How to interpret regression equation?
$begingroup$
I am trying to understand how to interpret the regression line given:
$y = -5.18 + 1.94x$ (regression line)
where $y$ is number of cold drinks sold and where $x$ is temperature
Interpret values of $a$ and $b$ in context
Interpreting $a$ in context
- To interpret $a$, I substituted $x$ (temp) as $0$.
- This tells me that $y$ (cold drinks sold) is $-5.18$. Therefore, we can interpret that when the temperature is $0$ degrees, the number of cold drinks sold is $-5.18$ (But this is impossible?)
How would I interpret $b$ in context as well?
statistics linear-regression
edited Dec 13 '18 at 21:56
Alex Vong
1,342819
asked Dec 13 '18 at 21:47
Newbie101Newbie101
154
$endgroup$
|
show 1 more comment
$begingroup$
I am trying to understand how to interpret the regression line given:
$y = -5.18 + 1.94x$ (regression line)
where $y$ is number of cold drinks sold and where $x$ is temperature
Interpret values of $a$ and $b$ in context
Interpreting $a$ in context
- To interpret $a$, I substituted $x$ (temp) as $0$.
- This tells me that $y$ (cold drinks sold) is $-5.18$. Therefore, we can interpret that when the temperature is $0$ degrees, the number of cold drinks sold is $-5.18$ (But this is impossible?)
How would I interpret $b$ in context as well?
statistics linear-regression
edited Dec 13 '18 at 21:56
Alex Vong
1,342819
asked Dec 13 '18 at 21:47
Newbie101Newbie101
154
$endgroup$
$begingroup$
Could someone also tell me how to type in maths symbols?
$endgroup$
– Newbie101
Dec 13 '18 at 21:57
$begingroup$
MathJax basic tutorial and quick reference
$endgroup$
– Alex Vong
Dec 13 '18 at 22:00
$begingroup$
what are $a$ and $b$ ? It seems it is $y=a+bx$ with $a=-5.18. Can you confirm ?
$endgroup$
– zwim
Dec 13 '18 at 22:24
$begingroup$
zwim yes can confirm
$endgroup$
– Newbie101
Dec 13 '18 at 22:29
$begingroup$
Possible duplicate: math.stackexchange.com/questions/3012843/…
$endgroup$
– Ethan Bolker
Dec 14 '18 at 1:18
|
show 1 more comment
$begingroup$
I am trying to understand how to interpret the regression line given:
$y = -5.18 + 1.94x$ (regression line)
where $y$ is number of cold drinks sold and where $x$ is temperature
Interpret values of $a$ and $b$ in context
Interpreting $a$ in context
- To interpret $a$, I substituted $x$ (temp) as $0$.
- This tells me that $y$ (cold drinks sold) is $-5.18$. Therefore, we can interpret that when the temperature is $0$ degrees, the number of cold drinks sold is $-5.18$ (But this is impossible?)
How would I interpret $b$ in context as well?
statistics linear-regression
edited Dec 13 '18 at 21:56
Alex Vong
1,342819
asked Dec 13 '18 at 21:47
Newbie101Newbie101
154
$endgroup$
I am trying to understand how to interpret the regression line given:
$y = -5.18 + 1.94x$ (regression line)
where $y$ is number of cold drinks sold and where $x$ is temperature
Interpret values of $a$ and $b$ in context
Interpreting $a$ in context
- To interpret $a$, I substituted $x$ (temp) as $0$.
- This tells me that $y$ (cold drinks sold) is $-5.18$. Therefore, we can interpret that when the temperature is $0$ degrees, the number of cold drinks sold is $-5.18$ (But this is impossible?)
How would I interpret $b$ in context as well?
statistics linear-regression
statistics linear-regression
edited Dec 13 '18 at 21:56
Alex Vong
1,342819
asked Dec 13 '18 at 21:47
Newbie101Newbie101
154
edited Dec 13 '18 at 21:56
Alex Vong
1,342819
asked Dec 13 '18 at 21:47
Newbie101Newbie101
154
edited Dec 13 '18 at 21:56
Alex Vong
1,342819
edited Dec 13 '18 at 21:56
Alex Vong
1,342819
edited Dec 13 '18 at 21:56
Alex Vong
1,342819
1,342819
asked Dec 13 '18 at 21:47
Newbie101Newbie101
154
asked Dec 13 '18 at 21:47
Newbie101Newbie101
154
asked Dec 13 '18 at 21:47
Newbie101Newbie101
154
154
$begingroup$
Could someone also tell me how to type in maths symbols?
$endgroup$
– Newbie101
Dec 13 '18 at 21:57
$begingroup$
MathJax basic tutorial and quick reference
$endgroup$
– Alex Vong
Dec 13 '18 at 22:00
$begingroup$
what are $a$ and $b$ ? It seems it is $y=a+bx$ with $a=-5.18. Can you confirm ?
$endgroup$
– zwim
Dec 13 '18 at 22:24
$begingroup$
zwim yes can confirm
$endgroup$
– Newbie101
Dec 13 '18 at 22:29
$begingroup$
Possible duplicate: math.stackexchange.com/questions/3012843/…
$endgroup$
– Ethan Bolker
Dec 14 '18 at 1:18
|
show 1 more comment
$begingroup$
Could someone also tell me how to type in maths symbols?
$endgroup$
– Newbie101
Dec 13 '18 at 21:57
$begingroup$
MathJax basic tutorial and quick reference
$endgroup$
– Alex Vong
Dec 13 '18 at 22:00
$begingroup$
what are $a$ and $b$ ? It seems it is $y=a+bx$ with $a=-5.18. Can you confirm ?
$endgroup$
– zwim
Dec 13 '18 at 22:24
$begingroup$
zwim yes can confirm
$endgroup$
– Newbie101
Dec 13 '18 at 22:29
$begingroup$
Possible duplicate: math.stackexchange.com/questions/3012843/…
$endgroup$
– Ethan Bolker
Dec 14 '18 at 1:18
$begingroup$
Could someone also tell me how to type in maths symbols?
$endgroup$
– Newbie101
Dec 13 '18 at 21:57
$begingroup$
Could someone also tell me how to type in maths symbols?
$endgroup$
– Newbie101
Dec 13 '18 at 21:57
$begingroup$
MathJax basic tutorial and quick reference
$endgroup$
– Alex Vong
Dec 13 '18 at 22:00
$begingroup$
MathJax basic tutorial and quick reference
$endgroup$
– Alex Vong
Dec 13 '18 at 22:00
$begingroup$
what are $a$ and $b$ ? It seems it is $y=a+bx$ with $a=-5.18. Can you confirm ?
$endgroup$
– zwim
Dec 13 '18 at 22:24
$begingroup$
what are $a$ and $b$ ? It seems it is $y=a+bx$ with $a=-5.18. Can you confirm ?
$endgroup$
– zwim
Dec 13 '18 at 22:24
$begingroup$
zwim yes can confirm
$endgroup$
– Newbie101
Dec 13 '18 at 22:29
$begingroup$
zwim yes can confirm
$endgroup$
– Newbie101
Dec 13 '18 at 22:29
$begingroup$
Possible duplicate: math.stackexchange.com/questions/3012843/…
$endgroup$
– Ethan Bolker
Dec 14 '18 at 1:18
$begingroup$
Possible duplicate: math.stackexchange.com/questions/3012843/…
$endgroup$
– Ethan Bolker
Dec 14 '18 at 1:18
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
The intercept term not always has a logical meaning. In your case, the intercept either insignificant (i.e., does not differ from zero in high enough probability) or "extrapolated" (i.e., you did not had measures with temperature in the vicinity of $0$, hence the intercept is just an out of data prediction for $x=0$).
Regarding $b$ - it is the derivative of the model w.r.t to $x$, namely for a change (increase) in the temperature in $1$ unit, the number of sold cold drinks changes (increases), on average, by $1.96$ units (of drinks).
answered Dec 14 '18 at 1:01
V. VancakV. Vancak
11.4k3926
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add a comment |
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$begingroup$
The intercept term not always has a logical meaning. In your case, the intercept either insignificant (i.e., does not differ from zero in high enough probability) or "extrapolated" (i.e., you did not had measures with temperature in the vicinity of $0$, hence the intercept is just an out of data prediction for $x=0$).
Regarding $b$ - it is the derivative of the model w.r.t to $x$, namely for a change (increase) in the temperature in $1$ unit, the number of sold cold drinks changes (increases), on average, by $1.96$ units (of drinks).
answered Dec 14 '18 at 1:01
V. VancakV. Vancak
11.4k3926
$endgroup$
add a comment |
$begingroup$
The intercept term not always has a logical meaning. In your case, the intercept either insignificant (i.e., does not differ from zero in high enough probability) or "extrapolated" (i.e., you did not had measures with temperature in the vicinity of $0$, hence the intercept is just an out of data prediction for $x=0$).
Regarding $b$ - it is the derivative of the model w.r.t to $x$, namely for a change (increase) in the temperature in $1$ unit, the number of sold cold drinks changes (increases), on average, by $1.96$ units (of drinks).
answered Dec 14 '18 at 1:01
V. VancakV. Vancak
11.4k3926
$endgroup$
add a comment |
$begingroup$
The intercept term not always has a logical meaning. In your case, the intercept either insignificant (i.e., does not differ from zero in high enough probability) or "extrapolated" (i.e., you did not had measures with temperature in the vicinity of $0$, hence the intercept is just an out of data prediction for $x=0$).
Regarding $b$ - it is the derivative of the model w.r.t to $x$, namely for a change (increase) in the temperature in $1$ unit, the number of sold cold drinks changes (increases), on average, by $1.96$ units (of drinks).
answered Dec 14 '18 at 1:01
V. VancakV. Vancak
11.4k3926
$endgroup$
The intercept term not always has a logical meaning. In your case, the intercept either insignificant (i.e., does not differ from zero in high enough probability) or "extrapolated" (i.e., you did not had measures with temperature in the vicinity of $0$, hence the intercept is just an out of data prediction for $x=0$).
Regarding $b$ - it is the derivative of the model w.r.t to $x$, namely for a change (increase) in the temperature in $1$ unit, the number of sold cold drinks changes (increases), on average, by $1.96$ units (of drinks).
answered Dec 14 '18 at 1:01
V. VancakV. Vancak
11.4k3926
answered Dec 14 '18 at 1:01
V. VancakV. Vancak
11.4k3926
answered Dec 14 '18 at 1:01
V. VancakV. Vancak
11.4k3926
answered Dec 14 '18 at 1:01
V. VancakV. Vancak
11.4k3926
11.4k3926
add a comment |
add a comment |
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$begingroup$
Could someone also tell me how to type in maths symbols?
$endgroup$
– Newbie101
Dec 13 '18 at 21:57
$begingroup$
MathJax basic tutorial and quick reference
$endgroup$
– Alex Vong
Dec 13 '18 at 22:00
$begingroup$
what are $a$ and $b$ ? It seems it is $y=a+bx$ with $a=-5.18. Can you confirm ?
$endgroup$
– zwim
Dec 13 '18 at 22:24
$begingroup$
zwim yes can confirm
$endgroup$
– Newbie101
Dec 13 '18 at 22:29
$begingroup$
Possible duplicate: math.stackexchange.com/questions/3012843/…
$endgroup$
– Ethan Bolker
Dec 14 '18 at 1:18