Linear regression basic concepts understanding

[ashp]

In Linear regression, how do we understand which column in a data set is an Input or Output Variable? Why is Input variable WC and output fat? Please refer to problem below.

Business Problem: Studies have shown that individual with excess FAT in the body have higher risk of Heart Disease.
Computed Tomography, commonly CT Scan is the only technique that allows for the precise and reliable measure of the FAT.
Is there simpler yet reasonably accurate way to predict the FAT area? i.e.,
The Waist Circumference - FAT data is a part of this study wherein the aim is to stud how well
waist circumference(WC) predicts the FAT.

Given: Input variable=Wait circumference-> x
Output variable = FAT-> y
Waist circumference is the Input, based on WC we need to predict how much is the FAT content in the patients

 

[tkhunny]

1) It doesn't matter which is input and which is output. With an assumed linear relationship, it is just as intuitive either way.
2) If we are talking about CAUSE, which regression doesn't, it would be more important.
3) Typically, the one you can control, the independent variable, should be on the x-axis. However, that's only a convention that may make the whole thing easier to communicate.
4) The premise is "Excess Fat" ==> "Higher Risk of Heart Disease".
5) The cheaper premise is "Waist Circumference" ==> "Excess Fat".
6) "Excess Fat" is not well-defined. "Fat" is okay, but we have been given no indication on the meaning of "excess".

So, there is some work before this is a meaningful study.

 

[Dr.Peterson]

In Linear regression, how do we understand which column in a data set is an Input or Output Variable? Why is Input variable WC and output fat? Please refer to problem below.

Business Problem: Studies have shown that individual with excess FAT in the body have higher risk of Heart Disease.
Computed Tomography, commonly CT Scan is the only technique that allows for the precise and reliable measure of the FAT.
Is there simpler yet reasonably accurate way to predict the FAT area? i.e.,
The Waist Circumference - FAT data is a part of this study wherein the aim is to stud how well
waist circumference(WC) predicts the FAT.

Given: Input variable=Wait circumference-> x
Output variable = FAT-> y
Waist circumference is the Input, based on WC we need to predict how much is the FAT content in the patients

I'd say the key word here is "predicts". You want to take the quantity you can directly measure, WC, as input, and output the quantity you want to know, fat (whatever unit that is being measured in - "area" makes no sense to me).