Interpreting studies from an equation
$begingroup$
I was studying how the number of singles ($x$ axis) affect the aging population of a country ($y$ axis), for Singapore people aged 65 years or older.
I made a scatter plot and got $y=0.8342 x - 474720$. How does this gradient $0.8342$, $y$ intercept $-474720$ relate to what i study?
How is it possible for my $y$ intercept to be a negative number ? That will mean a negative number of people aged 65 years or older.
As for the gradient, I understand that if the amount of singles increase by $1$ unit, there will be an increase in $0.8342$ of aged people.
analysis
edited Nov 25 '18 at 13:43
amWhy
1
asked Nov 25 '18 at 13:37
ErikienErikien
494
$endgroup$
add a comment |
$begingroup$
I was studying how the number of singles ($x$ axis) affect the aging population of a country ($y$ axis), for Singapore people aged 65 years or older.
I made a scatter plot and got $y=0.8342 x - 474720$. How does this gradient $0.8342$, $y$ intercept $-474720$ relate to what i study?
How is it possible for my $y$ intercept to be a negative number ? That will mean a negative number of people aged 65 years or older.
As for the gradient, I understand that if the amount of singles increase by $1$ unit, there will be an increase in $0.8342$ of aged people.
analysis
edited Nov 25 '18 at 13:43
amWhy
1
asked Nov 25 '18 at 13:37
ErikienErikien
494
$endgroup$
add a comment |
$begingroup$
I was studying how the number of singles ($x$ axis) affect the aging population of a country ($y$ axis), for Singapore people aged 65 years or older.
I made a scatter plot and got $y=0.8342 x - 474720$. How does this gradient $0.8342$, $y$ intercept $-474720$ relate to what i study?
How is it possible for my $y$ intercept to be a negative number ? That will mean a negative number of people aged 65 years or older.
As for the gradient, I understand that if the amount of singles increase by $1$ unit, there will be an increase in $0.8342$ of aged people.
analysis
edited Nov 25 '18 at 13:43
amWhy
1
asked Nov 25 '18 at 13:37
ErikienErikien
494
$endgroup$
I was studying how the number of singles ($x$ axis) affect the aging population of a country ($y$ axis), for Singapore people aged 65 years or older.
I made a scatter plot and got $y=0.8342 x - 474720$. How does this gradient $0.8342$, $y$ intercept $-474720$ relate to what i study?
How is it possible for my $y$ intercept to be a negative number ? That will mean a negative number of people aged 65 years or older.
As for the gradient, I understand that if the amount of singles increase by $1$ unit, there will be an increase in $0.8342$ of aged people.
analysis
analysis
edited Nov 25 '18 at 13:43
amWhy
1
asked Nov 25 '18 at 13:37
ErikienErikien
494
edited Nov 25 '18 at 13:43
amWhy
1
asked Nov 25 '18 at 13:37
ErikienErikien
494
edited Nov 25 '18 at 13:43
amWhy
1
edited Nov 25 '18 at 13:43
amWhy
1
edited Nov 25 '18 at 13:43
amWhy
1
1
asked Nov 25 '18 at 13:37
ErikienErikien
494
asked Nov 25 '18 at 13:37
ErikienErikien
494
asked Nov 25 '18 at 13:37
ErikienErikien
494
494
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You have calculated a regression line that shows a linear relationship suggesting that each increase in the number of single people correlates with an increase in the number of older people, and have correctly identified the slope as giving the rate of increase.
This relationship is only a correlation. You can't say one thing causes the other. And it will come close to matching the data only for the data you have. I assume you have no population counts for Singapore when there are no single people. That never happened. The intercept on the graph is mathematically correct but has no meaning in the context. The same could be said for the value of $y$ if you substitute $100$ billion for $x$.
You probably calculated this regression line with Excel. Ask it to draw the graph, but limit the values on the $x$ axis to a range only slightly larger than the values for which you have data.
answered Nov 25 '18 at 13:49
Ethan BolkerEthan Bolker
42.1k548111
$endgroup$
$begingroup$
i need to explain what does the intercept mean because this is an assignment i am doing. So do i explain it the "math" way. which mean the people aged 65 years or older is - 474720 people when there are 0 single people. "Does this just mean that if there are very less single people, the number of old people will drop by alot " if i dont add that statement in "" , it wouldn't make sense isn't it ?
$endgroup$
– Erikien
Nov 25 '18 at 13:59
$begingroup$
When I ask my students this question I expect them to explain, as I did, why the intercept is meaningless in the context of the problem. The regression line can only make sense near where the real data are. If your instructor wants another answer I think he is mistaken.The way you say "if there are fewer single people the aging people will drop by a lot" suggests that one causes the other, which is a serious mistake in logic even if the math is correct.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:03
$begingroup$
what do you mean by "The regression line can only make sense near where the real data are" because my data is taken from a gov website
$endgroup$
– Erikien
Nov 25 '18 at 14:20
$begingroup$
I mean near the values of $x$ you actually know $y$ for, not the source of your data. If you know $x$ each year for $10$ years and the value varies between, say $5$ million and $7$ million then it makes no sense to put $0$ million or $2$ million or $15$ million and compute a value for $y$. The math will be right but the interpretation about people will be nonsense.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:33
add a comment |
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1 Answer
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active
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1 Answer
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active
oldest
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active
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votes
$begingroup$
You have calculated a regression line that shows a linear relationship suggesting that each increase in the number of single people correlates with an increase in the number of older people, and have correctly identified the slope as giving the rate of increase.
This relationship is only a correlation. You can't say one thing causes the other. And it will come close to matching the data only for the data you have. I assume you have no population counts for Singapore when there are no single people. That never happened. The intercept on the graph is mathematically correct but has no meaning in the context. The same could be said for the value of $y$ if you substitute $100$ billion for $x$.
You probably calculated this regression line with Excel. Ask it to draw the graph, but limit the values on the $x$ axis to a range only slightly larger than the values for which you have data.
answered Nov 25 '18 at 13:49
Ethan BolkerEthan Bolker
42.1k548111
$endgroup$
$begingroup$
i need to explain what does the intercept mean because this is an assignment i am doing. So do i explain it the "math" way. which mean the people aged 65 years or older is - 474720 people when there are 0 single people. "Does this just mean that if there are very less single people, the number of old people will drop by alot " if i dont add that statement in "" , it wouldn't make sense isn't it ?
$endgroup$
– Erikien
Nov 25 '18 at 13:59
$begingroup$
When I ask my students this question I expect them to explain, as I did, why the intercept is meaningless in the context of the problem. The regression line can only make sense near where the real data are. If your instructor wants another answer I think he is mistaken.The way you say "if there are fewer single people the aging people will drop by a lot" suggests that one causes the other, which is a serious mistake in logic even if the math is correct.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:03
$begingroup$
what do you mean by "The regression line can only make sense near where the real data are" because my data is taken from a gov website
$endgroup$
– Erikien
Nov 25 '18 at 14:20
$begingroup$
I mean near the values of $x$ you actually know $y$ for, not the source of your data. If you know $x$ each year for $10$ years and the value varies between, say $5$ million and $7$ million then it makes no sense to put $0$ million or $2$ million or $15$ million and compute a value for $y$. The math will be right but the interpretation about people will be nonsense.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:33
add a comment |
$begingroup$
You have calculated a regression line that shows a linear relationship suggesting that each increase in the number of single people correlates with an increase in the number of older people, and have correctly identified the slope as giving the rate of increase.
This relationship is only a correlation. You can't say one thing causes the other. And it will come close to matching the data only for the data you have. I assume you have no population counts for Singapore when there are no single people. That never happened. The intercept on the graph is mathematically correct but has no meaning in the context. The same could be said for the value of $y$ if you substitute $100$ billion for $x$.
You probably calculated this regression line with Excel. Ask it to draw the graph, but limit the values on the $x$ axis to a range only slightly larger than the values for which you have data.
answered Nov 25 '18 at 13:49
Ethan BolkerEthan Bolker
42.1k548111
$endgroup$
$begingroup$
i need to explain what does the intercept mean because this is an assignment i am doing. So do i explain it the "math" way. which mean the people aged 65 years or older is - 474720 people when there are 0 single people. "Does this just mean that if there are very less single people, the number of old people will drop by alot " if i dont add that statement in "" , it wouldn't make sense isn't it ?
$endgroup$
– Erikien
Nov 25 '18 at 13:59
$begingroup$
When I ask my students this question I expect them to explain, as I did, why the intercept is meaningless in the context of the problem. The regression line can only make sense near where the real data are. If your instructor wants another answer I think he is mistaken.The way you say "if there are fewer single people the aging people will drop by a lot" suggests that one causes the other, which is a serious mistake in logic even if the math is correct.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:03
$begingroup$
what do you mean by "The regression line can only make sense near where the real data are" because my data is taken from a gov website
$endgroup$
– Erikien
Nov 25 '18 at 14:20
$begingroup$
I mean near the values of $x$ you actually know $y$ for, not the source of your data. If you know $x$ each year for $10$ years and the value varies between, say $5$ million and $7$ million then it makes no sense to put $0$ million or $2$ million or $15$ million and compute a value for $y$. The math will be right but the interpretation about people will be nonsense.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:33
add a comment |
$begingroup$
You have calculated a regression line that shows a linear relationship suggesting that each increase in the number of single people correlates with an increase in the number of older people, and have correctly identified the slope as giving the rate of increase.
This relationship is only a correlation. You can't say one thing causes the other. And it will come close to matching the data only for the data you have. I assume you have no population counts for Singapore when there are no single people. That never happened. The intercept on the graph is mathematically correct but has no meaning in the context. The same could be said for the value of $y$ if you substitute $100$ billion for $x$.
You probably calculated this regression line with Excel. Ask it to draw the graph, but limit the values on the $x$ axis to a range only slightly larger than the values for which you have data.
answered Nov 25 '18 at 13:49
Ethan BolkerEthan Bolker
42.1k548111
$endgroup$
You have calculated a regression line that shows a linear relationship suggesting that each increase in the number of single people correlates with an increase in the number of older people, and have correctly identified the slope as giving the rate of increase.
This relationship is only a correlation. You can't say one thing causes the other. And it will come close to matching the data only for the data you have. I assume you have no population counts for Singapore when there are no single people. That never happened. The intercept on the graph is mathematically correct but has no meaning in the context. The same could be said for the value of $y$ if you substitute $100$ billion for $x$.
You probably calculated this regression line with Excel. Ask it to draw the graph, but limit the values on the $x$ axis to a range only slightly larger than the values for which you have data.
answered Nov 25 '18 at 13:49
Ethan BolkerEthan Bolker
42.1k548111
answered Nov 25 '18 at 13:49
Ethan BolkerEthan Bolker
42.1k548111
answered Nov 25 '18 at 13:49
Ethan BolkerEthan Bolker
42.1k548111
answered Nov 25 '18 at 13:49
Ethan BolkerEthan Bolker
42.1k548111
42.1k548111
$begingroup$
i need to explain what does the intercept mean because this is an assignment i am doing. So do i explain it the "math" way. which mean the people aged 65 years or older is - 474720 people when there are 0 single people. "Does this just mean that if there are very less single people, the number of old people will drop by alot " if i dont add that statement in "" , it wouldn't make sense isn't it ?
$endgroup$
– Erikien
Nov 25 '18 at 13:59
$begingroup$
When I ask my students this question I expect them to explain, as I did, why the intercept is meaningless in the context of the problem. The regression line can only make sense near where the real data are. If your instructor wants another answer I think he is mistaken.The way you say "if there are fewer single people the aging people will drop by a lot" suggests that one causes the other, which is a serious mistake in logic even if the math is correct.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:03
$begingroup$
what do you mean by "The regression line can only make sense near where the real data are" because my data is taken from a gov website
$endgroup$
– Erikien
Nov 25 '18 at 14:20
$begingroup$
I mean near the values of $x$ you actually know $y$ for, not the source of your data. If you know $x$ each year for $10$ years and the value varies between, say $5$ million and $7$ million then it makes no sense to put $0$ million or $2$ million or $15$ million and compute a value for $y$. The math will be right but the interpretation about people will be nonsense.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:33
add a comment |
$begingroup$
i need to explain what does the intercept mean because this is an assignment i am doing. So do i explain it the "math" way. which mean the people aged 65 years or older is - 474720 people when there are 0 single people. "Does this just mean that if there are very less single people, the number of old people will drop by alot " if i dont add that statement in "" , it wouldn't make sense isn't it ?
$endgroup$
– Erikien
Nov 25 '18 at 13:59
$begingroup$
When I ask my students this question I expect them to explain, as I did, why the intercept is meaningless in the context of the problem. The regression line can only make sense near where the real data are. If your instructor wants another answer I think he is mistaken.The way you say "if there are fewer single people the aging people will drop by a lot" suggests that one causes the other, which is a serious mistake in logic even if the math is correct.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:03
$begingroup$
what do you mean by "The regression line can only make sense near where the real data are" because my data is taken from a gov website
$endgroup$
– Erikien
Nov 25 '18 at 14:20
$begingroup$
I mean near the values of $x$ you actually know $y$ for, not the source of your data. If you know $x$ each year for $10$ years and the value varies between, say $5$ million and $7$ million then it makes no sense to put $0$ million or $2$ million or $15$ million and compute a value for $y$. The math will be right but the interpretation about people will be nonsense.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:33
$begingroup$
i need to explain what does the intercept mean because this is an assignment i am doing. So do i explain it the "math" way. which mean the people aged 65 years or older is - 474720 people when there are 0 single people. "Does this just mean that if there are very less single people, the number of old people will drop by alot " if i dont add that statement in "" , it wouldn't make sense isn't it ?
$endgroup$
– Erikien
Nov 25 '18 at 13:59
$begingroup$
i need to explain what does the intercept mean because this is an assignment i am doing. So do i explain it the "math" way. which mean the people aged 65 years or older is - 474720 people when there are 0 single people. "Does this just mean that if there are very less single people, the number of old people will drop by alot " if i dont add that statement in "" , it wouldn't make sense isn't it ?
$endgroup$
– Erikien
Nov 25 '18 at 13:59
$begingroup$
When I ask my students this question I expect them to explain, as I did, why the intercept is meaningless in the context of the problem. The regression line can only make sense near where the real data are. If your instructor wants another answer I think he is mistaken.The way you say "if there are fewer single people the aging people will drop by a lot" suggests that one causes the other, which is a serious mistake in logic even if the math is correct.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:03
$begingroup$
When I ask my students this question I expect them to explain, as I did, why the intercept is meaningless in the context of the problem. The regression line can only make sense near where the real data are. If your instructor wants another answer I think he is mistaken.The way you say "if there are fewer single people the aging people will drop by a lot" suggests that one causes the other, which is a serious mistake in logic even if the math is correct.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:03
$begingroup$
what do you mean by "The regression line can only make sense near where the real data are" because my data is taken from a gov website
$endgroup$
– Erikien
Nov 25 '18 at 14:20
$begingroup$
what do you mean by "The regression line can only make sense near where the real data are" because my data is taken from a gov website
$endgroup$
– Erikien
Nov 25 '18 at 14:20
$begingroup$
I mean near the values of $x$ you actually know $y$ for, not the source of your data. If you know $x$ each year for $10$ years and the value varies between, say $5$ million and $7$ million then it makes no sense to put $0$ million or $2$ million or $15$ million and compute a value for $y$. The math will be right but the interpretation about people will be nonsense.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:33
$begingroup$
I mean near the values of $x$ you actually know $y$ for, not the source of your data. If you know $x$ each year for $10$ years and the value varies between, say $5$ million and $7$ million then it makes no sense to put $0$ million or $2$ million or $15$ million and compute a value for $y$. The math will be right but the interpretation about people will be nonsense.
$endgroup$
– Ethan Bolker
Nov 25 '18 at 14:33
add a comment |
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