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Correlation and Regression - Coggle Diagram
Correlation and Regression
Correlation
is a statistical technique that is used to measure and describe the relationship between two variables.
Usually the two variables in a correlational study are simply observed as they exist naturally in the environment—there is no attempt to control or manipulate the variables
positive correlation
the two variables tend to change in the same direction
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.
The Direction of the Relationship
the sign of the correlation, positive or negative, describes the direction of the relationship.
Pearson correlation
measures the degree and the direction of the linear relationship between two variables.
the most common correlation
The calculation of the Pearson correlation requires one new concept: the sum of products of deviations, or SP.
definitional formula for the sum of products is
The computational formula for the sum of products of deviations is
Where and Why Correlations Are Used
Prediction
Validity
Reliability
Theory Verification.
Interpreting Correlations
Correlation simply describes a relationship between two variables.
The value of a correlation can be affected greatly by the range of scores represented in the data.
One or two extreme data points, often called outliers , can have a dramatic effect on the value of a correlation.
When judging how “good” a relationship is, it is tempting to focus on the numerical value of the correlation
Correlation and Causation
One of the most common errors in interpreting correlations is to assume that a correlation necessarily implies a cause-and-effect relationship between the two variables.
The squared correlation measures the proportion of variability in the data that is explained by the relationship between X and Y. It is sometimes called the coefficient of determination .
An outlier is an individual with X and/or Y values that are substantially different (larger or smaller) from the values obtained for the other individuals in the data set.
Correlation and Restricted Range
Whenever a correlation is computed from scores that do not represent the full range of possible values, you should be cautious in interpreting the correlation.
Correlation and the Strength of the Relationship
A correlation measures the degree of relationship between two variables on a scale from 0 to 1.00. Although this number provides a measure of the degree of relationship, the squared correlation provides a better measure of the strength of the relationship
The value is called the coefficient of determination because it measures the proportion of variability in one variable that can be determined from the relationship with the other variable.
