3.Spatial Regression

Question 1

assumptions of linear regression: 5

Answer 1

• the relationship between the independent and dependent variables is linear, and
the equation of a straight line faithfully represents the relationship
• the observations are independent
• the variability of the observations around the line of best fit is constant
• the residuals are normally distributed
• there is no multicollinearity amongst independent variables

Question 2

Residuals?

Answer 2

• if we are working with spatial data, we can map
the residuals to identify where the regression
model overestimates or underestimates the
value of the dependent variable
• since spatial data usually display some form of
spatial autocorrelation, we might find that the
residuals cluster in groups – areas of
overestimation are spatially grouped, as are
areas of underestimation
• this is a sure sign of spatial dependence amongst
the observations and a violation of the
assumptions of linear regression

Question 3

global statistics

Answer 3

identify and measure the pattern of the entire study area
• ordinary least squares regression is a global statistical approach since it considers
all of the data available and produces a single set of coefficients that minimize
the error across the entire dataset

Question 4

local statistics

Answer 4

identify variation across the study area, focusing on individual features
and their relationship to nearby features
• some statistical approaches look at an individual point and create statistics or
coefficients that relate only to that point (eg, hot spot analysis)
• in order to complete these analyses, every point in the dataset must be treated
separately, then those separate results can be brought together to illustrate the
patterns

Question 5

regression coeffecients

Answer 5

egression coefficeints are averages over the entire dataset

Question 6

nuisance:

Substantive:

Answer 6

involves model residuals only – when this exists it reduces the model
efficiency and can be corrected by including a spatial error specification in the
model

where values of Y are systematically related to values of Y in
adjacent areas, generating model bias; this can be corrected by including an
explicit spatial lag term as an explanatory variable in the model

Question 7

Expansion model is a _____ approach

Answer 7

global-it considers all of the observation at once

Question 8

A local approach which does the same as the Expansion model is the…

Answer 8

geographically weighted regression

Question 9

A local approach which does the same as the Expansion model is the…

Answer 9

geographically weighted regression
• an alternative, local approach is to use
geographically weighted regression, where individual
observations are influenced more by nearby
observations and less by far away observations
• this approach needs to consider the connection
between points i and j, in terms of their connectivity
or distance of influence