barplot(apply(data,1,mean))#按行做均值条形图
多元数据直观表示+线性回归分析
1 多元数据直观表示
1.1 各省消费项目均值条形图
省份过多，各省的名称均不能全部显示
将横轴左边旋转90度，各省的名称均可显示
barplot(apply(data,1,mean),las=3)#按行做均值条形图
利用ggplot2包作图较为美观
data %>%
mutate(Average_Consumption = rowMeans(select(., -1), na.rm = TRUE)) %>%
ggplot(aes(x = reorder(row.names(data), -Average_Consumption), y = Average_Consumption)) +
geom_bar(stat = "identity", position = position_dodge(), colour = "black", fill = "steelblue") +
labs(title = "各省消费项目均值条形图", x = "", y = "均值") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 90, hjust = 1)) 
1.2 各消费项目均值条形图
按消费项目做均值图条形图
barplot(apply(data,2,mean))#按列做均值图条形图
对不同项目的条形添加不同颜色
barplot(apply(data,2,mean),col=1:8) #按列做彩色均值图条形图
去掉食品列后的数据按列做均值条形图
barplot(apply(data[,2:8],2,mean))
按消费项目做中位数条形图
barplot(apply(data,2,median))
利用ggplot作均值条形图
data %>% summarise(across(everything(), mean, na.rm = TRUE)) %>%
pivot_longer(cols = everything(), names_to = "Consumption_Type", values_to = "Average") %>%
mutate(
Consumption_Type=factor(Consumption_Type,level=c('食品','衣着','设备','医疗','交通','教育','居住','杂项')),
) %>%
ggplot(aes(x = Consumption_Type, y = Average, fill = Consumption_Type)) +
geom_bar(stat = "identity", position = position_dodge(), colour = "black") +
theme_minimal() +
labs(title = "各消费项目均值条形图", x = "类别", y = "均值",fill = "消费种类")Warning: There was 1 warning in `summarise()`.
ℹ In argument: `across(everything(), mean, na.rm = TRUE)`.
Caused by warning:
! The `...` argument of `across()` is deprecated as of dplyr 1.1.0.
Supply arguments directly to `.fns` through an anonymous function instead.
# Previously
across(a:b, mean, na.rm = TRUE)
# Now
across(a:b, \(x) mean(x, na.rm = TRUE))
使各条形的颜色相同
data %>% summarise(across(everything(), mean, na.rm = TRUE)) %>%
pivot_longer(cols = everything(), names_to = "Consumption_Type", values_to = "Average") %>%
mutate(
Consumption_Type=factor(Consumption_Type,level=c('食品','衣着','设备','医疗','交通','教育','居住','杂项')),
) %>%
ggplot(aes(x = Consumption_Type, y = Average)) +
geom_bar(stat = "identity", position = position_dodge(), colour = "black", fill = "steelblue") +
theme_minimal() +
labs(title = "各消费项目均值条形图", x = "类别", y = "均值")
1.3 各消费项目箱线图
boxplot函数直接作箱线图，默认每个变量（列）作一个箱线，并将全部变量的箱线在同一个图中展示。
boxplot(data)#按列做箱线图
boxplot(data,horizontal=T,las=1)#箱线图中图形按水平放置
利用ggplot函数作箱线图，需要对数据转化为长结果数据
data %>% pivot_longer(cols = 1:8, names_to = "Consumption_Type", values_to = "Value") %>%
mutate(
Consumption_Type=factor(Consumption_Type,level=c('食品','衣着','设备','医疗','交通','教育','居住','杂项')),
) %>%
ggplot(aes(x = Consumption_Type, y = Value)) +
geom_boxplot() +
labs(title = "各消费项目箱线图", x = "", y = "消费水平") +
theme_minimal() # + coord_flip() 
1.4 各消费项目星相图
stars(data)
stars(data,key.loc=c(17,5))
stars(data,full=F,key.loc=c(17,5))
绘制彩色全圆星相图
stars(data,draw.segments=T,key.loc=c(17,5))
绘制彩色半圆星相图
stars(data,full=F,draw.segments=T,key.loc=c(17,5))
1.5 各消费项目脸谱图
绘制彩色脸谱图
aplpack::faces(data)
effect of variables:
modified item Var
"height of face " "食品"
"width of face " "衣着"
"structure of face" "设备"
"height of mouth " "医疗"
"width of mouth " "交通"
"smiling " "教育"
"height of eyes " "居住"
"width of eyes " "杂项"
"height of hair " "食品"
"width of hair " "衣着"
"style of hair " "设备"
"height of nose " "医疗"
"width of nose " "交通"
"width of ear " "教育"
"height of ear " "居住"aplpack::faces(data[,2:8],ncol.plot=7)
effect of variables:
modified item Var
"height of face " "衣着"
"width of face " "设备"
"structure of face" "医疗"
"height of mouth " "交通"
"width of mouth " "教育"
"smiling " "居住"
"height of eyes " "杂项"
"width of eyes " "衣着"
"height of hair " "设备"
"width of hair " "医疗"
"style of hair " "交通"
"height of nose " "教育"
"width of nose " "居住"
"width of ear " "杂项"
"height of ear " "衣着"选取北京、上海、广州、甘肃、青海、宁夏六个脸谱图进行对比，以更清楚地知道每个省的差异
aplpack::faces(data[c(1,9,19,28,29,30),])
effect of variables:
modified item Var
"height of face " "食品"
"width of face " "衣着"
"structure of face" "设备"
"height of mouth " "医疗"
"width of mouth " "交通"
"smiling " "教育"
"height of eyes " "居住"
"width of eyes " "杂项"
"height of hair " "食品"
"width of hair " "衣着"
"style of hair " "设备"
"height of nose " "医疗"
"width of nose " "交通"
"width of ear " "教育"
"height of ear " "居住"TeachingDemos::faces2(data,ncols=7)
1.6 各消费项目雷达图
ggplot2的扩展包ggiraphExtra能作雷达图
data[c(1,9,19,28,29,30),] %>%
mutate(省份=rownames(.)) %>%
ggRadar(aes(group = 省份)) 
1.7 各消费项目调和曲线图
引用msaR.R函数做调和曲线图
source("msaR.R")
msa.andrews(data)
选取北京、上海、广东、甘肃、青海、宁夏六个省份的调和曲线作图，更简明的看出每个省的差异
msa.andrews(data[c(1,9,19,28,29,30),])
使用andrews包绘制标准化后的无图例调和曲线图
library(andrews)See the package vignette with `vignette("andrews")`andrews(data,clr=5,ymax=6)
andrews(data[c(1,9,19,28,29,30),],clr=5,ymax=6)
2 线性回归分析
2.1 一元线性回归2-1
每周加班工作时间(x)与签发新保单数目(y)呈明显正相关
每周加班工作时间(x)与签发新保单数目(y)的相关系数为0.95 。
利用每周加班工作时间(x)对签发新保单数目(y)作回归，回归方程为
\[ \widehat{y} =46.15+251.17\times x\]
随机误差\(\epsilon\)的标准差\(\sigma\)的估计值为127.06
2.2 多元线性回归2-2
利用广告预算(x1)和销售代理数目(x2)对年销售额(y)作回归，回归方程为：
term estimate std.error statistic p.value (Intercept) -22.74 30.69 -0.74 0.49 x1 0.15 0.11 1.33 0.24 x2 1.22 1.31 0.93 0.40 \[ \widehat{y} =-22.74+0.15\times x1+1.22\times x2\]
5%显著水平下，广告预算(x1)和销售代理数目(x2)的系数均不显著。
广告预算(x1)与销售额(y)相关系数为0.5797；销售代理数目(x2)与销售额(y)相关系数为0.4816 ；广告预算(x1)和销售代理数目(x2)与年销售额(y)的复相关系数为0.6586 。
2.3 多元线性回归2-3
从回归方程中可得出，在0.05的显著性水平下，年龄对起始工资的影响并不显著，而GPA对起始工资的影响显著较年龄更明显，说明在年龄不变的情况下，GPA每增加1单位，起始工资增加3295.67元
term estimate std.error statistic p.value (Intercept) -5213.1 12704.5 -0.41 0.70 GPA 8508.8 2721.6 3.13 0.03 年龄 181.6 283.5 0.64 0.55 \[ \widehat{起始工资} =-5213.12+8508.79\times GPA+181.58\times 年龄\]
从回归分析的结果得出，模型的修正后的R^2系数为53.5%，在0.05的显著性水平下，该模型F检验不能通过，即模型整体不显著。
summary(model_fit)Call: lm(formula = 起始工资 ~ ., data = data) Residuals: 1 2 3 4 5 6 7 8 1617 207 1282 -704 -2215 -770 -311 893 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -5213 12704 -0.41 0.699 GPA 8509 2722 3.13 0.026 * 年龄 182 284 0.64 0.550 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 1500 on 5 degrees of freedom Multiple R-squared: 0.668, Adjusted R-squared: 0.535 F-statistic: 5.02 on 2 and 5 DF, p-value: 0.0637当GPA=3,年龄=24，起始工资的预测值为2.4671^{4} 。
2.4 线性模型选择2-4
用货运总量(y)、工业总产值(x1)、农业总产值(x2)、居民非商品支出(x3)构造出来的相关系数矩阵为：
y x1 x2 x3 y 1.000 0.556 0.731 0.724 x1 0.556 1.000 0.113 0.398 x2 0.731 0.113 1.000 0.547 x3 0.724 0.398 0.547 1.000散点图矩阵为：
回归方程为：
\[ \widehat{y} =-348.28+3.75\times x1+7.1\times x2+12.45\times x3\]
回归模型的R方为：0.8055 ，说明该模型的拟合效果好
回归模型F检验说明 ，t检验说明在0.05的显著性水平下，x1与x3对y的影响不显著，而x2对y的影响显著
Call: lm(formula = y ~ ., data = data) Residuals: Min 1Q Median 3Q Max -25.20 -17.03 2.63 11.68 33.23 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -348.28 176.46 -1.97 0.096 . x1 3.75 1.93 1.94 0.100 x2 7.10 2.88 2.47 0.049 * x3 12.45 10.57 1.18 0.284 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 23.4 on 6 degrees of freedom Multiple R-squared: 0.806, Adjusted R-squared: 0.708 F-statistic: 8.28 on 3 and 6 DF, p-value: 0.0149剔除不显著的x1与x3后，回归模型为:y=-159.93+9.69x2
Call: lm(formula = y ~ x2, data = data) Residuals: Min 1Q Median 3Q Max -56.07 -18.79 5.81 25.50 32.38 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -159.93 129.71 -1.23 0.253 x2 9.69 3.20 3.03 0.016 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 31.4 on 8 degrees of freedom Multiple R-squared: 0.534, Adjusted R-squared: 0.476 F-statistic: 9.16 on 1 and 8 DF, p-value: 0.0164逐步回归的选择的模型为
Start: AIC=65.98 y ~ x1 + x2 + x3 Df Sum of Sq RSS AIC <none> 3297 66.0 - x3 1 762 4059 66.1 - x1 1 2072 5369 68.9 - x2 1 3340 6637 71.0Call: lm(formula = y ~ x1 + x2 + x3, data = data) Coefficients: (Intercept) x1 x2 x3 -348.28 3.75 7.10 12.45