date()
## [1] "Sat Nov 17 16:11:18 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 bachelor’s 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")
GeorgiaBach = readShapeSpatial("Georgia/GeorgiaEduc")
slotNames(GeorgiaBach)
## [1] "data" "polygons" "plotOrder" "bbox" "proj4string"
head(GeorgiaBach@data)
## FID_1 AREA PERIMETER G_UTM_ G_UTM_ID AREANAME AREAKEY
## 0 130 1.331e+09 207205 132 133 GA, Appling County 13001
## 1 155 8.929e+08 154640 157 158 GA, Atkinson County 13003
## 2 146 7.434e+08 130431 148 146 GA, Bacon County 13005
## 3 156 9.054e+08 185737 158 155 GA, Baker County 13007
## 4 74 6.942e+08 151347 76 79 GA, Baldwin County 13009
## 5 22 6.065e+08 103518 24 23 GA, Banks County 13011
## X_COORD Y_COORD KEY_VAL FID_2 AreaKey_1 Latitude Longitud TotPop90
## 0 941397 3521760 0 0 13001 31.75 -82.29 15744
## 1 895553 3471920 0 1 13003 31.29 -82.87 6213
## 2 930946 3502790 0 2 13005 31.56 -82.45 9566
## 3 745399 3474760 0 3 13007 31.33 -84.45 3615
## 4 849431 3665550 13009 4 13009 33.07 -83.25 39530
## 5 819317 3807620 13011 5 13011 34.35 -83.50 10308
## PctRural PctBach PctEld PctFB PctPov PctBlack ID X Y
## 0 75.6 8.2 11.43 0.64 19.9 20.76 133 941397 3521764
## 1 100.0 6.4 11.77 1.58 26.0 26.86 158 895553 3471916
## 2 61.7 6.6 11.11 0.27 24.1 15.42 146 930946 3502787
## 3 100.0 9.4 13.17 0.11 24.8 51.67 155 745399 3474765
## 4 42.7 13.3 8.64 1.43 17.5 42.39 79 849431 3665553
## 5 100.0 6.4 11.37 0.34 15.1 3.49 23 819317 3807616
## Distance
## 0 0
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
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)
Georgia.regress = lm(PctBach ~ TotPop90 + PctRural + PctEld + PctFB + PctPov +
PctBlack, data = GeorgiaBach)
summary(Georgia.regress)
##
## Call:
## lm(formula = PctBach ~ TotPop90 + PctRural + PctEld + PctFB +
## PctPov + PctBlack, data = GeorgiaBach)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.369 -2.052 -0.111 1.175 19.894
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.50e+01 1.60e+00 9.37 < 2e-16 ***
## TotPop90 2.33e-05 4.55e-06 5.11 8.7e-07 ***
## PctRural -4.27e-02 1.30e-02 -3.28 0.0013 **
## PctEld -7.88e-02 1.15e-01 -0.69 0.4935
## PctFB 1.25e+00 2.98e-01 4.18 4.6e-05 ***
## PctPov -1.55e-01 6.60e-02 -2.35 0.0201 *
## PctBlack 2.08e-02 2.37e-02 0.88 0.3809
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.35 on 167 degrees of freedom
## Multiple R-squared: 0.649, Adjusted R-squared: 0.637
## F-statistic: 51.6 on 6 and 167 DF, p-value: <2e-16
step(Georgia.regress)
## 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 = GeorgiaBach)
##
## Coefficients:
## (Intercept) TotPop90 PctRural PctFB PctPov
## 1.44e+01 2.37e-05 -4.64e-02 1.30e+00 -1.31e-01
Georgia.Final = lm(PctBach ~ TotPop90 + PctRural + PctFB + PctPov, data = GeorgiaBach)
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)
require(spgwr)
## Loading required package: spgwr
## NOTE: This package does not constitute approval of GWR as a method of
## spatial analysis
Georgia.bw = gwr.sel(PctBach ~ TotPop90 + PctRural + PctFB + PctPov, data = GeorgiaBach)
## 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
## Bandwidth: 168474 CV score: 1991
Georgia.gwr = gwr(PctBach ~ TotPop90 + PctRural + PctFB + PctPov, data = GeorgiaBach,
coords = cbind(GeorgiaBach$X_COORD, GeorgiaBach$Y_COORD), bandwidth = Georgia.bw)
## Warning: data is Spatial* object, ignoring coords argument
Georgia.gwr
## Call:
## gwr(formula = PctBach ~ TotPop90 + PctRural + PctFB + PctPov,
## data = GeorgiaBach, coords = cbind(GeorgiaBach$X_COORD, GeorgiaBach$Y_COORD),
## bandwidth = Georgia.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
brks = round(quantile(GeorgiaBach$PctBach, probs = seq(0, 1, 0.2)), digits = 2)
ints = findInterval(GeorgiaBach$PctBach, brks, all.inside = TRUE)
cls = rev(heat.colors(5))
plot(GeorgiaBach, col = cls[ints])
legend(x = "topleft", legend = leglabs(brks), cex = 0.9, fill = cls)
title(main = "Percent of Population with Bachelors by County")
d. Plot a choropleth map of the percent poverty coefficient. (10)
brks = round(quantile(GeorgiaBach$PctPov, probs = seq(0, 1, 0.2)), digits = 2)
ints = findInterval(GeorgiaBach$PctPov, brks, all.inside = TRUE)
cls = rev(heat.colors(5))
plot(GeorgiaBach, col = cls[ints])
legend(x = "topleft", legend = leglabs(brks), cex = 0.9, fill = cls)
title(main = "Percent of Population in Poverty")
e. Plot a choropleth map of the R squared value. (10).
df = slot(Georgia.gwr$SDF, "data")
brks = cut(df$localR2, 6)
ints = as.integer(brks)
cls = terrain.colors(6)
plot(GeorgiaBach, col = cls[ints])
legend(x = "topleft", legend = levels(brks), fill = cls, bty = "n", title = "Local R Squared",
horiz = FALSE, cex = 0.45)
title(main = "R Squared Value")
