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Chapter 14 Correlation and Regression - Coggle Diagram
Chapter 14 Correlation and Regression
Correlation
Correlation is a statistical technique that is used to measure and describe the relationship between two variables.
Characteristics of a Relationship
Direction:
positive--both variables increase or decrease
negative--one variable increases while the other decreases
Form: tends to be linear with clustering around a straight line
Strength/consistency: a perfect correlation is identified by 1.00 or -1.00
The sign (+ or -) and the strength of a correlation are independent.
Alternatives to the Pearson Correlation
The Spearman Correlation
used with data from an ordinal scale (ranks) and when the original raw scores are on an interval or ratio scale
also measures the degree of monotonic relationship between variables (sequence that is consistently increasing or decreasing)
The Point-Biserial Correlation
used to measure the relationship between two variables in situations in which one variable consists of regular, numerical scores, but the second variable only has two values.
the dichotomous variable is first converted to numerical values by assigning a 0 to one category and 1 to the other then the Pearson correlation formula is performed with the new data
The Phi-Coefficient
both variables are dichotomous
0 and 1 is assigned to each set of variables and then the regular Pearson formula is used with the converted scores
The Pearson Correlation
measures the degree and direction of the linear relationship between two variables
r = covariability of X & Y / variability of X & Y separately
r is for sample while rho is for population
The sum of products of deviations (SP) is used to measure the amount of covariability between two variances.
definitional formula
computational formula
The Pearson Correlation and z-scores
For a sample
For a population
The value r^2 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.
Regression
Y = bX + a
the statistical technique for finding the best-fitting straight line
the best-fitting line is also known as the least-squared error solution
df = n - 2
The 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.
