# Stats

• May 10th 2006, 02:12 PM
Natasha1
Stats

The ages and salaries (in thousands of $) of 10 employees in a firm are given below. Age - Salary 28 - 17 31 - 22 31 - 28 35 - 20 40 - 26 44 - 30 45 - 32 48 - 18 53 - 33 67 - 42 What is the correlation coefficient between age and salary? (Giving enough detail to understand the proceedings) Comment on its value (referring maybe back to the data, to note any individuals who figures make a particular contribution to the value of the coefficient) • May 10th 2006, 02:21 PM ThePerfectHacker Quote: Originally Posted by Natasha1 Could someone please help me with the following question. The ages and salaries (in thousands of$) of 10 employees in a firm are given below.

Age - Salary
28 - 17
31 - 22
31 - 28
35 - 20
40 - 26
44 - 30
45 - 32
48 - 18
53 - 33
67 - 42

What is the correlation coefficient between age and salary? (Giving enough detail to understand the proceedings)

Comment on its value (referring maybe back to the data, to note any individuals who figures make a particular contribution to the value of the coefficient)

I think it is,
$r=.761$
• May 10th 2006, 11:35 PM
CaptainBlack
Quote:

Originally Posted by Natasha1

The ages and salaries (in thousands of \$) of 10 employees in a firm are given below.

Age - Salary
28 - 17
31 - 22
31 - 28
35 - 20
40 - 26
44 - 30
45 - 32
48 - 18
53 - 33
67 - 42

What is the correlation coefficient between age and salary? (Giving enough detail to understand the proceedings)

Comment on its value (referring maybe back to the data, to note any individuals who figures make a particular contribution to the value of the coefficient)

There are a number of ways of expressing this but the one I usually use
is:

$
R=\frac{\sum_{i=1}^N (x_i-\bar x)(y_i-\bar y)}
{\sum_{i=1}^N \sqrt{(x_i-\bar x)^2}
\sum_{i=1}^N \sqrt{(y_i-\bar y)^2}}
$

Attached are figures from an Excel spread sheet evaluating this.

RonL
• May 11th 2006, 05:00 AM
Natasha1
Thanks RoL.

What does R = 0.76404 actually mean? (referring back to the last question)
• May 11th 2006, 06:04 AM
CaptainBlack
Quote:

Originally Posted by Natasha1
Thanks RoL.

What does R = 0.76404 actually mean? (referring back to the last question)

$R$ is the cosine of the angle between the $N$-vectors $[x_1,..,x_N]$ and $[y_1,..,y_N]$.

If the points fall on a line of positive slope $R=1$ of negative
slope $R=-1$. It is a measure of how well the regression line
fits the data.

RonL
• May 11th 2006, 07:10 AM
Natasha1
Quote:

Originally Posted by CaptainBlack

$R$ is the cosine of the angle between the $N$-vectors $[x_1,..,x_N]$ and $[y_1,..,y_N]$.

If the points fall on a line of positive slope $R=1$ of negative
slope $R=-1$. It is a measure of how well the regression line
fits the data.

RonL

Mmm not sure I get that. So how does this answer the last part of the question?

Comment on its value...
• May 11th 2006, 08:02 AM
CaptainBlack
Quote:

Originally Posted by Natasha1
Mmm not sure I get that. So how does this answer the last part of the question?

Comment on its value...

The value of R indicates a strong positive correlation between age and salary.

The (48,18) point is clearly far from the line and is reducing the value of R
that would be obtained with the remaining data.

Of the other points the first and last contribute the most to the correlation
coefficient (look at column F of the table)

RonL
• May 11th 2006, 08:07 AM
Natasha1
thanks Ron