# Two Variable Statistics

### Functional Relationship

Two variables x and y are functionally related when the value of the second variable can be calculated when the value of the first is known.

#### Example

If a stone is dropped, the formula that allows us to accurately calculate the height if it is a function of elapsed time is:

h = ½ g t².

### Statistical Relationship

Two variables x and y are related statistically when the value of the second variable can be approximately estimated when the first is known.

#### Examples

Income and expenses for a family.

Production and sales for a factory.

Advertising expenses and profits for a corporate enterprise.

If each pair of values is represented as the coordinates of a point, the set of all points on a graph is called a scatter plot or a scatter diagram.

A line can be drawn on a scatter plot which best represents the trend of the points. This line is called a regression line.

#### Examples

The scores of 12 students in their Mathematics and Physics classes are:

Mathematics | 2 | 3 | 4 | 4 | 5 | 6 | 6 | 7 | 7 | 8 | 10 | 10 |

Physics | 1 | 3 | 2 | 4 | 4 | 4 | 6 | 4 | 6 | 7 | 9 | 10 |