# Chapter 9 GWR and spatially lagged regression

## 9.1 Learning objectives

By the end of this practical you should be able to:

1. Explain hypothesis testing
2. Execute regression in R
3. Descrbie the assumptions associated with regression models
4. Explain steps to deal with spatially autocorrelated (spatial similarlity of nearby observations) residuals.

## 9.2 Homework

Outside of our schedulded sessions you should be doing around 12 hours of extra study per week. Feel free to follow your own GIS interests, but good places to start include the following:

Assignment

From weeks 6-9, learn and practice analysis from the course and identify appropriate techniques (from wider research) that might be applicable/relevant to your data. Conduct an extensive methodological review – this could include analysis from within academic literature and/or government departments (or any reputable source).

Remember this is just a starting point, explore the reading list, practical and lecture for more ideas.

## 9.4 Introduction

In this practical you will be introduced to a suite of different models that will allow you to test a variety of research questions and hypotheses through modelling the associations between two or more spatially reference variables.

In the worked example, we will explore the factors that might affect the average exam scores of 16 year-old across London. GSCEs are the exams taken at the end of secondary education and here have been aggregated for all pupils at their home addresses across the City for Ward geographies.

The London Data Store collates a range of other variables for each Ward and so we will see if any of these are able to help explain the patterns of exam performance that we see.

This practical will walk you through the common steps that you should go through when building a regression model using spatial data to test a stated research hypothsis; from carrying out some descriptive visualisation and summary statistics, to interpreting the results and using the outputs of the model to inform your next steps.

### 9.4.1 Setting up your Data

First, let’s set up R and read in some data to enable us to carry out our analysis.

``````#library a bunch of packages we may (or may not) use - install them first if not installed already.
library(tidyverse)
library(tmap)
library(geojsonio)
library(plotly)
library(rgdal)
library(broom)
library(mapview)
library(crosstalk)
library(sf)
library(sp)
library(spdep)
library(car)
library(fs)
library(janitor)``````

``````#download a zip file containing some boundaries we want to use

destfile="prac9_data/statistical-gis-boundaries-london.zip")``````

Get the zip file and extract it

``````listfiles<-dir_info(here::here("prac9_data")) %>%
dplyr::filter(str_detect(path, ".zip")) %>%
dplyr::select(path)%>%
pull()%>%
#print out the .gz file
print()%>%
as.character()%>%
utils::unzip(exdir=here::here("prac9_data"))``````

Look inside the zip and read in the `.shp`

``````#look what is inside the zip

Londonwards<-dir_info(here::here("prac9_data",
"statistical-gis-boundaries-london",
"ESRI"))%>%
#\$ means exact match
dplyr::filter(str_detect(path,
"London_Ward_CityMerged.shp\$"))%>%
dplyr::select(path)%>%
pull()%>%
``````## Reading layer `London_Ward_CityMerged' from data source `C:\Users\Andy\OneDrive - University College London\Teaching\CASA0005\2020_2021\CASA0005repo\prac9_data\statistical-gis-boundaries-london\ESRI\London_Ward_CityMerged.shp' using driver `ESRI Shapefile'
``````#check the data