div class="post-metadata">

**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [April 17, 2021, 10:34pm UTC](https://discourse.julialang.org/t/how-do-i-force-glm-to-pass-through-a-certain-y-intercept/59500/3 "2021-04-17T22:34:45Z")

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This might be the proper way (subtracting 100 from the data and fitting Y ~ 0 + X):

```julia
ydata = ydata .- 100
data = DataFrame(:X => xdata, :Y=> ydata)
Pt100_fit = lm(@formula(Y ~ 0 + X), data)

```

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**Author:** ![dave.f.kleinschmidt](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dave.f.kleinschmidt/32/55_2.png) [@dave.f.kleinschmidt](https://discourse.julialang.org/u/dave.f.kleinschmidt)\
**Post date:** [April 19, 2021, 3:07pm UTC](https://discourse.julialang.org/t/how-do-i-force-glm-to-pass-through-a-certain-y-intercept/59500/5 "2021-04-19T15:07:16Z")

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You can also do `@formula(y - 100 ~ 0 + X)` which will do the subtraction “lazily” (e.g., not create a new column in the table but subtract 100 from every element of `y` when generating the response vector).

Although to be fair, I’m not 100% sure this is a better solution than doing it in the table, because with this method you’re still going to have to remember to add 100 to predicted/fitted values to get them back on the original scale. At least if you’re predicted value is called `y_min_100` you have a reminder to do that 🙂 (I don’t think `predict` will name the column based on the coefname but I could be mistaken).