# What does the correlation coefficient tell us

**Scatterplot**. The scatterplot has the X variable (GPA) on the horizontal (X) axis, and the Y variable (MathSAT) on the vertical (Y) axis. Each individual is identified by a single point (dot) on the graph which is located so that the coordinates of the point (the X and Y values) match the individual's X (GPA) and Y (MathSAT) scores.

For example, the student named "Obs5" (in the sixth row of the datasheet) has GPA=2.30 and MathSAT=710. This student is represented in the scatterplot by high-lighted and labled ("5") dot in the upper-left part of the scatterplot. Note that is to the right of MathSAT of 710 and above GPA of 2.30.

**Pearson Correlation** :The Pearson correlation (explained below) between these two variables is .32.

**Correlations and Scatterplots** :

Correlations can tell us about the **direction**. and the **degree (strength)** of the relationship between two variables. Scatterplots can also tell us about the **form (shape)** of the relationship.

**The Direction of a Relationship**The correlation measure tells us about the direction of the relationship between the two variables. The direction can be**positive**or**negative**.**Positive**. In a positive relationship both variables tend to move in the same direction: If one variable increases, the other tends to also increase. If one decreases, the other tends to also.In the example above, GPA and MathSAT are positively related.

As GPA (or MathSAT) increases, the other variable also tends to increase.

**Negative**. In a negative relationship the variables tend to move in the opposite directions: If one variable increases, the other tends to decrease, and vice-versa.

The direction of the relationship between two variables is identified by the sign of the correlation coefficient for the variables. Postive relationships have a "plus" sign, whereas negative relationships have a "minus" sign.

**The Degree (Strength) of a Relationship**A correlation coefficient measures the

**degree (strength)**of the relationship between two variables. The Pearson Correlation Coefficient measures the strength of the

**linear**relationship between two variables. Two specific strengths are:

**Perfect Relationship**. When two variables are exactly (linearly) related the correlation coefficient is either +1.00 or -1.00. They are said to be perfectly linearly related, either positively or negatively.

**No relationship**. When two variables have no relationship at all, their correlation is 0.00.

There are strengths in between -1.00, 0.00 and +1.00. Note, though. that +1.00 is the largest postive correlation and -1.00 is the largest negative correlation that is possible.

**Examples:** Here are three examples. These examples concern variables measuring characteristics of automobiles. The variables are their weight, miles-per-gallon, horsepower and drive ratio (number of revolutions of the engine per revolution of the wheels).

Source: forrest.psych.unc.edu

Category: Forex