R Squared Theory - Practical Machine Learning Tutorial with Python p.10

Welcome to the 10th part of our of our machine learning regression tutorial within our Machine Learning with Python tutorial series. We've just recently finished creating a working linear regression model, and now we're curious what is next. Right now, we can easily look at the data, and decide how "accurate" the regression line is to some degree. What happens, however, when your linear regression model is applied within 20 hierarchical layers in a neural network? Not only this, but your model works in steps, or windows, of say 100 data points at a time, within a dataset of 5 million datapoints. You're going to need some sort of automated way of discovering how good your best fit line actually is.

[bobestes]

A key point, not mentioned, is that the use of squared error leads to the solution that was previously presented. Using other error measures implies a different optimization problem and results in other formulas for m and b. Furthermore, the properties of squared error are what lead to the nice, closed form solution we used previously. Many other error measures do not permit simple, closed form solutions.

[yaweichen]

you actually could use the absolute value of e, or e to any powers to calculate the norm of the error. But for least square problems, we generally use e^2 because we could easily differentiate the function.

[CannabiiiisX]

Realy enjoying the series sentdex ! i think its funny when looking at the views you see them decreasing every new episode, while i think its just getting funt at this point and i cant wait to have completed the series ! Your doing a great job, thx for your time and effort ! i was pleased for givning you the 420th like on this video :D

[wanderlust]

You could also use chi^2 or calculate the error of the slope. If you have a model, e.g. say the slope is the velocity (y the distancem x the time) it would give you the error of your best fit velocity.

[Marva]

@sentdex how do you know so much about programming. I'm interested in always learning from people who are very knowledgeable. What was your path of learning for all this different areas?

[shravilpotdar]

sentdex
Hi, why should we get a high value of r^2 (squared error) while calculating the squared error? Doesn't it mean that, the high value of r^2 means high error?
:)

[syedamanahilrizvi]

Hi Buddy! your explanation is absolutely excellent. I want to ask you that if possible please add a video on adjusted R square. Also tell the methods which are used to test accuracy of Linear Regression

[NamNguyễnHoài-fs]

Im studying this, along with Statquest of josh starmer and i could understand this much easier.

[ZarreenNaowalReza]

Can you please explain exactly how are we reducing the impact of outliers by squaring their distances from the best fit line?

[rasmusloqvist]

Hey! Very nice series!

I was just wondering if a viable way of doing a measurement of how good it fits can be done with the rmse between yhat and the original y's?

something like this:

rmse = sum([(k-l)**2 for k, l in zip(y, yhat)])**0.5

[geogeo]

Great video as usual but one thing I don't get is the purpose of doin all this if we already have y_hat, the best fit line. Isn't it what we are supposed to search for ? (sorry for naive question im totally new to ML and missing a lot of things XD)

[pg]

Is this the cost or the loss function??

[EditorsCanPlay]

So, just wondering, if you use e^6 does that change the r^2 equation in any way?

[willwombell]

Quick question, for the squared error of the y hat line do you take it perpendicular to the line like you do for the squared error of the y mean line or do you use the vertical error for both and if so why? Thanks, love the vids.

[rubinluitel]

i still don't understand why you cant take the absolute vale, because if you square it to any numbers, results should be the same right, in terms of the distance

[shakkur]

sendex any chance putting Spark training anytime soon!!

[parthshah]

Hey sentdex, really impressed with all your vids and efforts !!
I have a Q is it possible to grab the whether and news from online using python ?

[ygbr]

what if all the points have the same y value

[hansmeier]

What metric are you using when you say "e is the distance to the line"? 2:06

[skfkfkd]

Hello, great video! Is it possible to get the r^2 value for a curve fitted to a nonlinear regression