Question regarding data "points"

markraz

markraz

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Feb 19, 2014
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Hi Please see pic of the linear regression example below. It specifies 4 data points

(6,4,11) = 20,
(8,5,15) = 30
(12,9,25) = 50
(2,1,3) = 7

My question is, how are exactly are these considered points? they look like planes or something else. What am I missing ? thanks in advance.


1612326252159.png
 
markraz said:
...
(12,9,25) = 50
(2,1,3) = 7

My question is, how are exactly are these considered points? they look like planes or something else. What am I missing ? thanks in advance.
Click to expand...

NOTE: I have not studied linear regression myself, but I have a high level understanding that may or may not be correct. So consider this a "get the ball rolling" post and hopefully somebody will write a subsequent post if I'm wrong!

I think the final output from such a linear regression will be a 3d scalar field. That is, you can plug in any 3d point and you'll obtain a scalar value (a real number) as output. In order to train, or determine, the linear regression you need to supply a set of points as "training data". Each of these points must have a scalar value associated with it. These are like target values for the linear regression. So after you've determined the linear regression, and you plug in (2,1,3) from your example then you'd expect 7 as the output (if the training was "perfect"). BUT, if the training data had other, conflicting, targets near that same 3d point then the output would be a compromise.

EDIT: It would have been clearer if they had written something like f( [2,1,3] ) = 7, or just had a table
 
Last edited:
markraz said:
Hi Please see pic of the linear regression example below. It specifies 4 data points

(6,4,11) = 20,
(8,5,15) = 30
(12,9,25) = 50
(2,1,3) = 7

My question is, how are exactly are these considered points? they look like planes or something else. What am I missing ? thanks in advance.


View attachment 24858
Click to expand...
If you're just asking why they are called "points", that's because they are ordered n-tuples, which define points in some space. In this example, the notation (which I don't think I've seen before) means that for x=6, y=4, z=11, a fourth variable w=20, which can be taken to be a function of (x,y,z): f(6,4,11)=20. So this represents a point (6,4,11,20) in 4-space.
 
Dr.Peterson said:
If you're just asking why they are called "points", that's because they are ordered n-tuples, which define points in some space. In this example, the notation (which I don't think I've seen before) means that for x=6, y=4, z=11, a fourth variable w=20, which can be taken to be a function of (x,y,z): f(6,4,11)=20. So this represents a point (6,4,11,20) in 4-space.
Click to expand...
thanks appreciate it. So is w considered a "homogeneous" coordinate?

thanks
 
Cubist said:
NOTE: I have not studied linear regression myself, but I have a high level understanding that may or may not be correct. So consider this a "get the ball rolling" post and hopefully somebody will write a subsequent post if I'm wrong!

I think the final output from such a linear regression will be a 3d scalar field. That is, you can plug in any 3d point and you'll obtain a scalar value (a real number) as output. In order to train, or determine, the linear regression you need to supply a set of points as "training data". Each of these points must have a scalar value associated with it. These are like target values for the linear regression. So after you've determined the linear regression, and you plug in (2,1,3) from your example then you'd expect 7 as the output (if the training was "perfect"). BUT, if the training data had other, conflicting, targets near that same 3d point then the output would be a compromise.

EDIT: It would have been clearer if they had written something like f( [2,1,3] ) = 7, or just had a table
Click to expand...
thanks I'll have to read up on scalar fields. I have heard the term. Thanks appreciate it.
 
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