Scatter Diagram and Correlation

Scatter Diagram or Scatter Plot

A first step in finding whether or nor a relationship between two variables exists, is to plot each pair of independence observation {(Xi,Yi), i=1,2,3,...n} as a point on graph  paper, using the X-axis for the regression variable. Such a diagram is called scatter diagram or a scatter plot. If a relationship between a variable exists, then the points in scatter diagram will show a tendency to cluster around straight line or some curve. Such a line or curve or curve around which the points cluster, is called regression line or regression curve which can be used to estimate the expected value of the random variable Y from the values of the random variable X.
Another Definition of Scatter plot

"A scatter diagram is a graph that shows the relationship between two variables. Scatter diagrams can demonstrate a relationship between any element of a process, environment, or activity on one axis and a quality defect on the other axis." 

The scatter diagram shown below reveal that the relationship between two variables in

• (a)  is positive and linear
• (b) is negative and linear
• (c) is Negative Non-Linear
• (d) there is no relationship

Correlation 

Correlation, Like co-variance, is a measure of the degree to which any variables vary together. In other words, two variables are said to be correlated if they tend to simultaneously vary in some direction. If both variable tend to increase (or decrease) together, the correlation is said to be direct or positive, for example the length of an iron bar will increase as the temperature increases. If one variable tends to increase as the other variable decreases, the correlation is said to be negative or inverse,  for example the volume of gas will decrease as the pressure increases.

Types of Scatter Diagram Based on the Type of Correlation 

According to the type of correlation, scatter can be divided into following categories

1. Scatter diagram with no correlation 
2. Scatter diagram with moderate correlation 
3. Scatter diagram with strong correlation

Scatter Diagram with no Correlation

This type of diagram is also called "Scatter diagram with zero degree of correlation."

In this type of scatter, data points are speared so randomly that you cannot draw any line through them. In this case you case that their is no relationship between these two variables.

Scatter Diagram with Moderate Correlation

This type of diagram is also called "Scatter Diagram with low degree of correlation."

In this type of Scatter, data points are little close together and you can feel that some kind of relationship exits between these variables.

Scatter Diagram with Strong Correlation

This type of diagram is also called " Scatter diagram with high degree of Correlation."

In this type of scatter data points are grouped very close to each other such that you can draw a line a line through them.