Multiple regression-prectices
Jean Claude
2024-07-25
Load the necessary libraries
knitr::opts_chunk$set(echo = TRUE)#show code in the final document
library(knitr)#load for report generation
library(tinytex)#load to to compile latex and maths notations.pdfIn an R code Chunk, clear objects from work space, specify the path to your desired folder, import data, and check the structure of the variables in the data set
rm(list=ls())
# Clear a specific object
#rm(specific_object)
# Verify removal
#ls()
setwd("C:/Users/HP/Desktop/COMH 7066A Biostatistics for Health Researchers III/Week 1/4. Thursday")
library(readxl)
BCdata <- read_excel("BreastCancer.xlsx")
str(BCdata)## tibble [569 × 32] (S3: tbl_df/tbl/data.frame)
## $ id : num [1:569] 842302 842517 84300903 84348301 84358402 ...
## $ diagnosis : chr [1:569] "M" "M" "M" "M" ...
## $ radius_mean : num [1:569] 18 20.6 19.7 11.4 20.3 ...
## $ texture_mean : num [1:569] 10.4 17.8 21.2 20.4 14.3 ...
## $ perimeter_mean : num [1:569] 122.8 132.9 130 77.6 135.1 ...
## $ area_mean : num [1:569] 1001 1326 1203 386 1297 ...
## $ smoothness_mean : num [1:569] 0.1184 0.0847 0.1096 0.1425 0.1003 ...
## $ compactness_mean : num [1:569] 0.2776 0.0786 0.1599 0.2839 0.1328 ...
## $ concavity_mean : num [1:569] 0.3001 0.0869 0.1974 0.2414 0.198 ...
## $ concave points_mean : num [1:569] 0.1471 0.0702 0.1279 0.1052 0.1043 ...
## $ symmetry_mean : num [1:569] 0.242 0.181 0.207 0.26 0.181 ...
## $ fractal_dimension_mean : num [1:569] 0.0787 0.0567 0.06 0.0974 0.0588 ...
## $ radius_se : num [1:569] 1.095 0.543 0.746 0.496 0.757 ...
## $ texture_se : num [1:569] 0.905 0.734 0.787 1.156 0.781 ...
## $ perimeter_se : num [1:569] 8.59 3.4 4.58 3.44 5.44 ...
## $ area_se : num [1:569] 153.4 74.1 94 27.2 94.4 ...
## $ smoothness_se : num [1:569] 0.0064 0.00522 0.00615 0.00911 0.01149 ...
## $ compactness_se : num [1:569] 0.049 0.0131 0.0401 0.0746 0.0246 ...
## $ concavity_se : num [1:569] 0.0537 0.0186 0.0383 0.0566 0.0569 ...
## $ concave points_se : num [1:569] 0.0159 0.0134 0.0206 0.0187 0.0188 ...
## $ symmetry_se : num [1:569] 0.03 0.0139 0.0225 0.0596 0.0176 ...
## $ fractal_dimension_se : num [1:569] 0.00619 0.00353 0.00457 0.00921 0.00511 ...
## $ radius_worst : num [1:569] 25.4 25 23.6 14.9 22.5 ...
## $ texture_worst : num [1:569] 17.3 23.4 25.5 26.5 16.7 ...
## $ perimeter_worst : num [1:569] 184.6 158.8 152.5 98.9 152.2 ...
## $ area_worst : num [1:569] 2019 1956 1709 568 1575 ...
## $ smoothness_worst : num [1:569] 0.162 0.124 0.144 0.21 0.137 ...
## $ compactness_worst : num [1:569] 0.666 0.187 0.424 0.866 0.205 ...
## $ concavity_worst : num [1:569] 0.712 0.242 0.45 0.687 0.4 ...
## $ concave points_worst : num [1:569] 0.265 0.186 0.243 0.258 0.163 ...
## $ symmetry_worst : num [1:569] 0.46 0.275 0.361 0.664 0.236 ...
## $ fractal_dimension_worst: num [1:569] 0.1189 0.089 0.0876 0.173 0.0768 ...#assess missing
table(is.na(BCdata))##
## FALSE
## 18208table(is.na(BCdata$smoothness_se))##
## FALSE
## 569colSums(is.na(BCdata))## id diagnosis radius_mean
## 0 0 0
## texture_mean perimeter_mean area_mean
## 0 0 0
## smoothness_mean compactness_mean concavity_mean
## 0 0 0
## concave points_mean symmetry_mean fractal_dimension_mean
## 0 0 0
## radius_se texture_se perimeter_se
## 0 0 0
## area_se smoothness_se compactness_se
## 0 0 0
## concavity_se concave points_se symmetry_se
## 0 0 0
## fractal_dimension_se radius_worst texture_worst
## 0 0 0
## perimeter_worst area_worst smoothness_worst
## 0 0 0
## compactness_worst concavity_worst concave points_worst
## 0 0 0
## symmetry_worst fractal_dimension_worst
## 0 0summary(BCdata)#for each column## id diagnosis radius_mean texture_mean
## Min. : 8670 Length:569 Min. : 6.981 Min. : 9.71
## 1st Qu.: 869218 Class :character 1st Qu.:11.700 1st Qu.:16.17
## Median : 906024 Mode :character Median :13.370 Median :18.84
## Mean : 30371831 Mean :14.127 Mean :19.29
## 3rd Qu.: 8813129 3rd Qu.:15.780 3rd Qu.:21.80
## Max. :911320502 Max. :28.110 Max. :39.28
## perimeter_mean area_mean smoothness_mean compactness_mean
## Min. : 43.79 Min. : 143.5 Min. :0.05263 Min. :0.01938
## 1st Qu.: 75.17 1st Qu.: 420.3 1st Qu.:0.08637 1st Qu.:0.06492
## Median : 86.24 Median : 551.1 Median :0.09587 Median :0.09263
## Mean : 91.97 Mean : 654.9 Mean :0.09636 Mean :0.10434
## 3rd Qu.:104.10 3rd Qu.: 782.7 3rd Qu.:0.10530 3rd Qu.:0.13040
## Max. :188.50 Max. :2501.0 Max. :0.16340 Max. :0.34540
## concavity_mean concave points_mean symmetry_mean fractal_dimension_mean
## Min. :0.00000 Min. :0.00000 Min. :0.1060 Min. :0.04996
## 1st Qu.:0.02956 1st Qu.:0.02031 1st Qu.:0.1619 1st Qu.:0.05770
## Median :0.06154 Median :0.03350 Median :0.1792 Median :0.06154
## Mean :0.08880 Mean :0.04892 Mean :0.1812 Mean :0.06280
## 3rd Qu.:0.13070 3rd Qu.:0.07400 3rd Qu.:0.1957 3rd Qu.:0.06612
## Max. :0.42680 Max. :0.20120 Max. :0.3040 Max. :0.09744
## radius_se texture_se perimeter_se area_se
## Min. :0.1115 Min. :0.3602 Min. : 0.757 Min. : 6.802
## 1st Qu.:0.2324 1st Qu.:0.8339 1st Qu.: 1.606 1st Qu.: 17.850
## Median :0.3242 Median :1.1080 Median : 2.287 Median : 24.530
## Mean :0.4052 Mean :1.2169 Mean : 2.866 Mean : 40.337
## 3rd Qu.:0.4789 3rd Qu.:1.4740 3rd Qu.: 3.357 3rd Qu.: 45.190
## Max. :2.8730 Max. :4.8850 Max. :21.980 Max. :542.200
## smoothness_se compactness_se concavity_se concave points_se
## Min. :0.001713 Min. :0.002252 Min. :0.00000 Min. :0.000000
## 1st Qu.:0.005169 1st Qu.:0.013080 1st Qu.:0.01509 1st Qu.:0.007638
## Median :0.006380 Median :0.020450 Median :0.02589 Median :0.010930
## Mean :0.007041 Mean :0.025478 Mean :0.03189 Mean :0.011796
## 3rd Qu.:0.008146 3rd Qu.:0.032450 3rd Qu.:0.04205 3rd Qu.:0.014710
## Max. :0.031130 Max. :0.135400 Max. :0.39600 Max. :0.052790
## symmetry_se fractal_dimension_se radius_worst texture_worst
## Min. :0.007882 Min. :0.0008948 Min. : 7.93 Min. :12.02
## 1st Qu.:0.015160 1st Qu.:0.0022480 1st Qu.:13.01 1st Qu.:21.08
## Median :0.018730 Median :0.0031870 Median :14.97 Median :25.41
## Mean :0.020542 Mean :0.0037949 Mean :16.27 Mean :25.68
## 3rd Qu.:0.023480 3rd Qu.:0.0045580 3rd Qu.:18.79 3rd Qu.:29.72
## Max. :0.078950 Max. :0.0298400 Max. :36.04 Max. :49.54
## perimeter_worst area_worst smoothness_worst compactness_worst
## Min. : 50.41 Min. : 185.2 Min. :0.07117 Min. :0.02729
## 1st Qu.: 84.11 1st Qu.: 515.3 1st Qu.:0.11660 1st Qu.:0.14720
## Median : 97.66 Median : 686.5 Median :0.13130 Median :0.21190
## Mean :107.26 Mean : 880.6 Mean :0.13237 Mean :0.25427
## 3rd Qu.:125.40 3rd Qu.:1084.0 3rd Qu.:0.14600 3rd Qu.:0.33910
## Max. :251.20 Max. :4254.0 Max. :0.22260 Max. :1.05800
## concavity_worst concave points_worst symmetry_worst fractal_dimension_worst
## Min. :0.0000 Min. :0.00000 Min. :0.1565 Min. :0.05504
## 1st Qu.:0.1145 1st Qu.:0.06493 1st Qu.:0.2504 1st Qu.:0.07146
## Median :0.2267 Median :0.09993 Median :0.2822 Median :0.08004
## Mean :0.2722 Mean :0.11461 Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.3829 3rd Qu.:0.16140 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :1.2520 Max. :0.29100 Max. :0.6638 Max. :0.20750#Delete the ID variable from the data with date and etc.
BCdata <- BCdata[,-1]Tabulate the frequency of the categorical variable in the data and graphically visualize the categories. Also, assess the distribution of the continuous variables using both graphical and quantitative methods.
#Categorical variable
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
#convert the character format to factor and make a#Barplot for categorical variable
categorical <- BCdata[,1]
table(BCdata$diagnosis)##
## B M
## 357 212BCdata$diagnosis <- as.factor(BCdata$diagnosis)
#transform the factor
categorical <- categorical %>% #%>%=pipe operator to chain multiple operations
group_by_all() %>% #group data frame by its column values
summarise(COUNT = n())# calculate the count in each group
ggplot(categorical,aes(x=diagnosis,y=COUNT,fill=diagnosis,group=diagnosis))+ #add bar geometry to the plot
geom_bar(stat="identity",position=position_dodge())+ # count is default, we have used identity since we have y values and use position_doge since we do not want stack the bars
geom_text(aes(label = paste(COUNT)), size = 3.5, #add text annotation, paste the count on the plot with any size of your choice
position = position_dodge(0.85), vjust = -0.5)+ #align labels with bars anduse vertical adjustment to move the text above the plot
xlab("Diagnosis") + ylab("Count")
#visulise the distribution of the continous variables
cont <- BCdata[,c(2:31)]
cont2 <- data.frame(stack(cont)) # reshape to long format
ggplot(data = cont2, aes(x=ind, y=values)) +
geom_boxplot(fill="#f68060", alpha=.6, width=.8)+#alpha for transparency
theme(axis.text.x = element_text(angle = 90, hjust = 1))#use angle to set the text angle and hjust to adjust text
#reproduce boxplot for high and low values to clearly see the distribution
#
library(dplyr)
#identify highest maximum of each column
max <- BCdata %>% summarise_if(is.numeric, max)
#get their column number
which( colnames(BCdata)=="perimeter_mean")## [1] 4#reproduce for other cont. variables
cont3 <- BCdata[,c(6:11,16:20)]
cont4 <- data.frame(stack(cont3)) # reshape to long format
ggplot(data = cont4, aes(x=ind, y=values)) +
geom_boxplot(fill="#f68060", alpha=.2, width=.4)+
theme(axis.text.x = element_text(angle = 30, hjust = 1))