date()
## [1] "Tue Nov 20 13:24:54 2012"
Due Date: November 29, 2012
Total Points: 50
The file Georgia.zip contains ESRI shape files in a folder called GeorgiaEduc. The dbf contains the percentage of Georgia county residents with a bachelors degree along with other countywide information. Let the dependent variable be PctBach (percent of population with a bachelor's degree) and the explanatory variables be TotPop90, PctRural, PctEld, PctFB, PctPov, PctBlack.
a. Download the zip file, unzip it and use the readShapeSpatial() function from the maptools package to get the data into R. Hint: After unzipping the shape files are in the directory Georgia. (10)
require(maptools)
## Loading required package: maptools
## Loading required package: foreign
## Loading required package: sp
## Loading required package: lattice
## Checking rgeos availability: FALSE Note: when rgeos is not available,
## polygon geometry computations in maptools depend on gpclib, which has a
## restricted licence. It is disabled by default; to enable gpclib, type
## gpclibPermit()
tmp = download.file("http://myweb.fsu.edu/jelsner/Georgia.zip", "Georgia.zip",
mode = "wb")
unzip("Georgia.zip")
GA = readShapeSpatial("Georgia/GeorgiaEduc")
b. Start with a multiple regression model using all six explanatory variables listed above. Create a final model by removing variables that are not significant in explaining percentage of bachelor degrees. (10)
bachmodel = lm(PctBach ~ TotPop90 + PctRural + PctEld + PctFB + PctPov + PctBlack,
data = GA)
bachmodel
##
## Call:
## lm(formula = PctBach ~ TotPop90 + PctRural + PctEld + PctFB +
## PctPov + PctBlack, data = GA)
##
## Coefficients:
## (Intercept) TotPop90 PctRural PctEld PctFB
## 1.50e+01 2.33e-05 -4.27e-02 -7.88e-02 1.25e+00
## PctPov PctBlack
## -1.55e-01 2.08e-02
##
step(bachmodel)
## Start: AIC=427.2
## PctBach ~ TotPop90 + PctRural + PctEld + PctFB + PctPov + PctBlack
##
## Df Sum of Sq RSS AIC
## - PctEld 1 5.3 1876 426
## - PctBlack 1 8.6 1879 426
## <none> 1870 427
## - PctPov 1 61.7 1932 431
## - PctRural 1 120.5 1991 436
## - PctFB 1 195.9 2066 443
## - TotPop90 1 292.4 2163 450
##
## Step: AIC=425.7
## PctBach ~ TotPop90 + PctRural + PctFB + PctPov + PctBlack
##
## Df Sum of Sq RSS AIC
## - PctBlack 1 10.9 1886 425
## <none> 1876 426
## - PctPov 1 100.1 1976 433
## - PctRural 1 137.1 2013 436
## - PctFB 1 228.9 2104 444
## - TotPop90 1 287.2 2163 448
##
## Step: AIC=424.7
## PctBach ~ TotPop90 + PctRural + PctFB + PctPov
##
## Df Sum of Sq RSS AIC
## <none> 1886 425
## - PctPov 1 137 2024 435
## - PctRural 1 152 2038 436
## - PctFB 1 228 2114 443
## - TotPop90 1 320 2206 450
##
## Call:
## lm(formula = PctBach ~ TotPop90 + PctRural + PctFB + PctPov,
## data = GA)
##
## Coefficients:
## (Intercept) TotPop90 PctRural PctFB PctPov
## 1.44e+01 2.37e-05 -4.64e-02 1.30e+00 -1.31e-01
##
finalbachmodel = lm(formula = PctBach ~ TotPop90 + PctRural + PctFB + PctPov,
data = GA)
finalbachmodel
##
## Call:
## lm(formula = PctBach ~ TotPop90 + PctRural + PctFB + PctPov,
## data = GA)
##
## Coefficients:
## (Intercept) TotPop90 PctRural PctFB PctPov
## 1.44e+01 2.37e-05 -4.64e-02 1.30e+00 -1.31e-01
##
c. Use the significant explanatory variables and create a geographic regression model using a fixed bandwidth. Plot a choropleth map of the predictions from the model. (10)
suppressMessages(require(spgwr))
bachmodel.bw = gwr.sel(PctBach ~ TotPop90 + PctRural + PctFB + PctPov, data = GA)
## Bandwidth: 241605 CV score: 2012
## Bandwidth: 390534 CV score: 2052
## Bandwidth: 149561 CV score: 1995
## Bandwidth: 92675 CV score: 2100
## Bandwidth: 184719 CV score: 1993
## Bandwidth: 173020 CV score: 1991
## Bandwidth: 170165 CV score: 1991
## Bandwidth: 167827 CV score: 1991
## Bandwidth: 168455 CV score: 1991
## Bandwidth: 168480 CV score: 1991
## Bandwidth: 168474 CV score: 1991
## Bandwidth: 168474 CV score: 1991
## Bandwidth: 168474 CV score: 1991
## Bandwidth: 168476 CV score: 1991
## Bandwidth: 168475 CV score: 1991
## Bandwidth: 168474 CV score: 1991
## Bandwidth: 168474 CV score: 1991
## Bandwidth: 168474 CV score: 1991
## Bandwidth: 168474 CV score: 1991
## Bandwidth: 168474 CV score: 1991
## Bandwidth: 168474 CV score: 1991
bach.gwr = gwr(PctBach ~ TotPop90 + PctRural + PctFB + PctPov, data = GA, bandwidth = bachmodel.bw)
bach.gwr
## Call:
## gwr(formula = PctBach ~ TotPop90 + PctRural + PctFB + PctPov,
## data = GA, bandwidth = bachmodel.bw)
## Kernel function: gwr.Gauss
## Fixed bandwidth: 168474
## Summary of GWR coefficient estimates:
## Min. 1st Qu. Median 3rd Qu. Max. Global
## X.Intercept. 1.12e+01 1.33e+01 1.45e+01 1.52e+01 1.58e+01 14.39
## TotPop90 1.35e-05 1.83e-05 2.20e-05 2.62e-05 3.37e-05 0.00
## PctRural -6.24e-02 -5.14e-02 -4.46e-02 -3.89e-02 -2.58e-02 -0.05
## PctFB 4.54e-01 9.40e-01 1.43e+00 2.00e+00 2.52e+00 1.30
## PctPov -1.46e-01 -1.39e-01 -1.34e-01 -1.21e-01 -9.26e-02 -0.13
df = slot(bach.gwr$SDF, "data")
brks = round(quantile(df$pred, probs = seq(0, 1, 0.2)), digits = 2)
ints = findInterval(df$pred, brks, all.inside = TRUE)
cls = rev(heat.colors(5))
plot(GA, col = cls[ints])
legend(x = "topright", legend = leglabs(brks), fill = cls, bty = "n", title = "Predicted",
horiz = FALSE, cex = 0.8)
title(main = "Predicted (gwr) Bachelors degrees percentage by county")
d. Plot a choropleth map of the percent poverty coefficient. (10)
brks = cut(df$PctPov, 6)
ints = as.integer(brks)
cls = rev(terrain.colors(6))
plot(GA, col = cls[ints])
legend(x = "topright", legend = levels(brks), fill = cls, bty = "n", title = "Percent Poverty Coefficient",
horiz = FALSE, cex = 0.65)
e. Plot a choropleth map of the R squared value. (10).
brks = cut(df$localR2, 6)
ints = as.integer(brks)
cls = terrain.colors(6)
plot(GA, col = cls[ints])
legend(x = "topright", legend = levels(brks), fill = cls, bty = "n", title = "Local R Squared",
horiz = FALSE, cex = 0.8)
