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Correlation and Regression - Coggle Diagram
Correlation and Regression
Correlation- a statistical technique that is used to measure and describe the relationship between two variables
describes and measures 3 characteristics of the relationship between X and Y
1- Direction of the Relationship- positive or negative
positive correlation- 2 variables tend to change in the same direction
negative correlation- 2 variables tend to to in opposite directions
2- Form of the relationship
3- Strength of consistency of the Relationship
perfect correlation- correlation of 1.00 and indicates a perfectly consistent relationship
Pearson correlation- measures the degree and the direction of the linear relationship between two variables
linear relationship- how well the data points fit a straight line
Sum of products of deviations
to measure the amount of covariability between two variables
can be calculatied with either a definitional formula or a computational formula
Where and why correlations are used
1- Prediction- if 2 variables are known to be related in some systematic way it's possible to use one of the variables to make accurate predictions about the other
2- Validity- use a correlation
3- Reliability- when it produces stable, consistent measurements
4- Theory verification- prediction of the theory could be tested by determining the correlation between the two variables
Interpreting correlations
1- simply describes a relationship between 2 variables, does not explain why they are related
2- the value can be affected greatly by the range of scores
3- outliers can have a dramatic effect on the value of a correlation
4- correlation should not be interpreted as a proportion
Hypothesis- whether a correlation exists in the population
degrees of freedom for the t Statistics
The Spearman Correlation- when the Pearson correlation formula is used with data from an ordinal scale
1- measure the relationship between X and Y when both variables are measured on ordinal scales
2- valuable alternative to the Pearson correlation, to measure the degree to which a relationship is consistently one directional, independent of its form
Ranking Tied Scores
1- list the scores in order from smallest to largest, include tied values
2- assign a rank to each position
3- 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 score
Point-Biserial Correlation
used to measure the relationship between 2 variables in situations in which one variable consists of regular, numerical scores, but the second variable has only 2 values
dichotomous variable- only two values
The Phi-Coefficient- when both variables (X and Y) measured for each individual are dichotomous
1- convert each variable to numerical values (0 and 1)
2- use the regular Pearson formula with the converted scores
Regression- statistical technique for finding the best fitting straight line for a set of data
Least-Squares Solution- best fitting line that has the smallest total squared error
Regression equation for Y- formulas determine the linear equation that provides the best prediction of Y values
Standardized Form of the Regression Equation- transforming X and Y values into z-scores before finding the regression equation
Standard error of estimate- gives a measure of the standard distance between the predicted Y values on the regression line and the actual Y values in the data
provides a measure of standard distance
analysis of regression- process of testing the significance of a regression equation