pkgs <- c("sf", "mapview", "spdep", "spatialreg", "tmap", "viridisLite",
"plm", "splm", "SDPDmod")
lapply(pkgs, require, character.only = TRUE)12 Exercise II
Required packages
Session info
sessionInfo()R version 4.3.1 (2023-06-16 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19044)
Matrix products: default
locale:
[1] LC_COLLATE=English_United Kingdom.utf8
[2] LC_CTYPE=English_United Kingdom.utf8
[3] LC_MONETARY=English_United Kingdom.utf8
[4] LC_NUMERIC=C
[5] LC_TIME=English_United Kingdom.utf8
time zone: Europe/London
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods
[7] base
other attached packages:
[1] SDPDmod_0.0.3 splm_1.6-2 plm_2.6-3
[4] viridisLite_0.4.2 tmap_3.3-3 spatialreg_1.2-9
[7] Matrix_1.5-4.1 spdep_1.2-8 spData_2.2.2
[10] mapview_2.11.0 sf_1.0-13
loaded via a namespace (and not attached):
[1] tidyselect_1.2.0 dplyr_1.1.2 fastmap_1.1.1
[4] leaflet_2.1.2 TH.data_1.1-2 dotCall64_1.0-2
[7] XML_3.99-0.14 digest_0.6.31 lifecycle_1.0.3
[10] LearnBayes_2.15.1 survival_3.5-5 terra_1.7-29
[13] magrittr_2.0.3 compiler_4.3.1 rlang_1.1.1
[16] tools_4.3.1 utf8_1.2.3 collapse_1.9.6
[19] knitr_1.43 htmlwidgets_1.6.2 sp_1.6-1
[22] classInt_0.4-9 RColorBrewer_1.1-3 multcomp_1.4-24
[25] abind_1.4-5 KernSmooth_2.23-21 expm_0.999-7
[28] leafsync_0.1.0 grid_4.3.1 stats4_4.3.1
[31] fansi_1.0.4 xtable_1.8-4 lfe_2.9-0
[34] e1071_1.7-13 leafem_0.2.0 colorspace_2.1-0
[37] scales_1.2.1 MASS_7.3-60 dichromat_2.0-0.1
[40] cli_3.6.1 mvtnorm_1.2-2 rmarkdown_2.22
[43] miscTools_0.6-28 generics_0.1.3 RSpectra_0.16-1
[46] rstudioapi_0.14 tmaptools_3.1-1 bdsmatrix_1.3-6
[49] DBI_1.1.3 proxy_0.4-27 ibdreg_0.3.8
[52] splines_4.3.1 stars_0.6-1 parallel_4.3.1
[55] s2_1.1.4 base64enc_0.1-3 vctrs_0.6.3
[58] boot_1.3-28.1 webshot_0.5.4 sandwich_3.0-2
[61] jsonlite_1.8.5 Formula_1.2-5 crosstalk_1.2.0
[64] units_0.8-2 spam_2.9-1 glue_1.6.2
[67] lwgeom_0.2-13 codetools_0.2-19 deldir_1.0-9
[70] raster_3.6-20 lmtest_0.9-40 munsell_0.5.0
[73] tibble_3.2.1 pillar_1.9.0 htmltools_0.5.5
[76] satellite_1.0.4 R6_2.5.1 maxLik_1.5-2
[79] wk_0.7.3 Rdpack_2.4 evaluate_0.21
[82] lattice_0.21-8 rbibutils_2.2.13 png_0.1-8
[85] class_7.3-22 Rcpp_1.0.10 coda_0.19-4
[88] nlme_3.1-162 xfun_0.39 zoo_1.8-12
[91] pkgconfig_2.0.3 12.1 Inkar data
Below, we read and transform some characteristics of the INKAR data on German counties.
di <- c("_data/")
# Define the downloaded filed
j <- c("inkar.csv")
c <- 1
for(k in j){
header <- as.vector(t(read.table(paste0(di, k), nrows = 1, sep = ";")[1,]))
# Clean header
header <- stringi::stri_replace_all_fixed(
header,
c("ä", "ö", "ü", "Ä", "Ö", "Ü"),
c("ae", "oe", "ue", "Ae", "Oe", "Ue"),
vectorize_all = FALSE
)
header <- gsub(" ", "", header)
header <- gsub("\\.", "", header)
header <- iconv(header, "latin1", "ASCII", sub = "")
# Combine with second row header (year)
header2 <- as.vector(t(read.table(paste0(di, k), skip = 1, nrows = 1, sep = ";")[1,]))
header3 <- paste(header, header2, sep = "_")
header3 <- gsub("_NA", "", header3)
nc <- length(header3)
# Input and rename data
data <- read.csv(paste0(di, k), skip = 2, header = FALSE, sep = ";",
quote = "\"", dec = ",", stringsAsFactors = F,
colClasses = "character")
names(data) <- header3
data1 <- data
# Correct character vars (containing thousands separator)
vars <- which(sapply(data1, is.character))
vars <- vars[-which(vars %in% c(1:3))]
for(l in vars){
data1[,l] <- gsub("\\.", "", data1[,l])
data1[,l] <- gsub("\\,", ".", data1[,l])
data1[,l] <- as.numeric(data1[,l])
}
# #Save
# l <- paste("bearb", k, sep = "_")
# write.table(data1, file = l, row.names = FALSE, sep = ";", dec = ".", na = ".")
# #Reshape
# helpvar1 <- unique(header[4:length(header)])
# helpvar2 <- sort(unique(header2[!is.na(header2)]))
# n_vars <- length(helpvar1)
# n_times <- length(helpvar2)
# helpvar1 <- sort(rep(helpvar1, times = n_times))
# helpvar2 <- rep(helpvar2, times = n_vars)
# helpvar3 <- paste(helpvar1, helpvar2, sep = "_")
# count <- ncol(data1)+1
# for(v in helpvar3) {
# if(v %in% names(data1)) {}
# else{
# data1[,count] <- NA
# colnames(data1)[count] <- v
# count <- count+1
# }
# }
# data1 <- data1[c(colnames(data1)[1:3], sort(helpvar3))]
#
# data1 <- reshape(data1, direction = "long", varying = 4:ncol(data1),
# sep = "_")
data.long <- tidyr::pivot_longer(data1,
cols = 4:ncol(data1),
names_to = c(".value", "year"),
names_pattern = "(.*)_(.*)")
colnames(data.long) <- substr(colnames(data.long), 1, 30)
if(c == 1){
inkar.df <- data.long
}else{
inkar.df <- merge(inkar.df, data.long, all.x = TRUE, all.y = TRUE)
}
c <- c+1
}
inkar.df$year <- as.numeric(inkar.df$year)
names(inkar.df)[which(names(inkar.df) == "Pkw-Dichte")] <- "pkw_dichte"
save(inkar.df, file = "_data/inkar.Rdata")Variables are
| Variable | Description |
|---|---|
| “Kennziffer” | ID |
| “Raumeinheit” | Name |
| “Aggregat” | Level |
| “year” | Year |
| “Bruttoinlandsproduktin1000Euro” | Gross Domestic Product in 1000 euros |
| “HaushaltemitKindern” | Households with children |
| “Lebenserwartung” | Life expectancy |
| “KommunaleSchulden” | Municipal debts |
| “Pkw-Dichte” | Car density |
| “Straenverkehrsunfaelle” | Road traffic accidents |
| “Einpendler” | In-commuters |
| “Auspendler” | Out-commuters |
| “Beschaeftigtenquote” | Employment rate |
| “Bevoelkerunggesamt” | Population |
| “Krankenhausbetten” | Hospital beds per 1,000 inhabitants |
| “Gesamtwanderungssaldo” | Net migration balance |
12.2 County shapes
kreise.spdf <- st_read(dsn = "_data/Kreisgrenzen_2020_mit_Einwohnerzahl",
layer = "KRS_ew_20")Reading layer `KRS_ew_20' from data source
`C:\work\Lehre\Geodata_Spatial_Regression\_data\Kreisgrenzen_2020_mit_Einwohnerzahl'
using driver `ESRI Shapefile'
Simple feature collection with 401 features and 19 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 5.86625 ymin: 47.27012 xmax: 15.04182 ymax: 55.05878
Geodetic CRS: WGS 8412.3 Exercises
12.3.1 Please map the life expectancy across Germany
12.3.2 Test the effect of regional characteristics on life expectancy
- Chose some variables that could predict life expectancy
Merge data (as with conventional data)
# Merge
inkar_2015.spdf <- merge(kreise.spdf, inkar.df[inkar.df$year == 2015, ],
by.x = "ags", by.y = "Kennziffer")Plot it
cols <- viridis(n = 100, direction = -1, option = "G")
mp1 <- tm_shape(inkar_2015.spdf) +
tm_fill(col = "Lebenserwartung",
style = "cont", # algorithm to def cut points
palette = cols, # colours
stretch.palette = TRUE,
title = "in years"
) +
tm_borders(col = "white", lwd = 0.5, alpha = 0.5) +
tm_layout(frame = FALSE,
legend.frame = TRUE, legend.bg.color = TRUE,
legend.position = c("right", "bottom"),
legend.outside = FALSE,
main.title = "Life expectancy",
main.title.position = "center",
main.title.size = 1.6,
legend.title.size = 0.8,
legend.text.size = 0.8)
mp1
- Chose between:
Generate impacts
# nb <- poly2nb(kreise.spdf, row.names = "ags", queen = TRUE)
knn <- knearneigh(st_centroid(kreise.spdf), k = 10)Warning: st_centroid assumes attributes are constant over
geometriesnb <- knn2nb(knn, row.names = kreise.spdf$ags)
listw <- nb2listw(nb, style = "W")- Estimate a cross-sectional spatial model for a selected year
Use a spatial Durbin Error model
# Spec formula
fm <- Lebenserwartung ~ Beschaeftigtenquote + Krankenhausbetten + pkw_dichte + HaushaltemitKindern + Straenverkehrsunfaelle
# Estimate error model with Durbin = TRUE
mod_1.durb <- errorsarlm(fm,
data = inkar_2015.spdf,
listw = listw,
Durbin = TRUE)
summary(mod_1.durb)
Call:
errorsarlm(formula = fm, data = inkar_2015.spdf, listw = listw,
Durbin = TRUE)
Residuals:
Min 1Q Median 3Q Max
-2.3061430 -0.3833525 -0.0034956 0.4119499 1.8500085
Type: error
Coefficients: (asymptotic standard errors)
Estimate Std. Error z value
(Intercept) 7.5913e+01 2.3609e+00 32.1539
Beschaeftigtenquote -3.3911e-03 1.2187e-02 -0.2782
Krankenhausbetten -6.9723e-03 1.2376e-02 -0.5634
pkw_dichte 6.6503e-05 6.7611e-04 0.0984
HaushaltemitKindern 5.8928e-02 1.2635e-02 4.6639
Straenverkehrsunfaelle -2.7490e-04 4.5970e-04 -0.5980
lag.Beschaeftigtenquote 7.3011e-02 3.4370e-02 2.1243
lag.Krankenhausbetten -9.1317e-02 5.5370e-02 -1.6492
lag.pkw_dichte -7.5386e-03 2.5851e-03 -2.9162
lag.HaushaltemitKindern 7.1558e-02 3.6657e-02 1.9521
lag.Straenverkehrsunfaelle 3.9637e-03 1.5674e-03 2.5288
Pr(>|z|)
(Intercept) < 2.2e-16
Beschaeftigtenquote 0.780824
Krankenhausbetten 0.573192
pkw_dichte 0.921647
HaushaltemitKindern 3.103e-06
Straenverkehrsunfaelle 0.549846
lag.Beschaeftigtenquote 0.033644
lag.Krankenhausbetten 0.099104
lag.pkw_dichte 0.003543
lag.HaushaltemitKindern 0.050928
lag.Straenverkehrsunfaelle 0.011445
Lambda: 0.74639, LR test value: 93.205, p-value: < 2.22e-16
Asymptotic standard error: 0.049366
z-value: 15.12, p-value: < 2.22e-16
Wald statistic: 228.6, p-value: < 2.22e-16
Log likelihood: -387.8592 for error model
ML residual variance (sigma squared): 0.3768, (sigma: 0.61384)
Number of observations: 401
Number of parameters estimated: 13
AIC: NA (not available for weighted model), (AIC for lm: 892.92)# Calculate impacts (which is unnecessary in this case)
mod_1.durb.imp <- impacts(mod_1.durb, listw = listw, R = 300)
summary(mod_1.durb.imp, zstats = TRUE, short = TRUE)Impact measures (SDEM, glht, n):
Direct Indirect Total
Beschaeftigtenquote -0.0033910753 0.073011426 0.069620351
Krankenhausbetten -0.0069723369 -0.091317318 -0.098289655
pkw_dichte 0.0000665025 -0.007538584 -0.007472081
HaushaltemitKindern 0.0589281106 0.071558303 0.130486413
Straenverkehrsunfaelle -0.0002748972 0.003963678 0.003688781
========================================================
Standard errors:
Direct Indirect Total
Beschaeftigtenquote 0.0121873300 0.034369504 0.034414827
Krankenhausbetten 0.0123764058 0.055370186 0.062065936
pkw_dichte 0.0006761139 0.002585061 0.002876977
HaushaltemitKindern 0.0126350740 0.036657394 0.038305933
Straenverkehrsunfaelle 0.0004597008 0.001567400 0.001699889
========================================================
Z-values:
Direct Indirect Total
Beschaeftigtenquote -0.27824596 2.124308 2.022975
Krankenhausbetten -0.56335716 -1.649215 -1.583633
pkw_dichte 0.09835991 -2.916211 -2.597198
HaushaltemitKindern 4.66385163 1.952084 3.406428
Straenverkehrsunfaelle -0.59799155 2.528824 2.170013
p-values:
Direct Indirect Total
Beschaeftigtenquote 0.78082 0.0336444 0.04307568
Krankenhausbetten 0.57319 0.0991037 0.11327729
pkw_dichte 0.92165 0.0035431 0.00939876
HaushaltemitKindern 3.1035e-06 0.0509283 0.00065819
Straenverkehrsunfaelle 0.54985 0.0114446 0.03000584- Estimate a spatial panel model (use the specification you prefer)
I am estimating a spatial FE SAR model here:
# Drop NA
inkar_sub.df <- inkar.df[which(complete.cases(inkar.df[, all.vars(fm)])),]
### Esimate FE SEM model
sarfe.mod <- spml(formula = fm,
data = inkar_sub.df,
index = c("Kennziffer", "year"), # ID column
listw = listw, # listw
model = "within", # one of c("within", "random", "pooling").
effect = "individual", # type of fixed effects
lag = TRUE, # spatila lg of Y
spatial.error = "none", # "b" (Baltagi), "kkp" (Kapoor, Kelejian and Prucha)
method = "eigen", # estimation method, for large data e.g. ("spam", "Matrix" or "LU")
na.action = na.fail, # handling of missings
zero.policy = NULL) # handling of missings
summary(sarfe.mod)Spatial panel fixed effects lag model
Call:
spml(formula = fm, data = inkar_sub.df, index = c("Kennziffer",
"year"), listw = listw, na.action = na.fail, model = "within",
effect = "individual", lag = TRUE, spatial.error = "none",
method = "eigen", zero.policy = NULL)
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-0.8708649 -0.1206026 -0.0033267 0.1202969 0.7825994
Spatial autoregressive coefficient:
Estimate Std. Error t-value Pr(>|t|)
lambda 0.420096 0.028664 14.656 < 2.2e-16 ***
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
Beschaeftigtenquote 4.3692e-02 2.9643e-03 14.7398 < 2.2e-16 ***
Krankenhausbetten 1.9071e-02 8.6677e-03 2.2002 0.0277934 *
pkw_dichte 7.2763e-04 1.8913e-04 3.8472 0.0001195 ***
HaushaltemitKindern 1.6637e-02 5.8347e-03 2.8514 0.0043533 **
Straenverkehrsunfaelle 6.8419e-06 1.0239e-04 0.0668 0.9467237
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1### Impacts
# Number of years
T <- length(unique(inkar_sub.df$year))
# impacts
sarfe.mod.imp <- impacts(sarfe.mod,
listw = listw,
time = T)
summary(sarfe.mod.imp) Impact measures (lag, trace):
Direct Indirect Total
Beschaeftigtenquote 4.456706e-02 3.077723e-02 7.534429e-02
Krankenhausbetten 1.945235e-02 1.343345e-02 3.288580e-02
pkw_dichte 7.421961e-04 5.125476e-04 1.254744e-03
HaushaltemitKindern 1.696972e-02 1.171899e-02 2.868872e-02
Straenverkehrsunfaelle 6.978862e-06 4.819480e-06 1.179834e-05
========================================================
Simulation results ( variance matrix):
Direct:
Iterations = 1:200
Thinning interval = 1
Number of chains = 1
Sample size per chain = 200
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
Beschaeftigtenquote 4.459e-02 2.915e-03 2.061e-04 2.061e-04
Krankenhausbetten 1.970e-02 9.607e-03 6.793e-04 6.793e-04
pkw_dichte 7.398e-04 1.913e-04 1.353e-05 1.353e-05
HaushaltemitKindern 1.729e-02 5.564e-03 3.934e-04 3.934e-04
Straenverkehrsunfaelle 2.642e-06 9.953e-05 7.038e-06 5.581e-06
2. Quantiles for each variable:
2.5% 25% 50% 75%
Beschaeftigtenquote 0.0395345 4.271e-02 4.439e-02 4.654e-02
Krankenhausbetten 0.0023178 1.273e-02 2.052e-02 2.610e-02
pkw_dichte 0.0003934 5.904e-04 7.354e-04 8.639e-04
HaushaltemitKindern 0.0066456 1.350e-02 1.721e-02 2.102e-02
Straenverkehrsunfaelle -0.0001944 -6.492e-05 -1.803e-06 7.394e-05
97.5%
Beschaeftigtenquote 0.0503857
Krankenhausbetten 0.0378315
pkw_dichte 0.0011034
HaushaltemitKindern 0.0287736
Straenverkehrsunfaelle 0.0001771
========================================================
Indirect:
Iterations = 1:200
Thinning interval = 1
Number of chains = 1
Sample size per chain = 200
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
Beschaeftigtenquote 3.081e-02 0.0042273 2.989e-04 4.939e-04
Krankenhausbetten 1.349e-02 0.0067081 4.743e-04 4.743e-04
pkw_dichte 5.132e-04 0.0001535 1.085e-05 1.085e-05
HaushaltemitKindern 1.197e-02 0.0041969 2.968e-04 2.968e-04
Straenverkehrsunfaelle 2.023e-06 0.0000700 4.950e-06 3.991e-06
2. Quantiles for each variable:
2.5% 25% 50% 75%
Beschaeftigtenquote 0.0230406 2.825e-02 3.074e-02 3.311e-02
Krankenhausbetten 0.0016335 8.619e-03 1.344e-02 1.784e-02
pkw_dichte 0.0002607 3.996e-04 4.945e-04 6.111e-04
HaushaltemitKindern 0.0042322 9.199e-03 1.173e-02 1.463e-02
Straenverkehrsunfaelle -0.0001400 -4.243e-05 -1.254e-06 5.035e-05
97.5%
Beschaeftigtenquote 0.0397528
Krankenhausbetten 0.0273577
pkw_dichte 0.0008314
HaushaltemitKindern 0.0205899
Straenverkehrsunfaelle 0.0001292
========================================================
Total:
Iterations = 1:200
Thinning interval = 1
Number of chains = 1
Sample size per chain = 200
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
Beschaeftigtenquote 7.540e-02 0.0062141 4.394e-04 6.929e-04
Krankenhausbetten 3.320e-02 0.0161873 1.145e-03 1.145e-03
pkw_dichte 1.253e-03 0.0003369 2.383e-05 2.383e-05
HaushaltemitKindern 2.926e-02 0.0095948 6.785e-04 6.785e-04
Straenverkehrsunfaelle 4.665e-06 0.0001692 1.196e-05 9.546e-06
2. Quantiles for each variable:
2.5% 25% 50% 75%
Beschaeftigtenquote 0.0635934 0.0707996 7.555e-02 0.0788972
Krankenhausbetten 0.0038687 0.0212281 3.396e-02 0.0440139
pkw_dichte 0.0006616 0.0010025 1.260e-03 0.0014714
HaushaltemitKindern 0.0108200 0.0231673 2.858e-02 0.0353547
Straenverkehrsunfaelle -0.0003412 -0.0001057 -3.057e-06 0.0001213
97.5%
Beschaeftigtenquote 0.0889887
Krankenhausbetten 0.0638877
pkw_dichte 0.0018925
HaushaltemitKindern 0.0493892
Straenverkehrsunfaelle 0.0002914- Calculate the impacts
12.3.3 Esimate an FE model with SLX specification
Loops over years to generate WX
# All years where we have a balanced sample
years <- unique(inkar.df$year[which(complete.cases(inkar.df[, all.vars(fm)]))])
# All variables we want ot lag
vars <- all.vars(fm)
# create listw with the correct rownames (ID = Kennziffer)
kreise.spdf$Kennziffer <- kreise.spdf$ags
knn <- knearneigh(st_centroid(kreise.spdf), k = 10)Warning: st_centroid assumes attributes are constant over
geometriesnb <- knn2nb(knn, row.names = kreise.spdf$Kennziffer)
listw <- nb2listw(nb, style = "W")
for(y in years){
# Select singe year
tmp <- inkar.df[inkar.df$year == y ,]
# Select variables and make df
x <- st_drop_geometry(tmp[, vars])
# Add ID as rownames (we retreive them again later)
rownames(x) <- tmp$Kennziffer
# Perform lag transformation (rownames contian ids)
w.tmp <- create_WX(as.matrix(x),
listw = listw,
prefix = "w",
zero.policy = TRUE) # NAs will get zero
w.tmp <- as.data.frame(w.tmp)
# add indices back
w.tmp$Kennziffer <- row.names(w.tmp)
w.tmp$year <- y
if(y == years[1]){
w.inkar.df <- w.tmp
}else{
w.inkar.df <- rbind(w.inkar.df, w.tmp)
}
}Warning: Setting row names on a tibble is deprecated.Warning: Setting row names on a tibble is deprecated.
Setting row names on a tibble is deprecated.
Setting row names on a tibble is deprecated.
Setting row names on a tibble is deprecated.
Setting row names on a tibble is deprecated.
Setting row names on a tibble is deprecated.
Setting row names on a tibble is deprecated.head(w.inkar.df) w.Lebenserwartung w.Beschaeftigtenquote w.Krankenhausbetten
01001 80.181 52.686 5.694
01002 80.193 53.122 6.087
01003 80.281 55.042 6.950
01004 80.325 53.877 5.631
01051 80.145 53.762 5.281
01053 80.236 56.863 6.155
w.pkw_dichte w.HaushaltemitKindern w.Straenverkehrsunfaelle
01001 549.458 27.703 512.763
01002 542.982 27.285 519.162
01003 518.670 26.150 518.684
01004 538.232 27.124 516.199
01051 546.799 28.170 494.705
01053 523.272 26.562 513.071
Kennziffer year
01001 01001 2013
01002 01002 2013
01003 01003 2013
01004 01004 2013
01051 01051 2013
01053 01053 2013# Merge back
inkar.df <- merge(inkar.df, w.inkar.df, by = c("Kennziffer", "year"))Estimate a twoways FE panel model
fm2 <- Lebenserwartung ~ Beschaeftigtenquote + Krankenhausbetten + pkw_dichte + HaushaltemitKindern + Straenverkehrsunfaelle +
w.Beschaeftigtenquote + w.Krankenhausbetten + w.pkw_dichte + w.HaushaltemitKindern + w.Straenverkehrsunfaelle
slx.fe <- plm(fm2,
data = inkar.df,
effects = "twoways",
model = "within")
summary(slx.fe)Oneway (individual) effect Within Model
Call:
plm(formula = fm2, data = inkar.df, model = "within", effects = "twoways")
Balanced Panel: n = 401, T = 8, N = 3208
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-0.88591742 -0.12535845 -0.00049348 0.12743249 0.72005574
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
Beschaeftigtenquote 0.00553516 0.00753337 0.7348 0.462552
Krankenhausbetten 0.02732408 0.00960069 2.8461 0.004459
pkw_dichte 0.00058863 0.00021846 2.6945 0.007092
HaushaltemitKindern 0.02062436 0.00814937 2.5308 0.011435
Straenverkehrsunfaelle 0.00031042 0.00014097 2.2020 0.027748
w.Beschaeftigtenquote 0.06172600 0.00945493 6.5284 7.863e-11
w.Krankenhausbetten 0.02200257 0.03261281 0.6747 0.499947
w.pkw_dichte 0.00143784 0.00095524 1.5052 0.132382
w.HaushaltemitKindern -0.01053720 0.01275188 -0.8263 0.408690
w.Straenverkehrsunfaelle -0.00091095 0.00022556 -4.0387 5.519e-05
Beschaeftigtenquote
Krankenhausbetten **
pkw_dichte **
HaushaltemitKindern *
Straenverkehrsunfaelle *
w.Beschaeftigtenquote ***
w.Krankenhausbetten
w.pkw_dichte
w.HaushaltemitKindern
w.Straenverkehrsunfaelle ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Total Sum of Squares: 250.08
Residual Sum of Squares: 132.01
R-Squared: 0.47212
Adj. R-Squared: 0.39474
F-statistic: 250.159 on 10 and 2797 DF, p-value: < 2.22e-16