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Chapter 9: Introduction to the T-Statistic, Chapter 15: Correlation -…
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Chapter 15: Correlation
Correlation is a statistical technique that is used to measure and describe the relationship between two variables.
A correlation is a numerical value that describes and measures three characteristics of the relationship between X and Y.
The Direction of the Relationship The sign of the correlation, positive or negative, describes the direction of the relationship.
negative correlation, the two variables tend to go in opposite directions. As the X variable increases, the Y variable decreases. That is, it is an inverse relationship.
a positive correlation, the two variables tend to change in the same direction: as the value of the X variable increases from one individual to another, the Y variable also tends to increase; when the X variable decreases, the Y variable also decreases.
The Form of the Relationship the relationships tend to have a linear form; that is, the points in the scatter plot tend to cluster around a straight line.
The Strength or Consistency of the Relationship Finally, the correlation measures the consistency of the relationship
The consistency of the relationship is measured by the numerical value of the correlation. 
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perfect correlation
A relationship where the actual data points perfectly fit the specific form being measured. For a Pearson correlation, the data points fit perfectly on a straight line.
perfect linear relationship, every change in the X variable is accompanied by a corresponding change in the Y variable
when there is no linear relationship, a change in the X variable does not correspond to any predictable change in the Y variable
no covariability, correlation is zero
The Pearson correlation measures the degree and the direction of the linear relationship between two variables.
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the sum of products
A measure of the degree of covariability between two variables; the degree to which they vary together.
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partial correlation
association measures the relationship between two variables while controlling the influence of a third variable
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phi-coefficient
correlation between two variables, both of which are dichotomous
Correlation is used to determine predicatability, validity, and prediction