election.RdData frame with number of citizens eligible to vote and results of the elections in 2002 and 2005 for the German Bundestag, the first chamber of the German parliament.
data(election)
A data frame with 299 observations (corresponding to constituencies) on the following 13 variables.
statefactor, the 16 German federal states
eligible_02number of citizens eligible to vote in 2002
SPD_02a numeric vector, percentage for the Social Democrats SPD in 2002
UNION_02a numeric vector, percentage for the conservative Christian Democrats CDU/CSU in 2002
GREEN_02a numeric vector, percentage for the Greens in 2002
FDP_02a numeric vector, percentage for the Liberal Party FDP in 2002
LEFT_02a numeric vector, percentage for the Left Party PDS in 2002
eligible_05number of citizens eligible to vote in 2005
SPD_05a numeric vector, percentage for the Social Democrats SPD in 2005
UNION_05a numeric vector, percentage for the conservative Christian Democrats CDU/CSU in 2005
GREEN_05a numeric vector, percentage for the Greens in 2005
FDP_05a numeric vector, percentage for the Liberal Party FDP in 2005
LEFT_05a numeric vector, percentage for the Left Party in 2005
German Federal Elections
Half of the Members of the German Bundestag are elected directly from Germany's 299 constituencies, the other half one on the parties' land lists. Accordingly, each voter has two votes in the elections to the German Bundestag. The first vote, allowing voters to elect their local representatives to the Bundestag, decides which candidates are sent to Parliament from the constituencies. The second vote is cast for a party list. And it is this second vote that determines the relative strengths of the parties represented in the Bundestag. At least 598 Members of the German Bundestag are elected in this way. In addition to this, there are certain circumstances in which some candidates win what are known as 'overhang mandates' when the seats are being distributed.
The data set provides the percentage of second votes for each party, which determines the number of seats each party gets in parliament. These percentages are calculated by the number of votes for a party divided by number of valid votes.
The data is provided by the R package flexclust.
Kauermann, Goeran/Kuechenhoff, Helmut (2010): Stichproben. Methoden und praktische Umsetzung mit R. Springer.
Homepage of the Bundestag: http://www.bundestag.de.
Friedrich Leisch. A Toolbox for K-Centroids Cluster Analysis. Computational Statistics and Data Analysis, 51 (2), 526-544, 2006.
#> state eligible_02 SPD_02 UNION_02 #> Nordrhein-Westfalen:64 Min. :152670 Min. :0.1785 Min. :0.1285 #> Bayern :45 1st Qu.:190152 1st Qu.:0.3337 1st Qu.:0.3075 #> Baden-Wuerttemberg :37 Median :206148 Median :0.3845 Median :0.3628 #> Niedersachsen :29 Mean :205461 Mean :0.3861 Mean :0.3831 #> Hessen :21 3rd Qu.:219907 3rd Qu.:0.4459 3rd Qu.:0.4342 #> Sachsen :17 Max. :249388 Max. :0.6171 Max. :0.7282 #> (Other) :86 #> GREEN_02 FDP_02 LEFT_02 eligible_05 #> Min. :0.02251 Min. :0.02489 Min. :0.003352 Min. :154154 #> 1st Qu.:0.05734 1st Qu.:0.06001 1st Qu.:0.008415 1st Qu.:191819 #> Median :0.07638 Median :0.07428 Median :0.011201 Median :206345 #> Mean :0.08484 Mean :0.07342 Mean :0.041898 Mean :206924 #> 3rd Qu.:0.10650 3rd Qu.:0.08601 3rd Qu.:0.019522 3rd Qu.:220944 #> Max. :0.25029 Max. :0.12420 Max. :0.293128 Max. :254100 #> #> SPD_05 UNION_05 GREEN_05 FDP_05 #> Min. :0.1885 Min. :0.1104 Min. :0.02619 Min. :0.04565 #> 1st Qu.:0.2959 1st Qu.:0.2881 1st Qu.:0.05664 1st Qu.:0.08095 #> Median :0.3361 Median :0.3432 Median :0.07195 Median :0.09679 #> Mean :0.3427 Mean :0.3507 Mean :0.08060 Mean :0.09769 #> 3rd Qu.:0.3883 3rd Qu.:0.4045 3rd Qu.:0.09818 3rd Qu.:0.11241 #> Max. :0.5586 Max. :0.6048 Max. :0.22769 Max. :0.16630 #> #> LEFT_05 #> Min. :0.02275 #> 1st Qu.:0.03866 #> Median :0.04888 #> Mean :0.08870 #> 3rd Qu.:0.07176 #> Max. :0.35536 #># 1) Draw a simple sample of size n=20 n <- 20 set.seed(67396) index <- sample(1:nrow(election), size=n) sample1 <- election[index,] Smean(sample1$SPD_02, N=nrow(election))#> #> Smean object: Sample mean estimate #> With finite population correction: N=299 #> #> Mean estimate: 0.3515 #> Standard error: 0.0165 #> 95% confidence interval: [0.3192,0.3839] #>#> [1] 0.3861344# 2) Estimate sample size to forecast proportion of SPD in election of 2005 sample.size.prop(e=0.01, P=mean(election$SPD_02), N=Inf)#> #> sample.size.prop object: Sample size for proportion estimate #> Without finite population correction: N=Inf, precision e=0.01 and expected proportion P=0.3861 #> #> Sample size needed: 9106 #># 3) Usage of previous knowledge by model based estimation # draw sample of size n = 20 N <- nrow(election) set.seed(67396) sample <- election[sort(sample(1:N, size=20)),] # secondary information SPD in 2002 X.mean <- mean(election$SPD_02) # forecast proportion of SPD in election of 2005 mbes(SPD_05 ~ SPD_02, data=sample, aux=X.mean, N=N, method='all')#> #> mbes object: Model Based Estimation of Population Mean #> Population size N = 299, sample size n = 20 #> #> Values for auxiliary variable: #> X.mean.1 = 0.3861, x.mean.1 = 0.3515 #> ---------------------------------------------------------------- #> Simple Estimate #> #> Mean estimate: 0.3009 #> Standard error: 0.0119 #> #> 95% confidence interval [0.2775,0.3242] #> #> ---------------------------------------------------------------- #> Difference Estimate #> #> Mean estimate: 0.3355 #> Standard error: 0.0088 #> #> 95% confidence interval [0.3183,0.3526] #> #> ---------------------------------------------------------------- #> Ratio Estimate #> #> Mean estimate: 0.3305 #> Standard error: 0.0072 #> #> 95% confidence interval [0.3163,0.3447] #> #> ---------------------------------------------------------------- #> Linear Regression Estimate #> #> Mean estimate: 0.3223 #> Standard error: 0.0063 #> #> 95% confidence interval [0.31,0.3346] #> #> ---------------------------------------------------------------- #> Linear Regression Model: #> Call: #> lm(formula = formula, data = data) #> #> Residuals: #> Min 1Q Median 3Q Max #> -0.054727 -0.022938 -0.003066 0.027230 0.037138 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 0.08290 0.03137 2.643 0.0165 * #> SPD_02 0.62004 0.08729 7.103 1.28e-06 *** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 0.02908 on 18 degrees of freedom #> Multiple R-squared: 0.737, Adjusted R-squared: 0.7224 #> F-statistic: 50.45 on 1 and 18 DF, p-value: 1.277e-06 #>#> [1] 0.3426949# Use a second predictor variable X.mean2 <- c(mean(election$SPD_02),mean(election$GREEN_02)) # forecast proportion of SPD in election of 2005 with two predictors mbes(SPD_05 ~ SPD_02+GREEN_02, data=sample, aux=X.mean2, N=N, method= 'regr')#> #> mbes object: Model Based Estimation of Population Mean #> Population size N = 299, sample size n = 20 #> #> Values for auxiliary variable: #> X.mean.1 = 0.3861, x.mean.1 = 0.3515 #> X.mean.2 = 0.0848, x.mean.2 = 0.07 #> ---------------------------------------------------------------- #> Linear Regression Estimate #> #> Mean estimate: 0.3291 #> Standard error: 0.0051 #> #> 95% confidence interval [0.3191,0.3391] #> #> ---------------------------------------------------------------- #> Linear Regression Model: #> Call: #> lm(formula = formula, data = data) #> #> Residuals: #> Min 1Q Median 3Q Max #> -0.037753 -0.016922 -0.004229 0.016320 0.048000 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 0.04326 0.02843 1.521 0.14652 #> SPD_02 0.66001 0.07223 9.138 5.71e-08 *** #> GREEN_02 0.36537 0.11489 3.180 0.00547 ** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 0.0237 on 17 degrees of freedom #> Multiple R-squared: 0.8351, Adjusted R-squared: 0.8157 #> F-statistic: 43.06 on 2 and 17 DF, p-value: 2.217e-07 #>