I'm hoping there's someone here who's good at stats.
Basically I have the following situation. I have two variables (a, b), both of which I use as predictors of a third variable (c).
I use variables a and b in two separate regression analyses to obtain coefficients that indicate the relationship between variables a and b on the one hand, and variaible c on the other. I find that variable a is negatively linearly related to c. Variable b shows a positive linear relationship with variable c. There are no quadratic relationships between variable a or b, and variable c.
Now, if I instead use both variable a and b in a single regression analysis (so they are in the same model) this should give us coefficients that indicate the relationships between variables a and b to variable c, but independent of each other. By doing this we discard shared variance between a and b.
For some reason I can't get my head around, doing this makes a positively quadratically related to c, and b negatively quadratically related to c. The linear dependencies are also still there.
What do the quadratic relationships imply?
>>7733142
Is that... Boxxy?
>>7733160
I guess so
>>7733160
She's far too attractive to be Boxxy and only has 300 layers of makeup as opposed to over 9000.
>>7733163
Did you reverse image search it or did you literally guess? I really don't want to go through that effort because my browser extension broke.
>>7733166
I searched, and apparently it is.
>>7733179
Fuuuuck.
She's changed a lot. Damn.
>>7733160
FFFFFFFFFFFFFff--
>>7733142
Is this what they teach statisticians? You're over complicating something that is ridiculously simple if you understand random variables.
All you are doing is subtracting the co-variance. Look up the formula for adding variances, that may help. Do you know linear algebra? Thinking about this in terms of eigenvectors and eigenvalues is a lot simpler.
>>7733166
I literally guessed. I got this image off of /b/ right before I started the thread.
>>7733194
>You're over complicating something that is ridiculously simple
Well, then I'm hoping you could help me understand. I'm not a statistician, quite far from it actually and this is my first experience with regression to be honest.
Anyway, if this procedure is subtracting covariance, does it imply that variables b and c show a negative quadratic relationship with each other?
>>7733241
>Nothing to do with science or math
>>7733317
It's an eye catcher though
>>7733213
This formula is where I believe the quadratic relationship is coming from.
I don't completely understand your original explanation.
>Now, if I instead use both variable a and b in a single regression analysis (so they are in the same model) this should give us coefficients that indicate the relationships between variables a and b to variable c, but independent of each other. By doing this we discard shared variance between a and b.
They will not be independent, your model will just fail as it assumes independence.
>>7733350
I fear I'm missing the point.
Where exactly does that equation come from? Isn't my model imposing independence since we're removing shared variance? It might also be worth mentioning that a and b are uncorrelated.
>>7733375
What step in what you describes is removing the shared variance?
>>7733398
Including two predictors in the model is equivalent to hierarchical regression where I first regress a onto c, and then use the residuals (r) for another regression of b onto r. So we're looking at independent contributions of a and b to the variance of c.
But please correct me if that's wrong.
please respond
>>7733410
Oh okay. I see. That works. That would make a and b's contributions orthogonal to each other thus linearly independent. What quadratic relation are you seeing?
>>7733499
The same ones as mentioned in the OP.
>>7733514
Show it mathematically. I don't see why one would occur. Unless you are implying that distance is somehow the quadratic relation.
>>7733715
>I don't see why one would occur.
That is exactly the problem, neither do I. It's an empirical finding, and it doesn't make much sense to my why it happens.
>Show it mathematically.
If I could that'd be excellent, but I don't nearly know enough about the math to do that.
>>7733164
Pretty sure she's Boxxy.
>Realize you first saw Boxxy when you were 16.
>You're now 22.
What.
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