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