Spline Regression #tiktoklearningcampaign #mathematics #econometrics #statistics #datascience

Added: 2026-05-19

[00:00:00]All right, let's cover some basics of spline regression. Um, it's pretty advanced material, but we're going to try to cover some concepts. So, the idea is the relationship between two variables, i.e. the slope, changes depending on different sections of the value, i.e. the X variable.

[00:00:15]So, let's say we're trying to predict the numbers of hours studied per week based on age. Um, so here our age goes from 2 to 22 and it covers like preschool, elementary school, middle school, high school, college.

[00:00:26]So, if you do a regular linear regression, it'll be um, hour study plus some constant plus some slope times age.

[00:00:34]So, using linear regression, your mind line might look like this.

[00:00:39]Whereas with a spline regression, you might want to vary the slope based on whether they're in their preschool ages, their elementary school ages, um, middle school, high school, or college age. So, here, for example, in the preschool years, I mean they don't really study in the preschool years, so the slope might be very flat.

[00:00:57]Whereas with elementary school, maybe it's a bit um, sharper because you're kind of going from nothing to something.

[00:01:01]And then middle school, maybe it's a bit flattish again, um, because it's I don't know, not too extreme in terms of homework. And then high school, there's a huge difference between say freshman year and senior year, so maybe you have a very high slope.

[00:01:11]And then college, maybe you actually end up with a negative slope because I don't know, freshman year you're taking freshman requirements and then senior year you're taking the courses you like, so you don't actually need to study as much because you like them so much. So, maybe you have a negative slope there.

[00:01:22]So, the idea of the spline is instead of having just one single line represent the relationship, you can have sections of lines, sections of slope to represent the relationship in terms of different buckets of age.