Comment by 🚀 thoughtterminatingcliche
Re: "I have another question, yet again. I'm learning about…"
Math is fun is a helpful website, especially if you do his exercises in the order he provides them.
Mar 05 · 2 months ago
6 Later Comments ↓
control variables aren't really a (pure) mathematical thing, they have to do with how statistical experiments are conducted. that's outside of my wheelhouse so i can't really talk to it.
Using the car analogy, you have the independent variable that is how far the gas pedal is pushed and the dependent variable of the engine speed. The engine speed also depends on things like how much weight is on the engine, how the chassis is built, the incline the car is driving at, what gear the transmission is in, what the weather is like.
If you're designing an experiment where you're measuring the correlation between the gas pedal and the engine speed, you have to take into account all those other factors. Turning them into a control variable means that everytime you do the experiment, you use the same values---same weight, same chassis, same incline, same gear, same weather.
🚀 thoughtterminatingcliche · Mar 05 at 18:13:
@lamb-duh Well to be fair this is a requirement of equality of extraneous variables in control experiments. But there is a mathematical meaning for control variables in multiple variable regression. I will not explain it here, but because each b shows the in-/de-crease in y when all other variables are 0, by modelling other variables in the model you are partialling them out.
🗡️ The_Jackal [OP] · Mar 05 at 19:44:
@thoughtterminatingcliche I've heard of math is fun. I think I should also mention that I only got up to about 8th grade math in school. I'm wondering if I even got that far. If I did I just might not remember it. It was homeschool, but I did have a curriculum I followed. I'm currently studying so I can hopefully get a GED and be able to get an EE degree one day. I added some more to my note. Would this be a good enough explanation of them for myself for now?
An independent variable is a variable that can be either measured or manipulated to give us the value of the dependent variable, which is a variable whose value depends on how the independent variable is manipulated. For example, a file on a computer takes up 50 megabytes and you want to know what the total amount of storage it would take up for a certain number of copies on a hard drive. The number of copies would determine the total amount of storage taken up, and you can't tell what that is unless you have a specific number of copies. Therefore, the number of copies is our independent variable and the total amount of storage is our dependent variable. One way this could be represented is like so: 50f = s. If we rewrite this equation as f = s/50, s would be our independent variable and f the dependent variable. We would then be finding out how many copies of the file a specific number of megabytes make, and the value of f would depend on the value of s. There are times in other kinds of equations when you might not be able to directly manipulate the independent variable and instead try predicting the dependent variable from the independent variable.
In something like boolean algebra, there can be a limited number of values for the independent and dependent variable (input and output in this case), like how there are a limited number of inputs and outputs for different logic gates.
Another example could be this: Consider that you're driving a car. The gas pedal is your independent variable and the speed of the engine is the dependent variable. The speed of the engine is controlled indirectly by the gas pedal as well as other factors. In pure math, it could be said that we really have interdependent variables. We can change any of them, but it can cause others to change or restrict their possible values as well.
Generally, x is used for the independant variable and y for the dependant variable. x represents the x axis on a graph, and y represents the y axis.
Edit: I looked at mathisfun's explanation of a function and independent and dependent variables and it seems to be close to what I imagined when I heard those terms, input and output, and you have to have an input to get an output and the output will obviously be related to the input. At least that's how I'm understanding it in my head.
🗡️ The_Jackal [OP] · Mar 06 at 00:05:
I decided I'll just study what functions are first, and I think that's giving me a better understanding.
🚀 thoughtterminatingcliche · Mar 06 at 18:36:
You are in the right path. I will not be pedantic, since you are in a process of understanding and reshaping what you know. Take your time. The key to understand any function is that it maps a value from one set to a value from another set. There are some values allowed for the input set, and some for the output set. You take it from there. PS Don't give up. I was a drop out and learned math later in life. It is a ladder, just don't skip steps!
🗡️ The_Jackal [OP] · Mar 06 at 19:17:
@thoughtterminatingcliche Thank you. I've been writing a note that's essentially just taking the stuff from mathisfun's section on functions, Khan Academy's, and this video: https://www.youtube.com/watch?v=LNZl4GqVm58&t=257 and trying to find ways to slightly reword them and fit bits from each into it so it hopefully sticks. I write my notes more like I'm writing a lesson to myself instead of quick sections I jot down. It takes me a while to write so I type it on my phone, make sure it's correct and touched up, then copy it down in a notebook.
Original Post
I have another question, yet again. I'm learning about independent and dependent variables. Is this explanation I wrote for myself correct? I haven't written it in my note book yet so I can still change and add to it without much trouble if I need to. An independent variable is a variable that can be manipulated to give us the value of the dependent variable. A dependent variable is a variable that has a value that can only be found by substituting the independent variable for something. For...