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Correction:
13:39 I meant to put "Negative Log-Likelihood" instead of "Likelihood". 

A lot of people ask about 15:34 and how we are supposed to do Cross Validation with only one data point. At this point I was just trying to keep the example simple and if, in practice, you don't have enough data for cross validation then you can't fit a line with ridge regression. However, much more common is that you might  have 500 variables but only 400 observations - in this case you have enough data for cross validation and can fit a line with Ridge Regression, but since there are more variables than observations, you can't do ordinary least squares.
ALSO, a lot of people ask why can't lambda by negative. Remember, the goal of lambda is not to give us the optimal fit, but to prevent overfitting and to make the y-axis variable less sensitive to small changes in the x-axis variable. The only way we can reduce this sensitivity is to reduce the slope. If we increase the slope (by using a negative value for lambda), we will make the y-axis variable more sensitive to changes in the x-axis variable. If a positive value for lambda does not improve the situation, then the optimal value for lambda (discovered via cross validation) will be 0, and the line will fit no worse than the Ordinary Least Squares Line. 

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This channel is by far the best at explaining mathematical concepts related to machine learning. I'm in a machine learning class at my university and go to every class lecture. I leave not having understood an hour and fifteen minutes of lecture. I immediately pull up this channel and watch a video on the same concept and "BAM". It makes sense.

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@lucaspenna6009

Professors in general teach Ridge Regression with many complicated equations and notations. You made this topic very clear and easy to understand. Thank u very much again.

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I've spent so much time trying to read and understand what EXACTLY is ridge regression. This video made it much easier to understand. Thank you so much for simplifying this complex concept!

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The way you go through the logic step by step makes you a good teacher. In many of my research occasions they just say "adjust your alpha higher or lower until you don't overfit / underfit" but I don't even know what am I looking at. Bless you.

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