cut him some slack. it make me feel good sometimes that MIT students and professors makes silly mistakes which is normal by the way!!. the most important part is the learning process
Thanks for this problem solving and the methodology presented, but there is an error in the solution during multiplication of A_transpose with A. This error accumulates over time in the solution and results in the wrong answer. The correct answer should be y= 5/22 x^2 + 41/22 x
Computation is something that everybody is supposed to do on their own. What one really cares about are the ideas implemented to solve a problem. The remaining things seems to be of second grade.
I was not really doubting myself but I did not like it. This guy should know, right?! Anyway, answers I got were : C = 41/22 & D = 5/22. Thank you all!!!!!
This is a nice example. But it's a pity that there seems to an calculation error In the derivation of the projection matrix There should be an 18 instead of 10 in the matrix. And C and D should be 41/22 and 5/22, leading to (e1, e2, e3)=(-12/11, 4/11, -4/11) if my calculation is correct. If, as calculated in the video, C and D were indeed 11/2 and -5/2, then you would have (e1, e2, e3)=(-2, 4, 6). That didn't look like a "least mean square error".
There is a computation error in one of the steps. Final answer should be: (82/44, 10/44). To verify: import numpy as np from numpy.linalg import lstsq # Given points points = np.array([(1, 1), (2, 5), (-1, -2)]) # Separate x and y values x = points[:, 0] y = points[:, 1] # Set up the design matrix for a quadratic fit y = ax^2 + bx X = np.vstack([x, x**2]).T # Perform least squares fitting coefficients, _, _, _ = lstsq(X, y, rcond=None) print(coefficients) print(np.round([82/44, 10/44], 8)) Output: [1.86363636 0.22727273] [1.86363636 0.22727273]
Correct me if I'm wrong, but isn't an equation of the form ax^2 + bx + c = 0, isn't y = ax^2 + bx + c just a quadratic function. I know it should be obvious, but it threw me off a bit, I wrote the equation and realized quickly that only two values of x were even possible :D
@@RaselAhmed-ix5ee bro I just saw it by chance now. I searched it up because tomorrow is my exam.I tried to search answer too because I didn't understand like how you were back then. And I leave an answer simply for someone else to read it instead of the purpose of replying to your question.... Congrats man.👏
cut him some slack. it make me feel good sometimes that MIT students and professors makes silly mistakes which is normal by the way!!. the most important part is the learning process
"i'm gonna rush through this because you should know how to multiply by now"
*does it wrong*
LOL
rofl
XD
Yep
Thanks for this problem solving and the methodology presented, but there is an error in the solution during multiplication of A_transpose with A. This error accumulates over time in the solution and results in the wrong answer. The correct answer should be y= 5/22 x^2 + 41/22 x
goat comment
Computation is something that everybody is supposed to do on their own. What one really cares about are the ideas implemented to solve a problem. The remaining things seems to be of second grade.
Thanks for leaving the comment! I had a little different A and b (points in another order) and it's good to know i got to the right answer!
Hello everyone! The answer to A^T A is 18 at the 2,2 entry
yes
Where is the 10 coming from? Shouldn't it be 18?
Yes it should. The correct solution is then y = (41/22)*c + (5/22)*d^2. You can also see this if you plot both equations against the given points.
@@Rhinozekon y=(81/22)*c + (-25/22)*d^2
I was not really doubting myself but I did not like it. This guy should know, right?! Anyway, answers I got were : C = 41/22 & D = 5/22.
Thank you all!!!!!
Yep
It's still a nice example, I've never thought concepts of linear algebra could come together like this
y = 2.3*x - 0.1*x^2 fits much more correctly.
True, is it the best ?
I am still not able to get why we took square of 1st column as the 2nd column in A
This is a nice example. But it's a pity that there seems to an calculation error In the derivation of the projection matrix There should be an 18 instead of 10 in the matrix. And C and D should be 41/22 and 5/22, leading to (e1, e2, e3)=(-12/11, 4/11, -4/11) if my calculation is correct. If, as calculated in the video, C and D were indeed 11/2 and -5/2, then you would have (e1, e2, e3)=(-2, 4, 6). That didn't look like a "least mean square error".
Correct! Right answer should be b = 5/22 x^2 + 41/22
A'A would result in (6 8; 8 18).
There is a computation error in one of the steps. Final answer should be: (82/44, 10/44).
To verify:
import numpy as np
from numpy.linalg import lstsq
# Given points
points = np.array([(1, 1), (2, 5), (-1, -2)])
# Separate x and y values
x = points[:, 0]
y = points[:, 1]
# Set up the design matrix for a quadratic fit y = ax^2 + bx
X = np.vstack([x, x**2]).T
# Perform least squares fitting
coefficients, _, _, _ = lstsq(X, y, rcond=None)
print(coefficients)
print(np.round([82/44, 10/44], 8))
Output:
[1.86363636 0.22727273]
[1.86363636 0.22727273]
What 3 points is he talking about at the end?
I got the same answer, he made an error accidentally
Will be always take square of first elements of A?
Problem13 . If e components of e=b−Ax averages to zero, then so does ( A^T * A)^(−1) * A^T * e. Why?
shouldn't have rushed A transpose A
why not make it a quadratic in the form of ax^2 + bx + c?
instead of coefficients of only the 2nd and 1st power
because the curve is through the origin thus C the y-intercept is zero
TH-cam comments to the rescue. I thought I was going insane.
Correct me if I'm wrong, but isn't an equation of the form ax^2 + bx + c = 0, isn't y = ax^2 + bx + c just a quadratic function. I know it should be obvious, but it threw me off a bit, I wrote the equation and realized quickly that only two values of x were even possible :D
This quadratic function goes through the origin, so c must be zero (there is no shift).
@@ИльяЛомоносов-ю3м Why? Linear has a non-zero intercept, why not quadratic? the three points fits perfectly(0 error)
@@faizanmansoori The definition of the problem says "find a quadratic equation *through the origin*"
Why did he choose the quadratic function?
yes, 10 should be 18, and the correct formula is y=(81/22)*c + (-25/22)*d^2
I think it's more like
[6 8; 8 18] [c; d] = [13; 19]
then c = 41/22
d = 5/22
y = (41/22)*t + (5/22)*t^2
@@chotirawee how did you get that 41 please explain
@@RaselAhmed-ix5ee it's taken as
Eq1 and eq 2 for c and d variables.
Where it gets the answer by using substitution.
@@shironoyami7002 thanks for the quick reply, I am father now not a student anymore
@@RaselAhmed-ix5ee bro I just saw it by chance now.
I searched it up because tomorrow is my exam.I tried to search answer too because I didn't understand like how you were back then.
And I leave an answer simply for someone else to read it instead of the purpose of replying to your question....
Congrats man.👏
how to choose what kind of equation that is?
quadratic means y=ax²+bx+c
through the origin means y(0)=0 so c=0
Isn't it supposed to be x and not x-hat at 3:35? My reasoning is cause x-hat is the best answer we can get and x is the perfect answer.
@CoeusQuantitative why so serious
Ehren Mann
MIT lectures >>>>>> anyone else tryna teach
He reminds me a person that i used to bully.
And yet, he now has a Ph.D. from MIT and is now a professor of at Cornell, and you're... not.
@@nicksaba3882 i'm happy XD
Haha Eduardo trying to be hard on youtube while this lecturer is now a Prof at a prestigious university. Giad you're happy though Eddy x
@@jonpol770 if he has now phd in his field that just makes more to bully not less lol
You are pathetic
@ 5:17, it should be 18, not 10.
n3rd