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Correlation and Regression - Coggle Diagram
Correlation and Regression
The Characteristics of a Relationship
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 Form of the Relationship
The Strength or Consistency of the Relationship
a perfect correlation is identified by a correlation of 1.00 and indicates a perfectly consistent relationship
In a positive correlation, the two variables tend to change in the same direction
In a negative correlation, the two variables tend to go in opposite directions
The Pearson Correlation
What is it?
measures the degree and direction of the linear relationship between two variables
Sum of Products of Deviations
Definitional Formula:
Find the deviation and the Y deviation for each individual
Find the product of the deviations for each individual
Add the products
Computational Formula
Calculation of the Pearson Correlation
The Pearson Correlation and z-Scores
Using and Interpreting the Pearson Correlation
Where any why are correlations used?
Prediction
Validity
Reliability
Theory verification
When interpretating correlations there are 4 considerations to keep in mind:
Correlation simply describes a relationship between two variables
The value of correlation can be affected greatly by the range of scores represented in the data
One or more extreme data points (outliers) can have dramatic effects on the value of correlation
A correlation should not be interpreted as a proportion
Correlation and Causation
Correlation does not establish causation
Correlation and Strength of Relationship
A correlation measures the degree of relationship between two variables on a scale from 0 to 1.00
Hypothesis Tests with the Pearson Correlation
Alternatives to the Pearson Correlation
Spearman Correlation
Is used to measure the relationship between X and Y when both variables are measured on ordinal scales
Is used as a valuable alternative to the Pearson correlation
Ranking Tied Scores
List the scores in order from smallest to largest including the tied values
Assign a rank (first, second, and so on) to each position in the ordered list
When two (or more) scores are tied, compute the mean of their ranked positions, and assign this mean value as the final rank for each scores
Special Formula
