学生成绩分析实例
读入学生成绩
#setwd("E:\\DataAnalysis")
scores <- read.table("scores.txt", header=TRUE, row.names="num")
head(scores)
## class chn math eng phy chem politics bio history geo pe
## 158 3 99 120 114.0 70.0 49.50 50.0 49.0 48.5 49.5 60
## 442 7 107 120 118.5 68.6 43.00 49.0 48.5 48.5 49.0 56
## 249 4 98 120 116.0 70.0 47.50 47.0 49.0 47.5 49.0 60
## 573 9 102 113 111.5 70.0 47.00 49.0 49.0 49.0 49.5 60
## 310 5 103 120 111.5 70.0 44.75 46.5 48.0 48.0 48.0 60
## 613 10 98 120 113.0 70.0 46.75 47.5 47.5 47.0 48.5 60
str(scores)
## 'data.frame': 599 obs. of 11 variables:
## $ class : int 3 7 4 9 5 10 8 2 5 9 ...
## $ chn : num 99 107 98 102 103 ...
## $ math : int 120 120 120 113 120 120 120 117 120 118 ...
## $ eng : num 114 118 116 112 112 ...
## $ phy : num 70 68.6 70 70 70 70 68.6 70 64.4 66.5 ...
## $ chem : num 49.5 43 47.5 47 44.8 ...
## $ politics: num 50 49 47 49 46.5 47.5 46.5 50 49 47.5 ...
## $ bio : num 49 48.5 49 49 48 47.5 47.5 48 48.5 48.5 ...
## $ history : num 48.5 48.5 47.5 49 48 47 47.5 48 47.5 46.5 ...
## $ geo : num 49.5 49 49 49.5 48 48.5 48 48.5 49 49.5 ...
## $ pe : int 60 56 60 60 60 60 60 56 56 52 ...
names(scores)
## [1] "class" "chn" "math" "eng" "phy" "chem"
## [7] "politics" "bio" "history" "geo" "pe"
attach(scores)
给出数据的概略信息
summary(scores)
## class chn math eng
## Min. : 1.000 Min. : 26.50 Min. : 3.00 Min. : 15.00
## 1st Qu.: 3.000 1st Qu.: 78.25 1st Qu.: 84.00 1st Qu.: 74.00
## Median : 6.000 Median : 84.00 Median :100.00 Median : 93.00
## Mean : 5.519 Mean : 83.24 Mean : 93.98 Mean : 85.55
## 3rd Qu.: 8.000 3rd Qu.: 89.00 3rd Qu.:111.00 3rd Qu.:103.50
## Max. :10.000 Max. :107.00 Max. :120.00 Max. :118.50
## phy chem politics bio
## Min. : 7.00 Min. : 8.00 Min. :15.0 Min. :14.00
## 1st Qu.:49.00 1st Qu.:27.75 1st Qu.:39.5 1st Qu.:40.00
## Median :58.80 Median :37.00 Median :43.5 Median :44.00
## Mean :54.15 Mean :34.63 Mean :42.0 Mean :42.17
## 3rd Qu.:64.40 3rd Qu.:42.50 3rd Qu.:45.5 3rd Qu.:46.00
## Max. :70.00 Max. :49.75 Max. :50.0 Max. :50.00
## history geo pe
## Min. : 8.00 Min. :10.50 Min. :48.00
## 1st Qu.:32.50 1st Qu.:43.00 1st Qu.:52.00
## Median :39.00 Median :45.50 Median :56.00
## Mean :36.82 Mean :43.92 Mean :53.86
## 3rd Qu.:43.00 3rd Qu.:47.00 3rd Qu.:56.00
## Max. :49.00 Max. :50.00 Max. :60.00
summary(scores$math)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.00 84.00 100.00 93.98 111.00 120.00
选择某行，求一个学生总分
child <- scores['239',]
sum(child)
## [1] 647.45
scores.class4 <- scores[class==4,] # 挑出4班的
求每个班的平均数学成绩
aver <- tapply(math, class, mean)
aver
## 1 2 3 4 5 6 7 8
## 92.82258 93.17241 88.58621 97.29688 97.89286 92.40678 90.29310 98.65000
## 9 10
## 94.35484 94.08065
画条曲线看看每个班的数学平均成绩
plot(aver, type='b', ylim=c(80,100), main="Average Of Math In Class", xlab="Class", ylab="Average Of Math")
unnamed-chunk-5-1.png
生成数据的二维列联表
table(math,class)
## class
## math 1 2 3 4 5 6 7 8 9 10
## 3 0 0 0 0 0 0 1 0 0 0
## 9 1 0 0 0 0 0 0 0 0 0
## 10 1 0 1 0 0 0 0 0 0 0
## 18 0 0 0 1 0 1 0 0 1 0
## 19 0 0 0 0 0 0 1 0 0 0
## 20 0 0 1 0 0 0 0 1 0 0
## 22 0 0 1 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0 0 1 0
## 26 0 0 0 1 0 0 0 0 0 0
## 29 0 0 0 0 0 0 0 1 0 0
## 32 0 0 1 0 0 0 0 0 0 0
## 34 0 0 0 0 0 1 0 0 0 0
## 35 0 0 0 1 1 0 0 0 0 1
## 36 0 0 1 0 0 1 1 0 0 0
## 38 0 0 0 0 0 0 1 0 0 0
## 40 1 0 0 0 0 0 0 0 1 0
## 41 0 0 0 1 0 0 0 0 0 1
## 42 0 0 0 0 1 0 0 0 0 1
## 43 0 0 1 0 0 0 0 0 0 0
## 44 0 0 0 0 0 0 0 0 0 1
## 45 0 0 0 0 0 0 1 0 0 1
## 46 0 1 0 0 0 0 0 0 0 0
## 47 0 1 1 0 1 1 2 0 0 0
## 49 0 0 0 0 0 0 0 0 0 1
## 51 0 1 0 0 0 0 0 0 0 0
## 52 0 0 0 1 0 0 0 0 0 0
## 53 0 0 1 0 0 0 0 0 0 0
## 56 0 1 0 0 0 0 0 0 0 1
## 57 0 1 1 0 0 0 0 0 1 0
## 58 2 1 0 0 0 0 0 0 0 0
## 59 1 0 0 1 1 2 0 0 0 1
## 60 0 1 2 0 0 0 1 0 0 0
## 61 0 1 0 0 0 0 0 0 0 0
## 62 1 0 0 0 0 0 0 0 0 0
## 63 0 1 1 0 0 0 0 0 0 1
## 64 0 0 0 0 0 0 0 0 1 0
## 65 1 0 0 0 0 0 0 0 1 1
## 66 0 0 0 0 0 1 0 2 0 0
## 67 0 0 0 0 0 0 2 0 2 0
## 68 0 0 0 0 0 1 0 0 1 0
## 69 2 0 0 0 0 1 2 0 1 0
## 70 0 0 0 0 2 0 1 0 1 1
## 71 0 0 1 0 0 0 0 1 0 0
## 72 0 1 0 0 0 0 1 2 1 1
## 73 2 1 0 0 0 1 0 0 0 0
## 74 0 0 0 1 1 0 1 0 0 1
## 75 0 1 1 0 0 2 0 0 1 1
## 76 0 0 1 0 0 1 0 0 1 0
## 77 0 0 1 0 0 0 1 0 0 0
## 78 0 0 0 0 2 1 1 1 0 0
## 79 1 0 0 0 0 1 1 0 1 0
## 80 0 1 1 2 0 0 0 0 0 1
## 81 0 0 0 0 0 1 1 0 1 0
## 82 0 2 0 1 0 1 0 0 1 1
## 83 2 0 0 1 0 1 0 0 1 1
## 84 0 1 1 0 0 1 0 1 1 0
## 85 0 1 1 0 0 0 0 1 0 2
## 86 0 0 1 1 0 1 0 0 1 0
## 87 0 0 1 1 1 2 0 1 0 0
## 88 0 1 0 0 0 0 1 0 1 3
## 89 2 2 0 2 0 0 0 3 1 0
## 90 3 0 1 1 1 0 3 1 1 1
## 91 1 0 0 0 0 3 0 1 1 0
## 92 2 0 0 1 2 0 0 0 1 0
## 93 0 3 1 0 3 1 1 2 0 0
## 94 1 0 0 1 3 1 1 0 2 0
## 95 3 0 1 3 0 2 1 3 1 2
## 96 0 1 2 3 0 0 2 3 1 1
## 97 2 2 2 0 2 1 2 1 0 2
## 98 3 2 2 1 1 3 1 2 0 0
## 99 2 2 1 1 1 0 0 2 0 0
## 100 1 4 1 1 2 2 3 1 2 0
## 101 2 1 1 0 1 1 0 2 1 1
## 102 0 1 4 3 0 0 0 1 2 2
## 103 0 0 0 3 0 2 1 1 0 0
## 104 2 3 0 2 1 0 0 0 0 3
## 105 3 1 2 1 2 0 0 2 0 2
## 106 1 4 0 1 3 1 2 1 1 2
## 107 3 0 2 1 0 2 0 1 0 1
## 108 0 0 3 1 5 0 0 0 3 1
## 109 1 1 3 1 5 1 2 1 1 0
## 110 1 1 0 2 1 0 2 1 0 1
## 111 3 2 0 5 2 2 3 0 4 2
## 112 1 1 4 3 5 0 3 0 2 1
## 113 2 2 0 2 0 1 0 1 3 3
## 114 1 0 0 1 1 2 2 2 2 2
## 115 2 2 1 4 0 3 0 2 1 2
## 116 0 0 1 0 1 1 2 3 3 2
## 117 1 3 2 1 0 1 1 3 0 4
## 118 3 0 1 2 2 4 2 3 3 0
## 119 0 1 0 2 0 0 0 2 2 1
## 120 1 1 2 2 2 3 4 4 3 4
求4班每一科的平均成绩
subjects <- c('chn','math','eng','phy','chem','politics','bio','history','geo','pe')
sapply(scores[class==4, subjects], mean)
## chn math eng phy chem politics bio history
## 83.10938 97.29688 85.60156 54.30469 34.67969 42.41406 41.79688 36.77344
## geo pe
## 44.24219 54.31250
求各班各科的平均成绩
aggregate(scores[subjects], by=list(class), mean)
## Group.1 chn math eng phy chem politics bio
## 1 1 82.98387 92.82258 92.45161 56.04516 34.95161 42.57258 42.29839
## 2 2 81.57759 93.17241 85.01724 54.39483 34.60776 43.13793 42.05172
## 3 3 82.62069 88.58621 82.46552 51.59483 32.33190 41.99138 41.59483
## 4 4 83.10938 97.29688 85.60156 54.30469 34.67969 42.41406 41.79688
## 5 5 84.74107 97.89286 83.66964 56.10000 33.91518 42.05357 42.57143
## 6 6 83.14407 92.40678 78.57627 51.74068 33.36864 40.64407 41.55932
## 7 7 83.01724 90.29310 87.00862 51.75172 33.98276 41.63793 42.51724
## 8 8 83.65833 98.65000 86.91667 56.02333 36.07917 41.70000 42.40833
## 9 9 83.20968 94.35484 86.48387 54.29516 36.11694 41.94355 42.72581
## 10 10 84.33871 94.08065 86.66774 55.08548 36.01210 41.86290 42.22581
## history geo pe
## 1 37.03226 43.44355 54.12903
## 2 38.59483 43.60345 54.68966
## 3 35.49138 42.97414 54.55172
## 4 36.77344 44.24219 54.31250
## 5 37.77679 43.96429 54.00000
## 6 34.46610 43.37288 53.22034
## 7 37.46552 44.22414 53.72414
## 8 37.84167 44.81667 52.93333
## 9 36.07258 44.30645 53.48387
## 10 36.78226 44.14516 53.61290
## aggregate
看看数学成绩的分布图
hist(math)
unnamed-chunk-9-1.png
默认是按频数形成的直方图，设置freq参数可以画密度分布图。
hist(math, freq=FALSE)
lines(density(math), col='blue')
rug(jitter(math))
unnamed-chunk-10-1.png
#轴须图，在轴旁边出现一些小线段，jitter是加噪函数
核密度图
plot(density(chn), col='blue', lwd=2)
lines(density(math), col='red', lwd=2)
unnamed-chunk-11-1.png
箱线图
boxplot(math)
unnamed-chunk-12-1.png
boxplot.stats(math)
## $stats
## [1] 44 84 100 111 120
##
## $n
## [1] 599
##
## $conf
## [1] 98.25696 101.74304
##
## $out
## [1] 38 42 35 40 43 36 41 40 36 18 26 36 42 32 41 29 18 24 10 20 34 19 10
## [24] 3 35 20 35 18 22 9
#这个函数可以看到画出箱线图的具体的数据值
并列箱线图，看各班的数据分布情况
boxplot(math ~ class, data=scores)
#Add Average
lines(tapply(math,class,mean), col='blue', type='b')
unnamed-chunk-13-1.png
可以看出2班没有拖后腿的，4班有6个拖后腿的
看看各科成绩的相关性
cor(scores[,subjects])
## chn math eng phy chem politics
## chn 1.0000000 0.6588126 0.7326778 0.6578172 0.6271155 0.7257003
## math 0.6588126 1.0000000 0.8079255 0.8860467 0.8304643 0.7090681
## eng 0.7326778 0.8079255 1.0000000 0.8170998 0.7868710 0.7498946
## phy 0.6578172 0.8860467 0.8170998 1.0000000 0.8615512 0.7081717
## chem 0.6271155 0.8304643 0.7868710 0.8615512 1.0000000 0.6441334
## politics 0.7257003 0.7090681 0.7498946 0.7081717 0.6441334 1.0000000
## bio 0.6902282 0.7951987 0.7731044 0.8077105 0.7578770 0.7071181
## history 0.6971145 0.7732791 0.7948219 0.8100599 0.7993298 0.7192860
## geo 0.6438662 0.7723853 0.7265406 0.7814152 0.7264814 0.6906930
## pe 0.2712453 0.3300249 0.3159347 0.3251233 0.2769066 0.3033607
## bio history geo pe
## chn 0.6902282 0.6971145 0.6438662 0.2712453
## math 0.7951987 0.7732791 0.7723853 0.3300249
## eng 0.7731044 0.7948219 0.7265406 0.3159347
## phy 0.8077105 0.8100599 0.7814152 0.3251233
## chem 0.7578770 0.7993298 0.7264814 0.2769066
## politics 0.7071181 0.7192860 0.6906930 0.3033607
## bio 1.0000000 0.7771735 0.8382525 0.2428081
## history 0.7771735 1.0000000 0.7731044 0.2708434
## geo 0.8382525 0.7731044 1.0000000 0.2605251
## pe 0.2428081 0.2708434 0.2605251 1.0000000
可以看出：数学和物理的相关性达88%，物理和化学成绩的相关性达86%。
画个图出来看看
pairs(scores[,subjects])
unnamed-chunk-15-1.png
详细看看数学和物理的线性相关性
cor_phy_math <- lm(phy ~ math, scores)
plot(math, phy)
abline(cor_phy_math)
unnamed-chunk-16-1.png
cor_phy_math
##
## Call:
## lm(formula = phy ~ math, data = scores)
##
## Coefficients:
## (Intercept) math
## 4.7374 0.5258
也就是说拟合公式为：phy = 0.5258 * math + 4.7374,为什么是0.52？因为数学最高分为120，物理最高分为70