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
1、全角星相图，具有图例
stars(data,full = T,key.loc = c(18,6))
2、半角星相图，带图例
stars(data,full = F,key.loc = c(17,9))
3、圆形星相图，带有图例和色彩
stars(data,full = T,draw.segments=T,key.loc = c(17,9))
4、半圆星相图，带有图例和色彩
stars(data,full = F,draw.segments=T,key.loc = c(17,9))
5、星相图的每个角表示一个变量，从图中可以看出北京上海，广东，浙江这四个地区的各项消费较为突出
1.5 各消费项目脸谱图
1、彩色脸谱图，每行7个脸谱（下载包aplpack）
install.packages("aplpack")Warning: package 'aplpack' is in use and will not be installedlibrary(aplpack)
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"2、去掉第一个变量做彩色脸谱图
aplpack::faces(data[,2:8])
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"3、选择第1、7、9、19个脸谱
aplpack::faces(data[c(1,7,9,19),])
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"4、黑白脸谱图
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
1、改进调和曲线
msa.andrews(data)
2、选取第1，8，19个观测调和曲线
msa.andrews(data[c(1,8,19),])
2 线性回归分析
2.1 一元线性回归2-1
Warning: package 'readxl' was built under R version 4.3.3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0.949 。
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
5、x与y的决定系数：
R2=summary(model_fit2)$r.sq
R2[1] 0.90056、方差分析
anova(model_fit2)Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x 1 1168713 1168713 72.4 2.8e-05 ***
Residuals 8 129147 16143
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 17、残差图分析
e=resid(model_fit2) #计算残差
plot(model_fit2) #普通残差与拟合值的残差图、QQ残差图、位置图、残差杠杆图
残差图1折线较平缓，模型拟合效果较好；图2中的点落在45度直线上，说明模型满足正态假设；图3中的折线较曲折，无法确定模型满足同方差假设；图4检验是否有异常值，由图可知，三点都在0.5“等高线”内，所以数据没有极端值点。
8、计算y=1000时，x的值 模型：y =46.15+251.17x 当y=1000时，计算得x=3.798小时
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 \[ \widehat{y} =-22.74+0.15\times x1+1.22\times x2\]
y}=-22.74+0.15x1+1.22x2,模型系数表示每增加1千元广告预算，年销售额增加15万元；每增加一个销售代理数，年销售额增加122万元
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。
summary(model_fit3)
Call:
lm(formula = y ~ x1 + x2, data = data3)
Residuals:
1 2 3 4 5 6 7 8
-1.134 -3.943 -0.652 15.670 -0.594 2.718 -16.275 4.209
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -22.745 30.694 -0.74 0.49
x1 0.151 0.113 1.33 0.24
x2 1.217 1.309 0.93 0.40
Residual standard error: 10.5 on 5 degrees of freedom
Multiple R-squared: 0.434, Adjusted R-squared: 0.207
F-statistic: 1.92 on 2 and 5 DF, p-value: 0.241- 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0.4338 。
2.3 多元线性回归2-3
1、回归模型
model_fit5 <- lm(起始工资 ~ GPA+年龄, data5)
lm_eq(model_fit5)$$ \widehat{起始工资} =-5213.12+8508.79\times GPA+181.58\times 年龄$$系数1表示每增加一个单位的GPA，起始工资增加8508.79元；第二个系数表示每增加一岁，起始工资增加181.58元
2、summary
summary(lm(起始工资 ~ GPA+年龄, data5))
Call:
lm(formula = 起始工资 ~ GPA + 年龄, data = data5)
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: 0.0637GPA系数的p值小于0.05，说明该GPA对起始工资有显著影响；而年龄的系数p值大于0.05，说明年龄对起始工资影响不显著。
2.4 线性模型选择2-4
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)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 ，说明模型的拟合优度较好。
回归模型F检验说明所有系数对模型显著。 t检验说明：x2的系数p值小于0.05，系数显著，即农业总产值x2对货运总量影响显著。
Call: lm(formula = y ~ ., data = data4) 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,x3后，回归模型为
$$ \widehat{y} =-159.93+9.69\times x2$$Call: lm(formula = y ~ x2, data = data4) 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 y=-348.28+3.75x1+7.1x2+12.45x3
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 = data4) Coefficients: (Intercept) x1 x2 x3 -348.28 3.75 7.10 12.45