GIS Quiz 3 (copy)

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.