Linear regression looks great on paper since you can derive residuals, slopes compare the individual "effects" etc. But thats unnecessary and in some cases wrong when the goal is mere prediction and not explanation. The big difference between ML and statistics is that latter selects a "correct" linear model and then assumes a distribution for "errors" due to pesky reality. The effects are used for explanations (538 Nate Silver style wonk/punditry). Machine Learning on other hand tries to predict as close to observations as possible without imposing a model or caring about an explanation.
The simplest introductory Machine Learning approach should not be linear regression but rather a 1- nearest neighbor model.
E.g. rather than giving data about house prices and square footage. The question should be "How do you predict price of a house in given location?". "What are relavant features?" (location,location, location,school district,number of rooms,sq ft, etc), "How would you collect labels/data". (Zillow, exclued prices older than 2-3 years).
The simplest answer would be that the price is same as that of the neighboring house (closest lat/long) with similar sq foot sold recently.
This can then be implemented as a weighted distance metric and tested using Leave one out cross validation (I know not the best metric). But consider how Nearest Neighbors allows us to incorporate location information in a natural manner. That is very important and cannot incorporated in an elegant manner in a linear regression model.
A big part of ML is applying different set of methods across several domains. Thus for beginners Teaching ML should not be about teaching limear models or gradient descent but rather how do you start thinking from ML perspective.
The math is important for understanding and tweaking. But ML is not just fancy statistics (or math in general). It's _data_. An understanding of the math means understanding what data pairs best with what approach. It also means understanding error analysis. It means cross-validation. These are far more vulnerable areas to a beginner in ML.
But the ultimate point is ML is not magic. It's a framework - trenched in mathematics - that provides the building blocks for simulating understanding. You don't need to know the math to use it, but you need it to use it well.
As a data scientist, I often walk new clients through a linear regression exercise to convey some key concepts about the engagement and demystify what I'll be doing for them.
I'm often dealing with people who, much like you, haven't done much with stats since a college "Business Stats" course, so I get a lot of "oh yeah, I vaguely remember this" - but going through it again gives me a good foundation to relate back to as things get more complicated.
The first couple weeks are all about univariate and multivariate linear regression (as well as an optional linear algebra refresher on matrix operations).
Take classes in probability, and linear algebra, from there you'll begin to have the level of mathematics to be able to really dive in. You'll also have the computer science maturity to better understand the libraries in use, and in truth the field will have advanced a bit in the time it takes for you to get those foundations.
There was just a good reddit thread about what topics to focus on in linear algebra and probability that you should be paying attention to, because those two subjects are largely the mathematical foundations of machine learning.
* https://www.udacity.com/course/intro-to-artificial-intellige... (by Peter Norvig - director of research @ Google & Sebastian Thrun - lead dev of google self driving car and founder of google x, now at gerogia tech uni) - great if you want a more "deep thinking" style intro to AI
* https://www.udacity.com/course/intro-to-machine-learning--ud... (Sebastian Thrun & Katie Malone - former physicist and data scientist great at explaining stuff so that anyone can grok it) - great if you want a more "down to earth" engineering style intro with simple clear examples
* https://www.coursera.org/learn/machine-learning (Andrew Ng @ Stanford & chied scientist at Baidu, former Google researcher) - great if you want a "bottom up", from math, through code/engineering, with less fuzzy big picture stuff - this is a great intro, even if Andrew Ng is less of a rock-star-presenter, if you want to start from math details up take this one!
Oh, and kaggle: https://www.kaggle.com/ . If you get stuck on anything, google the relevant math, pick up just enough to have an intuition and carry on.
You're still in college so you have plenty of time to learn well the required math, it's better to get a broad picture of the field ASAP imho! Then when you'll take the math classes, you'll already have "aha, this feels my gap about X and Y" and "aha, now I get why Z" and you'll really love that math after you already know what problems it solves!
(PS if you're less of a "highly logico-intuitive" person and more "analytical rigorous thinker" instead, just ignore my last paragraph and focus on the math, but try to get some deep intuition of probability along the way)