# Univariate linear regression with each covariate of dataframe

**URL:** <https://discourse.julialang.org/t/univariate-linear-regression-with-each-covariate-of-dataframe/29951>\
**Category:** Statistics\
**Tags:** dataframes, regression\
**Created:** [October 15, 2019, 5:48pm UTC](https://discourse.julialang.org/t/univariate-linear-regression-with-each-covariate-of-dataframe/29951 "2019-10-15T17:48:48Z")\
**Posts on this page:** 6\
**Page:** 1

<div class="post-metadata">

**Author:** ![sergevic](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sergevic/32/9958_2.png) [@sergevic](https://discourse.julialang.org/u/sergevic)\
**Post date:** [October 15, 2019, 5:48pm UTC](https://discourse.julialang.org/t/univariate-linear-regression-with-each-covariate-of-dataframe/29951/1 "2019-10-15T17:48:48Z")

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I have a dataframe with 5 covariates `X1, X2, X3, X4, X5` and a dependent variable `Y`. I have to perform a univariate regression of `Y` on each covariate. I don’t want to do

```julia
using GLM
lm(@formula(Y~X1), data)
lm(@formula(Y~X2), data)
lm(@formula(Y~X3), data)
lm(@formula(Y~X4), data)
lm(@formula(Y~X5), data)

```

because it’s counterproductive, specially if I have a large number of covariates. I’m trying to build a loop, but I don’t know how to call each covariate from the dataframe with `@formula`. I tried

```julia
for i=1:5 
     lm(@formula(Y~data[:,i]), data)
end

```

but it does not work. Any hint?

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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:** [October 15, 2019, 6:06pm UTC](https://discourse.julialang.org/t/univariate-linear-regression-with-each-covariate-of-dataframe/29951/2 "2019-10-15T18:06:08Z")

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See the StatsModels docs on constructing a formula programmatically [here](https://juliastats.github.io/StatsModels.jl/stable/formula/#Constructing-a-formula-programmatically-1).

In particular, you don’t want to use the `@formula` macro here.

```julia
for covariate in names(df[!, r"X"])
     lm(term(:Y) ~ term(covariate), data)
end

```

Pining @dave.f.kleinschmidt in case there are any further developments that would make this process easier.

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<div class="post-metadata">

**Author:** ![sergevic](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sergevic/32/9958_2.png) [@sergevic](https://discourse.julialang.org/u/sergevic)\
**Post date:** [October 15, 2019, 6:15pm UTC](https://discourse.julialang.org/t/univariate-linear-regression-with-each-covariate-of-dataframe/29951/3 "2019-10-15T18:15:41Z")

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Where does the `covariate` appear in the loop? And there is no `name` for `term(name)`… Is it `term(covariate)` instead? Finally, is it possible in that loop to keep the iteration number so that I can save the results of each iteration?

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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:** [October 15, 2019, 6:21pm UTC](https://discourse.julialang.org/t/univariate-linear-regression-with-each-covariate-of-dataframe/29951/4 "2019-10-15T18:21:06Z")

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apologies, I didn’t test the code enough. I edited the example and now it should work.

You can use `enumerate` so the iterator returns a Pair of the item and the counter.

You can also do `term(Symbol(:X, i))` inside the loop to construct the vairable name programmatically.

One thing you can’t do is do `term(1)` to construct the covariate. That does something else (not really sure what)

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<div class="post-metadata">

**Author:** ![sergevic](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/sergevic/32/9958_2.png) [@sergevic](https://discourse.julialang.org/u/sergevic)\
**Post date:** [October 15, 2019, 6:29pm UTC](https://discourse.julialang.org/t/univariate-linear-regression-with-each-covariate-of-dataframe/29951/5 "2019-10-15T18:29:54Z")

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Yes, I just edited my question too because I figured out that it must be `term(covariate)` 🙂 And for the iteration, thank you! It worked 🙂 I did

```julia
for (index,covariate) in enumerate(names(df[!, r"X"]))
...
end

```

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<div class="post-metadata">

**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:** [October 15, 2019, 7:16pm UTC](https://discourse.julialang.org/t/univariate-linear-regression-with-each-covariate-of-dataframe/29951/6 "2019-10-15T19:16:47Z")

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That’s about what I’d recommend! The `term(1)` constructs the same thing that `1` in a formula does (e.g., `@formula(y ~ 1 + x)` is the same as `term(:y) ~ term(1) + term(:x)`). Same with other numbers (`0` is the only one that has special meaning).

If you get into a situation where it’s going to be expensive to keep computing the schema for the data you can precompute it and provide a concrete formula to `lm`, like:

```julia
sch = schema(data)
for covariate in names(df[!, r"X"])
    f = apply_schema(term(:Y) ~ term(covariate), sch, LinearModel)
    lm(f, data)
end

```

(You need the third argument of `apply_schema` to be `LinearModel` to get the “implicit intercept” behavior that you probably expect)

But that shouldn’t make a huge difference unless your data is _really_ big, because there’s minimal overlap between the schema that’s required for each model (just `Y`). But if you were re-fitting models that have more overlapping terms and the dataset is very large then you might benefit from precomputing the schema.