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Covariance
A tool used to determine the relationship between 2 random variables.
Scatter plot
A graph used to determine whether a linear correlation exists between two variables.
High positive covariance
Occurs when paired x and y values both tend to be above or below their means at the same time.
High negative covariance
Occurs when paired x and y values tend to be on opposite sides of their respective means.
Zero covariance
Indicates no systematic tendencies of any sort between paired x and y values.
Pearson’s correlation coefficient
A measure of the strength and direction of a linear relationship between two variables, ranging from -1 to 1.
Caveats of correlation
Correlations only work with interval or ratio data and demonstrate linear relationships; correlation doesn’t imply causation.
Regression
Quantifies the relationship between variables, where causation is implied, with independent and dependent variables.
Least squares regression
A mathematical procedure for finding the best-fitting curve to a given set of points.
Residual
The difference between the observed and predicted values for y.
R2
A statistical measure of how close the data are to the fitted regression line.
0% R2
Indicates that the model explains none of the variability of the response data around its mean.
100% R2
Indicates that the model explains all the variability of the response data.
Assumptions of regression
Dependent variable should be normally distributed; predictors shouldn’t be strongly correlated; observations should be independent; 10 observations per independent variable.
Difference between correlation and regression
Regression attempts to establish causality and produces an entire equation, while correlation is a single statistic.
Spatial regression
Attempts to account for variation across a landscape with one equation.
Geographically weighted regression
Allows coefficients to vary between areas across a landscape.
