# Linear Correlation and Modeling

## Key Questions

• The possible values of the correlation coefficient are, $- 1 \le r \le 1$.

An $r$ value near $1$ indicates a positive correlation.
An $r$ value near $- 1$ indicates a negative correlation.
An $r$ value near $0$ indicates no correlation.

See explanation. I would suggest that you look it up in a book. Dictionary of mathematics perhaps.

#### Explanation:

$\textcolor{b l u e}{\text{Finding the coefficient}}$

This is one of those questions that is rather like: "how long is a piece of string".

It all depends on the structure of the relationship which has many variations. So it is hard to give a definitive answer.

Linea points to a fixed value coefficient.

By example:

Let the independent variable be $x$
Let the dependant variable be $y$
Let the correlation coefficient be $k$

Then we have the general form of;

$y = k x$

To find the value of $k$ divide both sides by $x$ giving:

$k = \frac{y}{x}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Interpreting the coefficient}}$

Again this is dependant on context. Basically it fixes the major relationship between the dependant and independent variables.

It could be described as a conversion factor