基础统计分析
准备工作
如果没有相关的包，则使用install.packages('package_name')进行安装以下包。
读取数据，使用H1N1流感数据集和波士顿房价数据集。
1 多种方法获取描述性统计量
1.1 基础方法
通过summary计算数值型变量的最大值、最小值、分位数以及均值，类别变量计算频数统计。
## household_children sex
## Min. :0.0000 Length:26707
## 1st Qu.:0.0000 Class :character
## Median :0.0000 Mode :character
## Mean :0.5346
## 3rd Qu.:1.0000
## Max. :3.0000
## NA's :249## h1n1_concern h1n1_knowledge
## Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :1.000
## Mean :1.618 Mean :1.263
## 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :3.000 Max. :2.000
## NA's :92 NA's :116通过 sapply() 计算描述性统计量，先定义统计函数，在进行聚合计算。
mystats <- function(x, na.omit = FALSE) {
if (na.omit)
x <- x[!is.na(x)]
m <- mean(x)
n <- length(x)
s <- sd(x)
skew <- sum((x - m)^3/s^3)/n
kurt <- sum((x - m)^4/s^4)/n - 3
return(c(n = n, mean = m, stdev = s, skew = skew, kurtosis = kurt))
}
sapply(flu[c("h1n1_concern", "h1n1_knowledge")], mystats)## h1n1_concern h1n1_knowledge
## n 26707 26707
## mean NA NA
## stdev NA NA
## skew NA NA
## kurtosis NA NA1.2 拓展包方法
通过pastecs包中的 stat.desc()函数计算描述性统计量，可以得到中位数、平均数、平均数的标准误、平均数置信度为95%的置信区间、方差、标准差以及变异系数。
## household_children sex
## nbr.val 2.645800e+04 NA
## nbr.null 1.867200e+04 NA
## nbr.na 2.490000e+02 NA
## min 0.000000e+00 NA
## max 3.000000e+00 NA
## range 3.000000e+00 NA
## sum 1.414400e+04 NA
## median 0.000000e+00 NA
## mean 5.345831e-01 NA
## SE.mean 5.706247e-03 NA
## CI.mean.0.95 1.118455e-02 NA
## var 8.615057e-01 NA
## std.dev 9.281733e-01 NA
## coef.var 1.736256e+00 NA通过psych包中的describe()计算描述性统计量。
## vars n mean sd median trimmed mad min max range skew
## household_children 1 26458 0.53 0.93 0 0.34 0 0 3 3 1.54
## sex* 2 26707 1.41 0.49 1 1.38 0 1 2 1 0.38
## kurtosis se
## household_children 1.04 0.01
## sex* -1.85 0.002 分组计算描述性统计
2.1 基础方法
使用aggregate()分组获取描述性统计
- 分组计算不同性别收入贫困计数。
- 是否属于查尔斯河的房价中位数平均值。
## sex income_poverty
## 1 Female 15858
## 2 Male 10849## medv x
## 1 0 22.09384
## 2 1 28.440004 相关
4.1 相关的类型
Pearson、Spearman和Kendall相关
R可以计算多种相关系数，包括Pearson相关系数、Spearman相关系数、Kendall相关系数、偏相关系数、多分格（polychoric）相关系数和多系列（polyserial）相关系数。 1. 计算房价数据的相关系数，默认是Pearson相关系数。
## X crim zn indus chas
## X 1.000000000 0.40740717 -0.10339336 0.39943885 -0.003759115
## crim 0.407407172 1.00000000 -0.20046922 0.40658341 -0.055891582
## zn -0.103393357 -0.20046922 1.00000000 -0.53382819 -0.042696719
## indus 0.399438850 0.40658341 -0.53382819 1.00000000 0.062938027
## chas -0.003759115 -0.05589158 -0.04269672 0.06293803 1.000000000
## nox 0.398736174 0.42097171 -0.51660371 0.76365145 0.091202807
## rm -0.079971150 -0.21924670 0.31199059 -0.39167585 0.091251225
## age 0.203783510 0.35273425 -0.56953734 0.64477851 0.086517774
## dis -0.302210959 -0.37967009 0.66440822 -0.70802699 -0.099175780
## rad 0.686001976 0.62550515 -0.31194783 0.59512927 -0.007368241
## tax 0.666625924 0.58276431 -0.31456332 0.72076018 -0.035586518
## ptratio 0.291074227 0.28994558 -0.39167855 0.38324756 -0.121515174
## b -0.295041232 -0.38506394 0.17552032 -0.35697654 0.048788485
## lstat 0.258464770 0.45562148 -0.41299457 0.60379972 -0.053929298
## medv -0.226603643 -0.38830461 0.36044534 -0.48372516 0.175260177
## nox rm age dis rad
## X 0.39873617 -0.07997115 0.20378351 -0.30221096 0.686001976
## crim 0.42097171 -0.21924670 0.35273425 -0.37967009 0.625505145
## zn -0.51660371 0.31199059 -0.56953734 0.66440822 -0.311947826
## indus 0.76365145 -0.39167585 0.64477851 -0.70802699 0.595129275
## chas 0.09120281 0.09125123 0.08651777 -0.09917578 -0.007368241
## nox 1.00000000 -0.30218819 0.73147010 -0.76923011 0.611440563
## rm -0.30218819 1.00000000 -0.24026493 0.20524621 -0.209846668
## age 0.73147010 -0.24026493 1.00000000 -0.74788054 0.456022452
## dis -0.76923011 0.20524621 -0.74788054 1.00000000 -0.494587930
## rad 0.61144056 -0.20984667 0.45602245 -0.49458793 1.000000000
## tax 0.66802320 -0.29204783 0.50645559 -0.53443158 0.910228189
## ptratio 0.18893268 -0.35550149 0.26151501 -0.23247054 0.464741179
## b -0.38005064 0.12806864 -0.27353398 0.29151167 -0.444412816
## lstat 0.59087892 -0.61380827 0.60233853 -0.49699583 0.488676335
## medv -0.42732077 0.69535995 -0.37695457 0.24992873 -0.381626231
## tax ptratio b lstat medv
## X 0.66662592 0.2910742 -0.29504123 0.2584648 -0.2266036
## crim 0.58276431 0.2899456 -0.38506394 0.4556215 -0.3883046
## zn -0.31456332 -0.3916785 0.17552032 -0.4129946 0.3604453
## indus 0.72076018 0.3832476 -0.35697654 0.6037997 -0.4837252
## chas -0.03558652 -0.1215152 0.04878848 -0.0539293 0.1752602
## nox 0.66802320 0.1889327 -0.38005064 0.5908789 -0.4273208
## rm -0.29204783 -0.3555015 0.12806864 -0.6138083 0.6953599
## age 0.50645559 0.2615150 -0.27353398 0.6023385 -0.3769546
## dis -0.53443158 -0.2324705 0.29151167 -0.4969958 0.2499287
## rad 0.91022819 0.4647412 -0.44441282 0.4886763 -0.3816262
## tax 1.00000000 0.4608530 -0.44180801 0.5439934 -0.4685359
## ptratio 0.46085304 1.0000000 -0.17738330 0.3740443 -0.5077867
## b -0.44180801 -0.1773833 1.00000000 -0.3660869 0.3334608
## lstat 0.54399341 0.3740443 -0.36608690 1.0000000 -0.7376627
## medv -0.46853593 -0.5077867 0.33346082 -0.7376627 1.0000000- 指定计算Spearman相关系数
## X crim zn indus chas
## X 1.000000000 0.46103705 -0.1605047 0.32462127 -0.003759115
## crim 0.461037054 1.00000000 -0.5716602 0.73552374 0.041536888
## zn -0.160504702 -0.57166021 1.0000000 -0.64281060 -0.041936998
## indus 0.324621271 0.73552374 -0.6428106 1.00000000 0.089841379
## chas -0.003759115 0.04153689 -0.0419370 0.08984138 1.000000000
## nox 0.432491886 0.82146466 -0.6348284 0.79118913 0.068426283
## rm -0.035641354 -0.30911647 0.3610737 -0.41530129 0.058812916
## age 0.208323439 0.70413998 -0.5444226 0.67948671 0.067791779
## dis -0.373498683 -0.74498614 0.6146265 -0.75707970 -0.080248080
## rad 0.588480705 0.72780697 -0.2787672 0.45550745 0.024578885
## tax 0.536928176 0.72904490 -0.3713945 0.66436139 -0.044485772
## ptratio 0.297897432 0.46528319 -0.4484754 0.43371046 -0.136064621
## b -0.154474321 -0.36055532 0.1631351 -0.28583984 -0.039810497
## lstat 0.257542491 0.63476026 -0.4900739 0.63874741 -0.050574829
## medv -0.273633481 -0.55889095 0.4381790 -0.57825539 0.140612154
## nox rm age dis rad tax
## X 0.43249189 -0.03564135 0.20832344 -0.37349868 0.58848071 0.53692818
## crim 0.82146466 -0.30911647 0.70413998 -0.74498614 0.72780697 0.72904490
## zn -0.63482840 0.36107373 -0.54442256 0.61462654 -0.27876717 -0.37139450
## indus 0.79118913 -0.41530129 0.67948671 -0.75707970 0.45550745 0.66436139
## chas 0.06842628 0.05881292 0.06779178 -0.08024808 0.02457888 -0.04448577
## nox 1.00000000 -0.31034391 0.79515291 -0.88001486 0.58642870 0.64952656
## rm -0.31034391 1.00000000 -0.27808202 0.26316822 -0.10749220 -0.27189846
## age 0.79515291 -0.27808202 1.00000000 -0.80160979 0.41798261 0.52636644
## dis -0.88001486 0.26316822 -0.80160979 1.00000000 -0.49580647 -0.57433641
## rad 0.58642870 -0.10749220 0.41798261 -0.49580647 1.00000000 0.70487572
## tax 0.64952656 -0.27189846 0.52636644 -0.57433641 0.70487572 1.00000000
## ptratio 0.39130908 -0.31292257 0.35538428 -0.32204056 0.31832966 0.45334546
## b -0.29666158 0.05366004 -0.22802200 0.24959532 -0.28253261 -0.32984308
## lstat 0.63682829 -0.64083156 0.65707079 -0.56426219 0.39432245 0.53442319
## medv -0.56260883 0.63357643 -0.54756169 0.44585685 -0.34677626 -0.56241063
## ptratio b lstat medv
## X 0.29789743 -0.15447432 0.25754249 -0.2736335
## crim 0.46528319 -0.36055532 0.63476026 -0.5588909
## zn -0.44847543 0.16313510 -0.49007389 0.4381790
## indus 0.43371046 -0.28583984 0.63874741 -0.5782554
## chas -0.13606462 -0.03981050 -0.05057483 0.1406122
## nox 0.39130908 -0.29666158 0.63682829 -0.5626088
## rm -0.31292257 0.05366004 -0.64083156 0.6335764
## age 0.35538428 -0.22802200 0.65707079 -0.5475617
## dis -0.32204056 0.24959532 -0.56426219 0.4458569
## rad 0.31832966 -0.28253261 0.39432245 -0.3467763
## tax 0.45334546 -0.32984308 0.53442319 -0.5624106
## ptratio 1.00000000 -0.07202734 0.46725885 -0.5559047
## b -0.07202734 1.00000000 -0.21056185 0.1856641
## lstat 0.46725885 -0.21056185 1.00000000 -0.8529141
## medv -0.55590468 0.18566412 -0.85291414 1.0000000- 城镇人均犯罪率与房价的相关系数
## medv
## X -0.2266036
## crim -0.3883046
## zn 0.3604453
## indus -0.4837252
## chas 0.1752602
## nox -0.4273208
## rm 0.6953599
## age -0.3769546
## dis 0.2499287
## rad -0.3816262
## tax -0.4685359
## ptratio -0.5077867
## b 0.3334608
## lstat -0.7376627
## medv 1.0000000偏相关
偏相关是指在控制一个或多个定量变量时，另外两个定量变量之间的相互关系。使用ggm 包中的 pcor() 函数计算偏相关系数。
4.2 相关性的显著性检验
##
## Pearson's product-moment correlation
##
## data: housing[, c("crim")] and housing[, c("medv")]
## t = -9.4597, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4599064 -0.3116859
## sample estimates:
## cor
## -0.38830465 方差分析
方差分析（ANOVA）又称“变异数分析”或“F检验”，用于两个及两个以上样本均数差别的显著性检验。
5.1 单因素方差分析
从输出结果的F检验值来看，p<0.05比较显著，说明是否在查尔斯河对房价有影响。
## Df Sum Sq Mean Sq F value Pr(>F)
## housing$chas 1 1312 1312.1 15.97 7.39e-05 ***
## Residuals 504 41404 82.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 15.2 多因素方差分析
构建多因素方差分析，查看因子对房价的影响是否显著。
## Df Sum Sq Mean Sq F value Pr(>F)
## housing$crim 1 6441 6441 96.05 < 2e-16 ***
## housing$b 1 1697 1697 25.30 6.83e-07 ***
## housing$crim:housing$b 1 917 917 13.68 0.000241 ***
## Residuals 502 33662 67
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1