## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

# Chapter 15. Multiple Regression

I don’t look at a problem and put variables in there that don’t affect it.

Bill Parcells

Although the VP is pretty impressed with your predictive model, she thinks you can do better. To that end, you’ve collected additional data: you know how many hours each of your users works each day, and whether they have a PhD. You’d like to use this additional data to improve your model.

Accordingly, you hypothesize a linear model with more independent variables:

$minutes equals alpha plus beta 1 friends plus beta 2 work hours plus beta 3 phd plus epsilon$

Obviously, whether a user has a PhD is not a number—but, as we mentioned in Chapter 11, we can introduce a dummy variable that equals 1 for users with PhDs and 0 for users without, after which it’s just as numeric as the other variables.

# The Model

Recall that in Chapter 14 we fit a model of the form:

$y Subscript i Baseline equals alpha plus beta x Subscript i Baseline plus epsilon Subscript i$

Now imagine that each input ${x}_{i}$ is not a single number but rather a vector of k numbers, ${x}_{i1},...,{x}_{ik}$. The multiple regression model assumes that:

$y Subscript i Baseline equals alpha plus beta 1 x Subscript i Baseline 1 Baseline plus period period period plus beta Subscript k Baseline x Subscript i k Baseline plus epsilon Subscript i Baseline$

In multiple regression the vector of parameters is usually called β. We’ll want this to include the constant term as well, which we can achieve by adding a column of 1s to our data:

``beta` `=` `[``alpha``,` `beta_1``,` `...``,` `beta_k``]``

and:

``x_i` `=` `[``1``,` `x_i1``,` `...``,` `x_ik``]``

Then our model is just:

````from` `scratch.linear_algebra` `import` `dot``,` `Vector`

`def` `predict``(``x``:` `Vector``,` `beta``:` `Vector``)` `->` `float``:`
`"""assumes that the first ...````

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required