R语言对红酒各因素进行探索性分析
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红酒之间各元素相关性分析
knitr::opts_chunk$set(echo=FALSE, warning=FALSE, message=FALSE)
数据集介绍
本数据分析的是红酒葡萄质量，这个数据集包含1,599种红酒，以及 11 个关于酒的化学成分的变量。至少3名葡萄酒专家对每种酒的质量进了评分，分数在0（常差）和10（常好）之间。
现在我们导入数据集
library(ggplot2)
library(dplyr)
library(knitr)
library(GGally)
wine <- read.csv('D:\\wineQualityReds.csv')
对数据集变量介绍
该数据集一共包含13个变量
对各变量分别进行介绍：
fixed.acidity：该变量指的是葡萄酒中的固定或者非挥发性酸度
volatile.acidity：挥发酸，葡萄酒中的醋酸含量过高，会导致醋的味道不愉快。
citric.acid：柠檬酸，柠檬酸含量小，能给葡萄酒增添新鲜感和风味。
residual.sugar：剩余糖分，发酵结束后剩下的糖分，很少发现低于1克/升的葡萄酒，超过45克/升的葡萄酒被认为是甜的。
chlorides：酒中的盐量。
free.sulfur.dioxide：酒中带硫元素的离子，它可以防止微生物的生长和葡萄酒的氧化。
total.sulfur.dioxide:二氧化硫，低浓度时检测不到，当浓度超过50 ppm时用鼻子可以闻到。
density：密度，大致接近于水，具体取决于酒精和糖的含量。
pH：用于描述酒的酸碱度。
sulphates：硫酸盐，葡萄酒的添加剂，用于控制二氧化硫比例。
alcohol：酒中的酒精浓度。
quality：酒的质量，从0到10分不等。
单变量分析
qplot(x= quality, data= wine)
我们对红酒数量分析发现，市场质量特别好的红酒和质量特比差的红酒数量都相对较少，更多的是质量中等的红酒。不同质量的红酒基本满足正态分布。
qplot(x= residual.sugar, data= wine)
对红酒甜度分析发现，普遍红酒甜度都很低，甜度较高的红酒相对稀少，甜度极高的红酒极度稀少。
qplot(x= alcohol, data= wine)+
scale_x_continuous(breaks = seq(8,15,1))
对红酒的酒精含量分析发现，红酒酒精含量普遍不高，大概在9%~12%之间。
qplot(x= pH, data= wine)
对红酒pH分析发现，pH主要集中在3.0~3.5之间，可见大部分红酒是弱酸性的，因为红酒是葡萄发酵酿制而成，事实上根据常识也不难得出此结论。
qplot(volatile.acidity, data= wine)+
scale_x_continuous(breaks = seq(0,1.6,0.2))
从图中可以看出，红酒的柠檬酸的含量普遍比较集中，大致在0.2~0.8左右。
qplot(fixed.acidity, data= wine)+
scale_x_continuous(breaks = seq(4,16,2))
从图中可以看出，红葡萄酒中非挥发性酸相对分散一些，主要集中在6~10之间。
qplot(volatile.acidity, data = wine)+
scale_x_continuous(breaks = seq(0,1.2,0.2))
从图中可以看出红葡萄酒中挥发性酸主要集中在0.2~0.8之间。
qplot(density, data = wine)
从图中可以看出红葡萄酒的密度与水十分接近，尽可能存在微小的差距。
qplot(alcohol, data = wine)+
scale_x_continuous(breaks = seq(8,14,1),
limits = c(8,14))
分析发现酒精含量主要在9%~12%之间，酒精含量过低的酒和酒精含量过高的酒都十分罕见。
summary(wine$alcohol)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.50 10.20 10.42 11.10 14.90
分析红酒含量的均值和中位数也可以发现，均值为10.42，中位数为10.2，酒精含量最高值为14.9，最低值为8.4。可见红酒中酒精含量分布比较紧凑。红酒属于酒精含量较低的酒类。
qplot(sulphates, data = wine)+
scale_x_continuous(breaks = seq(0.3,1.2,0.1),
limits = c(0.3,1.2))
分析发现，红酒中的硫酸盐添加剂主要分布在0.4~0.8之间，近似于正太分布。
qplot(quality , data =wine)
![这里写图片描述](data:image/png;base64,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