# Can someone replicate this GLM problem with linear regression on your computer?

**URL:** <https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098>\
**Category:** Statistics\
**Tags:** linearalgebra, glm\
**Created:** [April 27, 2021, 11:26am UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098 "2021-04-27T11:26:40Z")\
**Posts on this page:** 14\
**Page:** 1

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**Author:** ![Chen](https://avatars.discourse-cdn.com/v4/letter/c/3d9bf3/32.png) [@Chen](https://discourse.julialang.org/u/Chen)\
**Post date:** [April 27, 2021, 11:26am UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/1 "2021-04-27T11:26:40Z")

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The CSV file is here: [https://github.com/JuliaStats/GLM.jl/files/6384056/Car-Training.csv](https://github.com/JuliaStats/GLM.jl/files/6384056/Car-Training.csv)

The GLM issue that I reported is here: [https://github.com/JuliaStats/GLM.jl/issues/426](https://github.com/JuliaStats/GLM.jl/issues/426)

The codes are very simple:

```julia
using GLM
using DataFrames
using CSV

data = CSV.read( "Car-Training.csv", DataFrame )
model = @formula( Price ~ Year + Mileage )
results = lm( model, data )

```

Could you see if I did something wrong here? It seems so basic but yet I got strange results that are wrong:

```julia
StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Array{Float64,1}},GLM.DensePredChol{Float64,LinearAlgebra.CholeskyPivoted{Float64,Array{Float64,2}}}},Array{Float64,2}}

Price ~ 1 + Year + Mileage

Coefficients:
─────────────────────────────────────────────────────────────────────────────────
                  Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95%
─────────────────────────────────────────────────────────────────────────────────
(Intercept) 0.0 NaN NaN NaN NaN NaN
Year 8.17971 0.167978 48.70 <1e-73 7.84664 8.51278
Mileage -0.0580528 0.00949846 -6.11 <1e-7 -0.0768865 -0.0392191
─────────────────────────────────────────────────────────────────────────────────

```

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**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 27, 2021, 12:03pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/2 "2021-04-27T12:03:10Z")

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Could this be a problem of input data normalization?  
In any event subtracting 2000 from the input Year seems to unlock the issue.

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**Author:** ![Chen](https://avatars.discourse-cdn.com/v4/letter/c/3d9bf3/32.png) [@Chen](https://discourse.julialang.org/u/Chen)\
**Post date:** [April 27, 2021, 12:09pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/3 "2021-04-27T12:09:42Z")

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Thank you vey much!

I wasn’t sure if I had become crazy, because the problem was so basic and yet there was this error.

I think normalization could be the culprit.

I’m teaching a course that uses basic regression and conducts simple forecasting. Subtracting 2000 will solve the problem. However, it also means that when forecasting, one needs to pay attention to this as well, which is unnecessarily complicating the issue.

And this is a part of a take-home exam. So it will not be very welcomed by students to have this extra complexity.

I hope that the GLM’s maintainer or someone who knows better Julia-fu can fix the issue and publish a newer version of GLM, so that I can simply ask students to update the GLM package. This will be a better and simpler solution, I think.

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<div class="post-metadata">

**Author:** ![Chen](https://avatars.discourse-cdn.com/v4/letter/c/3d9bf3/32.png) [@Chen](https://discourse.julialang.org/u/Chen)\
**Post date:** [April 27, 2021, 12:16pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/4 "2021-04-27T12:16:17Z")

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Linear regression is the most basic regression. Is there an alternative package that can perform linear regression?

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**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 27, 2021, 12:21pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/5 "2021-04-27T12:21:57Z")

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Check [LsqFit.jl](https://github.com/JuliaNLSolvers/LsqFit.jl) out.

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<div class="post-metadata">

**Author:** ![Chen](https://avatars.discourse-cdn.com/v4/letter/c/3d9bf3/32.png) [@Chen](https://discourse.julialang.org/u/Chen)\
**Post date:** [April 27, 2021, 12:31pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/6 "2021-04-27T12:31:59Z")

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Thank you very much again!

LsqFit.jl is probably fine. However, one needs to specify x data, y data, and initial values.

I plan to wait a bit and see if a maintainer of GLM.jl can fix the issue. The take-home exam has a deadline that is in two weeks. I can wait a bit.

If GLM.jl cannot be fixed, then probably LsqFit.jl will have to be used, or I have to write a linear regression package myself.

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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 27, 2021, 12:56pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/7 "2021-04-27T12:56:02Z")

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Uhm, it does just not sound right that LsqFit.jl is a solution here, but just a workaround.

Not an expert on numerical analysis but there should be a best practice for data normalization (assuming this is the problem) when the input variables are so different, before throwing them into GLM _(ex: subtract mean and divide by standard deviation, or something like that)._

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<div class="post-metadata">

**Author:** ![Chen](https://avatars.discourse-cdn.com/v4/letter/c/3d9bf3/32.png) [@Chen](https://discourse.julialang.org/u/Chen)\
**Post date:** [April 27, 2021, 12:58pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/8 "2021-04-27T12:58:58Z")

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Thank you.

For the most elementary use of regression, I think by default one does not transform data. Data is thrown to regression, without transformation. And results are produced.

The silly part is that I have been telling students that Julia is much better than Excel for basic data analyses. Now Excel runs the simple regression correctly, but not Julia. The laugh is on me. 🤣

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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 27, 2021, 1:00pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/9 "2021-04-27T13:00:42Z")

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Please wait for the feedback from the GLM experts on this matter.

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<div class="post-metadata">

**Author:** ![Chen](https://avatars.discourse-cdn.com/v4/letter/c/3d9bf3/32.png) [@Chen](https://discourse.julialang.org/u/Chen)\
**Post date:** [April 27, 2021, 1:08pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/10 "2021-04-27T13:08:50Z")

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Yeah!

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<div class="post-metadata">

**Author:** ![pdeffebach](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pdeffebach/32/10320_2.png) [@pdeffebach](https://discourse.julialang.org/u/pdeffebach)\
**Post date:** [April 27, 2021, 1:15pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/11 "2021-04-27T13:15:33Z")

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The bug is from `dropcollinear` keyword argument. Set `dropcollinear=false` as a kw in `lm` and you will get the same results as `R`. I’m commenting on the issue as well and will explore this throughout the day.

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<div class="post-metadata">

**Author:** ![Chen](https://avatars.discourse-cdn.com/v4/letter/c/3d9bf3/32.png) [@Chen](https://discourse.julialang.org/u/Chen)\
**Post date:** [April 27, 2021, 1:24pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/12 "2021-04-27T13:24:40Z")

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This solved the issue. Thank you very much!

As a side comment, I’m not sure if this is a sane option to set `dropcollinear=true` as the default. I have used a number of statistical software. This is the first time such an option is set as the default.

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**Author:** ![pdeffebach](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pdeffebach/32/10320_2.png) [@pdeffebach](https://discourse.julialang.org/u/pdeffebach)\
**Post date:** [April 27, 2021, 1:26pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/13 "2021-04-27T13:26:58Z")

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It’s the default in Stata, at least.

Fwiw, I think this is a bug, possibly introduced by me. I don’t think that having `dropcollinear=true` should behave differently when `X` is full rank. So having this be the default _shouldn’t_ cause this type of problem.

EDIT: It’s also the default in R

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<div class="post-metadata">

**Author:** ![Chen](https://avatars.discourse-cdn.com/v4/letter/c/3d9bf3/32.png) [@Chen](https://discourse.julialang.org/u/Chen)\
**Post date:** [April 27, 2021, 1:31pm UTC](https://discourse.julialang.org/t/can-someone-replicate-this-glm-problem-with-linear-regression-on-your-computer/60098/14 "2021-04-27T13:31:59Z")

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Good to know. I have used Stata in some datasets. I didn’t know about it. Thanks!