### Coefficient of Correlation

• Calculate the value of correlation coefficient and interpret it.

### Solved Example:

#### 10-2-01

In simple linear regression problem, r and b,

Solution:
In simple linear regression problem, the equation of the best-fit straight line is: $y = a + bx$
Here, b represents the slope of the straight line, which can have positive or negative value. If the slope is positive, the line will be 'uphill' and also the coefficient of correlation will be positive. The same is true is b is negative, at that time r will be negative. Hence, they must have same signs.

### Solved Example:

#### 10-2-02

If the correlation coefficient r = 1, then

### Solved Example:

#### 10-2-03

The strength of the linear relationship between two numerical variables may be assumed by the:

Solution:
The coefficient of correlation gives the strength of the linear relationship between two numerical variables.

### Solved Example:

#### 10-2-04

A regression model is used to express a variable Y as a function of another variable X.This implies that:

Solution:
If the scatter diagram indicates some relationship between two variables X and Y, then the dots of the scatter diagram will be concentrated round a curve. This curve is called the curve of regression. Regression analysis is used for estimating the unknown values of one variable corresponding to the known value of another variable.

### Solved Example:

#### 10-2-05

Calculate Pearson's coefficient for the following data: Solution: $\bar{x}$ = 4, $\bar{y}$ = 6

$\Sigma$ (x-$\bar{x}$)(y-$\bar{y}$)= 19,
$\Sigma$ (x-$\bar{x})^2$ = 14,
$\Sigma$ (y-$\bar{y})^2$ = 26

Let $\hat{X}$ = (x-$\bar{x})^2$ and $\hat{Y}$ = (y-$\bar{y})^2$

$r = \dfrac{19}{\sqrt{14} \sqrt{26}} = 0.9959$