b:head_first_statistics:visualization
Table of Contents
정보의 시각화: 첫인상
Charts
- 모은 데이터를 분석하는 한 방법
- 상황을 파악하고 결론을 내려 결정을 (decision making) 할 수 있도록 한다.
- 그러나, 데이터의 시각화에는 많은 허점이 따른다.
- the same data
- different axis
Pie Chart
Good to go with
- frequency data for categories which should add up to 100 percent
- side note for actual numbers and
- table
- 각 게임 장르별 사용자의 만족도 퍼센티지를 모아 놓은 파이차트는 유용하지 않다.
Bar chart
Histogram
ser | freq |
---|---|
1 | 100 |
2 | 88 |
3 | 159 |
4 | 201 |
5 | 250 |
6 | 250 |
7 | 254 |
8 | 288 |
9 | 356 |
10 | 380 |
11 | 430 |
12 | 450 |
13 | 433 |
14 | 543 |
15 | 540 |
16 | 570 |
17 | 450 |
18 | 433 |
19 | 543 |
20 | 690 |
21 | 640 |
22 | 720 |
23 | 777 |
24 | 720 |
25 | 880 |
26 | 900 |
Excel에서의 histogram
Bin | Frequency |
199 | 3 |
399 | 7 |
599 | 9 |
799 | 5 |
999 | 2 |
in R . . . .
dat <- c(100, 88, 159, 201, 250, 250, 254, 288, 356, 380, 430, 450, 433, 543, 540, 570, 450, 433, 543, 690, 640, 720, 777, 720, 880, 900) dat hist(dat) hist(dat, breaks=5)
Scatter plot
hist(mtcars$hp) mpg cyl disp hp drat wt qsec vs am gear carb Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4 Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4 Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1 Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1 Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2 Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1 Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4 Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2 Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2 Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4 Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4 Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3 Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3 Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3 Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4 Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4 Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4 Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1 Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2 Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1 Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1 Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2 AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2 Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4 Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2 Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1 Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2 Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2 Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4 Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6 Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8 Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
# Simple Scatterplot attach(mtcars) plot(wt, mpg, main="Scatterplot Example", xlab="Car Weight ", ylab="Miles Per Gallon ", pch=19)
explanatory (설명) variable at x axis
response (반응) at y axis
But, it does mean no causal relationship between the two variables. Association between two does not guarantee a causal relationship.
Drawing a line among the data.
# Add fit lines abline(lm(mpg~wt), col="red") # regression line (y~x)
Outlier에 대한 주의
Presentation
For a very good example, see
https://www.gapminder.org/answers/how-does-income-relate-to-life-expectancy/
- Life expectancy data: life.exp.csv
Histogram skewedness
#### # left-skewed distribution # 1. set.seed(1) data <- rbeta(500, shape1 = 10, shape2 = 2) hist(data, probability = TRUE, main = "Histogram with Left-skewed data", xlab = "Value", ylab = "Density", col = "lightblue", border = "white") # 2. # install.packages("fitdistrplus") library(fitdistrplus) fit <- fitdist(data, "beta") alpha_est <- fit$estimate["shape1"] beta_est <- fit$estimate["shape2"] # 3. curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), add = TRUE, col = "red", lwd = 2)
set.seed(1) data <- rbeta(500, shape1 = 10, shape2 = 10) hist(data, probability = TRUE, main = "Histogram with Normal Distribution Data", xlab = "Value", ylab = "Density", col = "lightblue", border = "white") # 2. # install.packages("fitdistrplus") library(fitdistrplus) fit <- fitdist(data, "beta") alpha_est <- fit$estimate["shape1"] beta_est <- fit$estimate["shape2"] # 3. curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), add = TRUE, col = "red", lwd = 2)
## # right-skewed distribution # 1. set.seed(1) data <- rbeta(500, shape1 = 2, shape2 = 10) hist(data, probability = TRUE, main = "Histogram with Right-skewed Distribution", xlab = "Value", ylab = "Density", col = "lightblue", border = "white") # install.packages("fitdistrplus") library(fitdistrplus) fit <- fitdist(data, "beta") alpha_est <- fit$estimate["shape1"] beta_est <- fit$estimate["shape2"] # curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), add = TRUE, col = "red", lwd = 2)
Histogram Modality
Unimodal
### unimodal data set.seed(1) d.1 <- rnorm(500, 10, 2) hist(d.1, breaks = 30, probability = T, main = "Hist with Unimodal distrib", xlab = "Value", ylab = "Density", col = "lightblue", border = "black") lines(density(d.1), col = "darkred", lwd = 2)
Bimodal distribution
### bimodal data set.seed(1) d.1 <- rnorm(500, 10, 2) d.2 <- rnorm(500, 20, 2) d.all <- c(d.1, d.2) hist(d.all, breaks = 30, probability = T, main = "Hist with bimodal distrib", xlab = "Value", ylab = "Density", col = "lightblue", border = "black") lines(density(d.all), col = "darkred", lwd = 2)
### multi-modal data # Parameters for the first normal distribution (Mode 1) m.1 <- 50 sd.1 <- 5 # Parameters for the second normal distribution (Mode 2) m.2 <- 100 sd.2 <- 8 m.3 <- 160 sd.3 <- 6 # Mixing proportion for Mode 1 prop.1 <- 0.3 # Mixing proportion for Mode 2 prop.2 <- 0.4 # This is 1 - prop1 # Mixing proportion for Mode 2 prop.3 <- 0.3 # This is 1 - prop1 # Number of samples to generate n.sam <- 1000 # Create an empty vector to store the combined samples mm.dist <- numeric(n.sam) set.seed(1) for (i in 1:n.sam) { # Randomly choose which distribution to sample from tmp <- runif(1) if (tmp < prop.1) { mm.dist[i] <- rnorm(1, mean = m.1, sd = sd.1) } else if (tmp < prop.2) { mm.dist[i] <- rnorm(1, mean = m.2, sd = sd.2) } else { mm.dist[i] <- rnorm(1, mean = m.3, sd = sd.3) } } hist(mm.dist, breaks = 30, main = "Multimodal Distribution", xlab = "Value", ylab = "Density", freq = FALSE, probability = T, col = "lightblue", border = "black") lines(density(mm.dist), col = "darkred", lwd = 2)
box plot
# Boxplot of MPG by Car Cylinders boxplot(mpg~cyl,data=mtcars, main="Car Milage Data", xlab="Number of Cylinders", ylab="Miles Per Gallon")
see also
b/head_first_statistics/visualization.txt · Last modified: 2025/09/03 08:44 by hkimscil