Mixing
What is a deviation vector?
$begingroup$
LINEAR ALGEBRA: I've looked online for this and can't find anything...
What is a deviation vector and how do I compute them? (specifically how did my teacher get those vectors in part b?)
Here is the problem I'm referring to:
[4 points] Suppose we have nonnzero deviation vectors $vec x,vec y$ of two characteristics, such that $vec x=cvec y$. Show carefully what this implies about the correlation coefficient $r$ between the two characteristics.
[6 points] Find the correlation coefficient between the daily profit and number of paintings inside three CA coffee shops.
$$begin{array}{|c|c|c|}
hline
text{Shop} & text{Profit (in 100s)} & text{Paintings} \hline
text{A} & -1 & 1 \hline
text{B} & -1 & 2 \hline
text{C} & 2 & 3 \hline
end{array}$$
Answer.
- We have that:
$$r=frac{vec xcdotvec y}{|vec x||vec y|}=frac{c(vec ycdotvec y)}{|c||vec y||vec y|}=frac{c}{|c|}=begin{cases} 1, & text{if }c>0, \ -1, & text{if }c<0. end{cases}$$
[6 points] We find deviation vectors $vec x=(-1,-1,2)^T$ and $vec y=(-1,0,1)^T$. This gives:
$$r=frac{vec xcdotvec y}{|vec x||vec y|}=frac{3}{sqrt6sqrt2}left(=frac{sqrt3}{2}right).$$
Question image
linear-algebra correlation
edited Jun 6 '16 at 14:00
Martin Sleziak
44.7k10118272
asked Jun 6 '16 at 8:59
timtim
61
$endgroup$
add a comment |
$begingroup$
LINEAR ALGEBRA: I've looked online for this and can't find anything...
What is a deviation vector and how do I compute them? (specifically how did my teacher get those vectors in part b?)
Here is the problem I'm referring to:
[4 points] Suppose we have nonnzero deviation vectors $vec x,vec y$ of two characteristics, such that $vec x=cvec y$. Show carefully what this implies about the correlation coefficient $r$ between the two characteristics.
[6 points] Find the correlation coefficient between the daily profit and number of paintings inside three CA coffee shops.
$$begin{array}{|c|c|c|}
hline
text{Shop} & text{Profit (in 100s)} & text{Paintings} \hline
text{A} & -1 & 1 \hline
text{B} & -1 & 2 \hline
text{C} & 2 & 3 \hline
end{array}$$
Answer.
- We have that:
$$r=frac{vec xcdotvec y}{|vec x||vec y|}=frac{c(vec ycdotvec y)}{|c||vec y||vec y|}=frac{c}{|c|}=begin{cases} 1, & text{if }c>0, \ -1, & text{if }c<0. end{cases}$$
[6 points] We find deviation vectors $vec x=(-1,-1,2)^T$ and $vec y=(-1,0,1)^T$. This gives:
$$r=frac{vec xcdotvec y}{|vec x||vec y|}=frac{3}{sqrt6sqrt2}left(=frac{sqrt3}{2}right).$$
Question image
linear-algebra correlation
edited Jun 6 '16 at 14:00
Martin Sleziak
44.7k10118272
asked Jun 6 '16 at 8:59
timtim
61
$endgroup$
add a comment |
$begingroup$
LINEAR ALGEBRA: I've looked online for this and can't find anything...
What is a deviation vector and how do I compute them? (specifically how did my teacher get those vectors in part b?)
Here is the problem I'm referring to:
[4 points] Suppose we have nonnzero deviation vectors $vec x,vec y$ of two characteristics, such that $vec x=cvec y$. Show carefully what this implies about the correlation coefficient $r$ between the two characteristics.
[6 points] Find the correlation coefficient between the daily profit and number of paintings inside three CA coffee shops.
$$begin{array}{|c|c|c|}
hline
text{Shop} & text{Profit (in 100s)} & text{Paintings} \hline
text{A} & -1 & 1 \hline
text{B} & -1 & 2 \hline
text{C} & 2 & 3 \hline
end{array}$$
Answer.
- We have that:
$$r=frac{vec xcdotvec y}{|vec x||vec y|}=frac{c(vec ycdotvec y)}{|c||vec y||vec y|}=frac{c}{|c|}=begin{cases} 1, & text{if }c>0, \ -1, & text{if }c<0. end{cases}$$
[6 points] We find deviation vectors $vec x=(-1,-1,2)^T$ and $vec y=(-1,0,1)^T$. This gives:
$$r=frac{vec xcdotvec y}{|vec x||vec y|}=frac{3}{sqrt6sqrt2}left(=frac{sqrt3}{2}right).$$
Question image
linear-algebra correlation
edited Jun 6 '16 at 14:00
Martin Sleziak
44.7k10118272
asked Jun 6 '16 at 8:59
timtim
61
$endgroup$
LINEAR ALGEBRA: I've looked online for this and can't find anything...
What is a deviation vector and how do I compute them? (specifically how did my teacher get those vectors in part b?)
Here is the problem I'm referring to:
[4 points] Suppose we have nonnzero deviation vectors $vec x,vec y$ of two characteristics, such that $vec x=cvec y$. Show carefully what this implies about the correlation coefficient $r$ between the two characteristics.
[6 points] Find the correlation coefficient between the daily profit and number of paintings inside three CA coffee shops.
$$begin{array}{|c|c|c|}
hline
text{Shop} & text{Profit (in 100s)} & text{Paintings} \hline
text{A} & -1 & 1 \hline
text{B} & -1 & 2 \hline
text{C} & 2 & 3 \hline
end{array}$$
Answer.
- We have that:
$$r=frac{vec xcdotvec y}{|vec x||vec y|}=frac{c(vec ycdotvec y)}{|c||vec y||vec y|}=frac{c}{|c|}=begin{cases} 1, & text{if }c>0, \ -1, & text{if }c<0. end{cases}$$
[6 points] We find deviation vectors $vec x=(-1,-1,2)^T$ and $vec y=(-1,0,1)^T$. This gives:
$$r=frac{vec xcdotvec y}{|vec x||vec y|}=frac{3}{sqrt6sqrt2}left(=frac{sqrt3}{2}right).$$
Question image
linear-algebra correlation
linear-algebra correlation
edited Jun 6 '16 at 14:00
Martin Sleziak
44.7k10118272
asked Jun 6 '16 at 8:59
timtim
61
edited Jun 6 '16 at 14:00
Martin Sleziak
44.7k10118272
asked Jun 6 '16 at 8:59
timtim
61
edited Jun 6 '16 at 14:00
Martin Sleziak
44.7k10118272
edited Jun 6 '16 at 14:00
Martin Sleziak
44.7k10118272
edited Jun 6 '16 at 14:00
Martin Sleziak
44.7k10118272
44.7k10118272
asked Jun 6 '16 at 8:59
timtim
61
asked Jun 6 '16 at 8:59
timtim
61
asked Jun 6 '16 at 8:59
timtim
61
61
add a comment |
add a comment |
1 Answer
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$begingroup$
Deviation typically means $X-E(X)$, where $E(X)$ is the expected value/mean.
Notice that in the first column you have values $-1$, $-1$ and $2$. Their average is $0$, so after subtracting the average you get $vec x=(-1,-1,2)$.
In the second column you have the values $1$, $2$ and $3$. The average of these values is $2$ after subtracting the average you get the values $1-2=-1$, $2-2=0$ and $3-2=1$. Your teacher written them into a single vector $vec y=(-1,0,1)$.
The formula $$r=frac{vec xcdotvec y}{|vec x||vec y|}$$
is then the formula for correlation coefficient. It is just written a bit differently. You can find this formula also in the Wikipedia article I linked above - in the section geometric interpretation. The example given there is very similar to this one. (Basically the only difference is that the Wikipedia article discusses uncentered and centered correlation coefficient.)
answered Jun 6 '16 at 14:05
Martin SleziakMartin Sleziak
44.7k10118272
$endgroup$
add a comment |
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1 Answer
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active
oldest
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1 Answer
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active
oldest
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$begingroup$
Deviation typically means $X-E(X)$, where $E(X)$ is the expected value/mean.
Notice that in the first column you have values $-1$, $-1$ and $2$. Their average is $0$, so after subtracting the average you get $vec x=(-1,-1,2)$.
In the second column you have the values $1$, $2$ and $3$. The average of these values is $2$ after subtracting the average you get the values $1-2=-1$, $2-2=0$ and $3-2=1$. Your teacher written them into a single vector $vec y=(-1,0,1)$.
The formula $$r=frac{vec xcdotvec y}{|vec x||vec y|}$$
is then the formula for correlation coefficient. It is just written a bit differently. You can find this formula also in the Wikipedia article I linked above - in the section geometric interpretation. The example given there is very similar to this one. (Basically the only difference is that the Wikipedia article discusses uncentered and centered correlation coefficient.)
answered Jun 6 '16 at 14:05
Martin SleziakMartin Sleziak
44.7k10118272
$endgroup$
add a comment |
$begingroup$
Deviation typically means $X-E(X)$, where $E(X)$ is the expected value/mean.
Notice that in the first column you have values $-1$, $-1$ and $2$. Their average is $0$, so after subtracting the average you get $vec x=(-1,-1,2)$.
In the second column you have the values $1$, $2$ and $3$. The average of these values is $2$ after subtracting the average you get the values $1-2=-1$, $2-2=0$ and $3-2=1$. Your teacher written them into a single vector $vec y=(-1,0,1)$.
The formula $$r=frac{vec xcdotvec y}{|vec x||vec y|}$$
is then the formula for correlation coefficient. It is just written a bit differently. You can find this formula also in the Wikipedia article I linked above - in the section geometric interpretation. The example given there is very similar to this one. (Basically the only difference is that the Wikipedia article discusses uncentered and centered correlation coefficient.)
answered Jun 6 '16 at 14:05
Martin SleziakMartin Sleziak
44.7k10118272
$endgroup$
add a comment |
$begingroup$
Deviation typically means $X-E(X)$, where $E(X)$ is the expected value/mean.
Notice that in the first column you have values $-1$, $-1$ and $2$. Their average is $0$, so after subtracting the average you get $vec x=(-1,-1,2)$.
In the second column you have the values $1$, $2$ and $3$. The average of these values is $2$ after subtracting the average you get the values $1-2=-1$, $2-2=0$ and $3-2=1$. Your teacher written them into a single vector $vec y=(-1,0,1)$.
The formula $$r=frac{vec xcdotvec y}{|vec x||vec y|}$$
is then the formula for correlation coefficient. It is just written a bit differently. You can find this formula also in the Wikipedia article I linked above - in the section geometric interpretation. The example given there is very similar to this one. (Basically the only difference is that the Wikipedia article discusses uncentered and centered correlation coefficient.)
answered Jun 6 '16 at 14:05
Martin SleziakMartin Sleziak
44.7k10118272
$endgroup$
Deviation typically means $X-E(X)$, where $E(X)$ is the expected value/mean.
Notice that in the first column you have values $-1$, $-1$ and $2$. Their average is $0$, so after subtracting the average you get $vec x=(-1,-1,2)$.
In the second column you have the values $1$, $2$ and $3$. The average of these values is $2$ after subtracting the average you get the values $1-2=-1$, $2-2=0$ and $3-2=1$. Your teacher written them into a single vector $vec y=(-1,0,1)$.
The formula $$r=frac{vec xcdotvec y}{|vec x||vec y|}$$
is then the formula for correlation coefficient. It is just written a bit differently. You can find this formula also in the Wikipedia article I linked above - in the section geometric interpretation. The example given there is very similar to this one. (Basically the only difference is that the Wikipedia article discusses uncentered and centered correlation coefficient.)
answered Jun 6 '16 at 14:05
Martin SleziakMartin Sleziak
44.7k10118272
edited Jun 6 '16 at 14:10
answered Jun 6 '16 at 14:05
Martin SleziakMartin Sleziak
44.7k10118272
answered Jun 6 '16 at 14:05
Martin SleziakMartin Sleziak
44.7k10118272
answered Jun 6 '16 at 14:05
Martin SleziakMartin Sleziak
44.7k10118272
44.7k10118272
add a comment |
add a comment |
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