Thinking glasses on: What to do when the relationship between the two variables is not linear? Watch Mike working through an example to explain the Transformations of the Dependent and Independent Variables, Polynomial Regression, or using a Nonlinear Regression to address the nonlinearity in linear regression.
Dudes writing mirrored in reverse with his left hand. I've practiced things like this along with using "I Am ambidextrous" confirmations to reprogram my subconscious mind and indeed I have become much more mentally creative and left/right handed in function. REALLY HELPS WITH GUITAR. 🎸
Oh my god! After you said what log does as it compresses the results at low values and stretches the results at high values I could literally immediately see in my mind the scatter plot on your board becoming linear! After 5 years in theoretical physics education I have never heard such an awesome visual explanation of the the graphic of ln!
Which approach is considered to be best.? I used log transformation and my professor questioned why I used it.? I had no idea but it helped me address the non-linearity issue.
Each has its pros/cons, but one approach is not universally better than others. Eg categorizing X is flexible and easy to interpret, but requires subjectivity in creating categories. Transformations of X can work well, but lose interpretability…and so on. Log(x) works well for growth type variables, as effect of x on y often increases multiplicatively as x increases. Hope that helps a bit…
One of the cons for approach #4 (categorizing X) is that we lose (n-1) degrees of freedom in the model (n is the number of categories). That means, we have more parameters in the model. If we don't have enough sample, this could cause a saturated model.
Great video! I have one thing to add: you do not lose interpretation of the effects in case 1) or 2). For example in case 1) you can interpret the b1 coefficient as "if we change x by 1 unit, we’d expect our y variable to change by 100⋅b1 percent". (log-level)
thanks we appreciate that. you do lose interpretation with these though. Suppose X=years experience and Y=salary (in $), if you take the log(y), then the model slope (b1) is going to have the following interpretation..."for every increase of 1 year in experience, we associate that with an increase of b1 log-dollars in salary" this of course doesn't have a meaningful interpretation. if you were to take log(X) instead, then the model slope would have the following interpretation: "when experience increases by 1 log-year, we associate that with an increase of b1 in salary (in $)"...again, a change of 1 log-year isn't really easily interpretable....we want to know, for each additional year of experience, how would we expect salary to change.
Thinking glasses on: What to do when the relationship between the two variables is not linear? Watch Mike working through an example to explain the Transformations of the Dependent and Independent Variables, Polynomial Regression, or using a Nonlinear Regression to address the nonlinearity in linear regression.
Dudes writing mirrored in reverse with his left hand. I've practiced things like this along with using "I Am ambidextrous" confirmations to reprogram my subconscious mind and indeed I have become much more mentally creative and left/right handed in function. REALLY HELPS WITH GUITAR. 🎸
Oh my god! After you said what log does as it compresses the results at low values and stretches the results at high values I could literally immediately see in my mind the scatter plot on your board becoming linear! After 5 years in theoretical physics education I have never heard such an awesome visual explanation of the the graphic of ln!
Thanks sir for tremendously explaining the non linearity in regression .
Who saw those thinking glasses in the video ? Genius
You are just AWESOME man, keep doing these videos, you just saved my thesis
Great to hear!
Which approach is considered to be best.? I used log transformation and my professor questioned why I used it.? I had no idea but it helped me address the non-linearity issue.
Each has its pros/cons, but one approach is not universally better than others. Eg categorizing X is flexible and easy to interpret, but requires subjectivity in creating categories. Transformations of X can work well, but lose interpretability…and so on. Log(x) works well for growth type variables, as effect of x on y often increases multiplicatively as x increases.
Hope that helps a bit…
One of the cons for approach #4 (categorizing X) is that we lose (n-1) degrees of freedom in the model (n is the number of categories). That means, we have more parameters in the model. If we don't have enough sample, this could cause a saturated model.
good note, if you have a small sample size, then this is something to be careful of
Sir any explanations on lack of fit test for simple linear regression an example calculation.
Great video! I have one thing to add: you do not lose interpretation of the effects in case 1) or 2). For example in case 1) you can interpret the b1 coefficient as "if we change x by 1 unit, we’d expect our y variable to change by 100⋅b1 percent". (log-level)
thanks we appreciate that. you do lose interpretation with these though. Suppose X=years experience and Y=salary (in $), if you take the log(y), then the model slope (b1) is going to have the following interpretation..."for every increase of 1 year in experience, we associate that with an increase of b1 log-dollars in salary" this of course doesn't have a meaningful interpretation. if you were to take log(X) instead, then the model slope would have the following interpretation: "when experience increases by 1 log-year, we associate that with an increase of b1 in salary (in $)"...again, a change of 1 log-year isn't really easily interpretable....we want to know, for each additional year of experience, how would we expect salary to change.
Sir, is Z standard kind of transformation?
Excellent, but what about non linear activation function, in deep learning they use that to capture non linearity but how it's done?
The exact question I'm trying to figure out :) The only thing I cannot quite intuitively grasp in deep learning yet.
@@Satelliteua i'm in the same spot lol, if you find the answer share it please !
@@aghileslounis sounds good! Please let me know as well if you find a good explanation ;)
Great series of video lectures, thanks. Can you recommend the best stats book in your opinion that gives a broad overview of most things. Thanks
That’s hard to say, as it really depends on the subject area, etc...but I’d probably recommend the following...and it’s free!
r4ds.had.co.nz
excellent!!
too good
doesn't this guy have to write backwards?
Yes, I was thinking the same!
I don't see how he can do this any other way