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Why is it often said that dependent variable depends on the values of independent variable
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I hear it often from my teachers that dependent variable is called "dependent" because it depends on the values of independent variable.
But I think, you can say the same for independent variable, how is independent variable any different then?
Eg : $y = 5x$
$y$ is dependent variable.
$x$ is independent variable.
If I put $x= 5$, then $y= 25$. Surely I can also say, if $y = 25$ then $x$ has to be $5$.
Don't they kinda depend on each other? Then what's the point of calling one dependent and other independent? Why do we even call them that in the first place?
functions terminology
asked Jul 21 at 13:07
William
801214
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up vote
2
down vote
favorite
I hear it often from my teachers that dependent variable is called "dependent" because it depends on the values of independent variable.
But I think, you can say the same for independent variable, how is independent variable any different then?
Eg : $y = 5x$
$y$ is dependent variable.
$x$ is independent variable.
If I put $x= 5$, then $y= 25$. Surely I can also say, if $y = 25$ then $x$ has to be $5$.
Don't they kinda depend on each other? Then what's the point of calling one dependent and other independent? Why do we even call them that in the first place?
functions terminology
asked Jul 21 at 13:07
William
801214
Q: "Do you go swimming in sea tomorrow?" A:"That depends on the weather". Another answer could have been: "That depends on the question whether Harry is going swimming in sea tomorrow". This in the understanding that I know that Harry always goes swimming iff the weather is good. Is my swimming depending on Harry's swimming? Somehow it does. In e.g. probability theory the (in)dependence between two events always has a mutual character.
– drhab
Jul 21 at 13:33
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I hear it often from my teachers that dependent variable is called "dependent" because it depends on the values of independent variable.
But I think, you can say the same for independent variable, how is independent variable any different then?
Eg : $y = 5x$
$y$ is dependent variable.
$x$ is independent variable.
If I put $x= 5$, then $y= 25$. Surely I can also say, if $y = 25$ then $x$ has to be $5$.
Don't they kinda depend on each other? Then what's the point of calling one dependent and other independent? Why do we even call them that in the first place?
functions terminology
asked Jul 21 at 13:07
William
801214
I hear it often from my teachers that dependent variable is called "dependent" because it depends on the values of independent variable.
But I think, you can say the same for independent variable, how is independent variable any different then?
Eg : $y = 5x$
$y$ is dependent variable.
$x$ is independent variable.
If I put $x= 5$, then $y= 25$. Surely I can also say, if $y = 25$ then $x$ has to be $5$.
Don't they kinda depend on each other? Then what's the point of calling one dependent and other independent? Why do we even call them that in the first place?
functions terminology
asked Jul 21 at 13:07
William
801214
asked Jul 21 at 13:07
William
801214
asked Jul 21 at 13:07
William
801214
asked Jul 21 at 13:07
William
801214
801214
Q: "Do you go swimming in sea tomorrow?" A:"That depends on the weather". Another answer could have been: "That depends on the question whether Harry is going swimming in sea tomorrow". This in the understanding that I know that Harry always goes swimming iff the weather is good. Is my swimming depending on Harry's swimming? Somehow it does. In e.g. probability theory the (in)dependence between two events always has a mutual character.
– drhab
Jul 21 at 13:33
add a comment |Â
Q: "Do you go swimming in sea tomorrow?" A:"That depends on the weather". Another answer could have been: "That depends on the question whether Harry is going swimming in sea tomorrow". This in the understanding that I know that Harry always goes swimming iff the weather is good. Is my swimming depending on Harry's swimming? Somehow it does. In e.g. probability theory the (in)dependence between two events always has a mutual character.
– drhab
Jul 21 at 13:33
Q: "Do you go swimming in sea tomorrow?" A:"That depends on the weather". Another answer could have been: "That depends on the question whether Harry is going swimming in sea tomorrow". This in the understanding that I know that Harry always goes swimming iff the weather is good. Is my swimming depending on Harry's swimming? Somehow it does. In e.g. probability theory the (in)dependence between two events always has a mutual character.
– drhab
Jul 21 at 13:33
Q: "Do you go swimming in sea tomorrow?" A:"That depends on the weather". Another answer could have been: "That depends on the question whether Harry is going swimming in sea tomorrow". This in the understanding that I know that Harry always goes swimming iff the weather is good. Is my swimming depending on Harry's swimming? Somehow it does. In e.g. probability theory the (in)dependence between two events always has a mutual character.
– drhab
Jul 21 at 13:33
add a comment |Â
2 Answers
2
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oldest
votes
up vote
2
down vote
accepted
Indeed in this case they do depend on each other. The particular function is invertible: knowing $x$ you can find $y$ and vice versa.
So sometimes you can think of either variable as the "independent one".
If you are driving at $30$ miles per hour and you want to know how far you can get in three hours you are thinking of time as the independent variable and distance as dependent: if you know how much time you take you can figure out how far you go.
You could equally well think of the same relationship the other way around. If you need to travel a certain distance you can figure out how long it will take. The time depends on the distance.
When the variables are "$x$" and "$y$" it's traditional to think of $x$ as the independent variable. In your example you can solve for $x$ in terms of $y$ and think of $y$ as independent. If the relation happened to be $y = x^2$ or $y = sin x$ you couldn't do that.
answered Jul 21 at 13:18
Ethan Bolker
35.7k54199
add a comment |Â
up vote
1
down vote
There is nothing mathematically objective about dependent and independent variables. It's all about interpretation. In an applied setting (for instance, $x$ is an amount of something you buy and $y$ is the resulting cost, or $x$ is the time you spend doing something and $y$ is the amount you finish) the independent variable is often the one you have direct control over, while the dependent variable is the result.
answered Jul 21 at 13:17
Arthur
98.7k793174
you don't need to have control over the independent variable; think of a model where you try to explain economic growth based on unemployment
– LinAlg
Jul 21 at 13:22
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
Indeed in this case they do depend on each other. The particular function is invertible: knowing $x$ you can find $y$ and vice versa.
So sometimes you can think of either variable as the "independent one".
If you are driving at $30$ miles per hour and you want to know how far you can get in three hours you are thinking of time as the independent variable and distance as dependent: if you know how much time you take you can figure out how far you go.
You could equally well think of the same relationship the other way around. If you need to travel a certain distance you can figure out how long it will take. The time depends on the distance.
When the variables are "$x$" and "$y$" it's traditional to think of $x$ as the independent variable. In your example you can solve for $x$ in terms of $y$ and think of $y$ as independent. If the relation happened to be $y = x^2$ or $y = sin x$ you couldn't do that.
answered Jul 21 at 13:18
Ethan Bolker
35.7k54199
add a comment |Â
up vote
2
down vote
accepted
Indeed in this case they do depend on each other. The particular function is invertible: knowing $x$ you can find $y$ and vice versa.
So sometimes you can think of either variable as the "independent one".
If you are driving at $30$ miles per hour and you want to know how far you can get in three hours you are thinking of time as the independent variable and distance as dependent: if you know how much time you take you can figure out how far you go.
You could equally well think of the same relationship the other way around. If you need to travel a certain distance you can figure out how long it will take. The time depends on the distance.
When the variables are "$x$" and "$y$" it's traditional to think of $x$ as the independent variable. In your example you can solve for $x$ in terms of $y$ and think of $y$ as independent. If the relation happened to be $y = x^2$ or $y = sin x$ you couldn't do that.
answered Jul 21 at 13:18
Ethan Bolker
35.7k54199
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
Indeed in this case they do depend on each other. The particular function is invertible: knowing $x$ you can find $y$ and vice versa.
So sometimes you can think of either variable as the "independent one".
If you are driving at $30$ miles per hour and you want to know how far you can get in three hours you are thinking of time as the independent variable and distance as dependent: if you know how much time you take you can figure out how far you go.
You could equally well think of the same relationship the other way around. If you need to travel a certain distance you can figure out how long it will take. The time depends on the distance.
When the variables are "$x$" and "$y$" it's traditional to think of $x$ as the independent variable. In your example you can solve for $x$ in terms of $y$ and think of $y$ as independent. If the relation happened to be $y = x^2$ or $y = sin x$ you couldn't do that.
answered Jul 21 at 13:18
Ethan Bolker
35.7k54199
Indeed in this case they do depend on each other. The particular function is invertible: knowing $x$ you can find $y$ and vice versa.
So sometimes you can think of either variable as the "independent one".
If you are driving at $30$ miles per hour and you want to know how far you can get in three hours you are thinking of time as the independent variable and distance as dependent: if you know how much time you take you can figure out how far you go.
You could equally well think of the same relationship the other way around. If you need to travel a certain distance you can figure out how long it will take. The time depends on the distance.
When the variables are "$x$" and "$y$" it's traditional to think of $x$ as the independent variable. In your example you can solve for $x$ in terms of $y$ and think of $y$ as independent. If the relation happened to be $y = x^2$ or $y = sin x$ you couldn't do that.
answered Jul 21 at 13:18
Ethan Bolker
35.7k54199
answered Jul 21 at 13:18
Ethan Bolker
35.7k54199
answered Jul 21 at 13:18
Ethan Bolker
35.7k54199
answered Jul 21 at 13:18
Ethan Bolker
35.7k54199
35.7k54199
add a comment |Â
add a comment |Â
up vote
1
down vote
There is nothing mathematically objective about dependent and independent variables. It's all about interpretation. In an applied setting (for instance, $x$ is an amount of something you buy and $y$ is the resulting cost, or $x$ is the time you spend doing something and $y$ is the amount you finish) the independent variable is often the one you have direct control over, while the dependent variable is the result.
answered Jul 21 at 13:17
Arthur
98.7k793174
you don't need to have control over the independent variable; think of a model where you try to explain economic growth based on unemployment
– LinAlg
Jul 21 at 13:22
add a comment |Â
up vote
1
down vote
There is nothing mathematically objective about dependent and independent variables. It's all about interpretation. In an applied setting (for instance, $x$ is an amount of something you buy and $y$ is the resulting cost, or $x$ is the time you spend doing something and $y$ is the amount you finish) the independent variable is often the one you have direct control over, while the dependent variable is the result.
answered Jul 21 at 13:17
Arthur
98.7k793174
you don't need to have control over the independent variable; think of a model where you try to explain economic growth based on unemployment
– LinAlg
Jul 21 at 13:22
add a comment |Â
up vote
1
down vote
up vote
1
down vote
There is nothing mathematically objective about dependent and independent variables. It's all about interpretation. In an applied setting (for instance, $x$ is an amount of something you buy and $y$ is the resulting cost, or $x$ is the time you spend doing something and $y$ is the amount you finish) the independent variable is often the one you have direct control over, while the dependent variable is the result.
answered Jul 21 at 13:17
Arthur
98.7k793174
There is nothing mathematically objective about dependent and independent variables. It's all about interpretation. In an applied setting (for instance, $x$ is an amount of something you buy and $y$ is the resulting cost, or $x$ is the time you spend doing something and $y$ is the amount you finish) the independent variable is often the one you have direct control over, while the dependent variable is the result.
answered Jul 21 at 13:17
Arthur
98.7k793174
edited Jul 21 at 13:43
answered Jul 21 at 13:17
Arthur
98.7k793174
answered Jul 21 at 13:17
Arthur
98.7k793174
answered Jul 21 at 13:17
Arthur
98.7k793174
98.7k793174
you don't need to have control over the independent variable; think of a model where you try to explain economic growth based on unemployment
– LinAlg
Jul 21 at 13:22
add a comment |Â
you don't need to have control over the independent variable; think of a model where you try to explain economic growth based on unemployment
– LinAlg
Jul 21 at 13:22
you don't need to have control over the independent variable; think of a model where you try to explain economic growth based on unemployment
– LinAlg
Jul 21 at 13:22
you don't need to have control over the independent variable; think of a model where you try to explain economic growth based on unemployment
– LinAlg
Jul 21 at 13:22
add a comment |Â
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Q: "Do you go swimming in sea tomorrow?" A:"That depends on the weather". Another answer could have been: "That depends on the question whether Harry is going swimming in sea tomorrow". This in the understanding that I know that Harry always goes swimming iff the weather is good. Is my swimming depending on Harry's swimming? Somehow it does. In e.g. probability theory the (in)dependence between two events always has a mutual character.
– drhab
Jul 21 at 13:33