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Correlation and Regresion - Coggle Diagram
Correlation and Regresion
Correlation
A statistical technique that is used to measure and describe the relationship between two variables.
Scatter Plot
A data visualization tool used to identify relationships, trends, or correlations between two numerical variables by plotting paired data points on an
xy-axis. They are created by placing the independent variable on the x-axis and the dependent variable on the y-axis, highlighting correlations, patterns, and outliers.
Positive Correlation
When 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.
Negative Correlation
When two variables tend to go in opposite directions. As the X variable increases, the Y variable decreases. That is, it is an inverse relationship.
Perfect Correlation
always is identified by a correlation of 1.00 and indicates a perfectly consistent relationship. For a correlation of 1.00 (or −1.00), each change in X is accompanied by a perfectly predictable change in Y.
Envelope
A line where it encloses the data, often helps you to see the overall trend in the data.
Pearson Correlation
Measures the degree and the direction of the linear relationship between two variables
Linear Relationship
which measures the degree of how well the data points fit a straight line.
Sum of Products
This new value is similar to SS (the sum of squared deviations), which is used to measure variability for a single variable. Now, we use SP to measure the amount of covariability between two variables. The value for SP can be calculated with either a definitional formula or a computational formula.
Defintional Formula
Computational Formula
Outliers
One or two extreme data points, can have a dramatic effect on the value of a correlation
Restricted Range
occurs when a sample’s data covers only a limited, narrow portion of the total possible scores, failing to represent the full population variability
Coeffcient of Determination
The value r2 measures the proportion of variability in one variable that can be determined from the relationship with the other variable. A correlation of (or −0.80), for example, means that (or 64%) of the variability in the Y scores can be predicted from the relationship with X.
Correlation Matrix
A table that reports the results of multiple correlations
Spearman Correlation
The result when the pearson correlation formula is used with data from an ordinal scale
Monotonic
The relationship when there is a consistently one-directional relationship between two variables
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Linear Equation
algebraic equations where variables have a highest power of one, forming a straight line when graphed.
y=bx+a
Slope
The value of b
Y-Intercept
The value of a
Regression
The statistical technique for finding the best-fitting straight line for a set of data
Regression Line
The resulting straight line
Least-Squared-Error Solution
a mathematical approach to finding the "best-fit" line or curve for a dataset by minimizing the sum of the squares of the vertical differences (residuals) between observed data points and the fitted model
Regression Equation for Y
Standardized Form of the Regression Equation
Standard Error of Estimate
a measure of the standard distance between the predicted Y values on the regression line and the actual Y values in the data.
Predicted Variability
Unpredicted Variability
Analysis of Regression
The process of testing the significance of a regression equation
