정보의 시각화: 첫인상 * {{:info.vis.01.xlsx}} ====== Charts ====== {{what.is.stats.jpg?600}} * 모은 데이터를 분석하는 한 방법 * 상황을 파악하고 결론을 내려 결정을 (decision making) 할 수 있도록 한다. * 그러나, 데이터의 시각화에는 많은 허점이 따른다. {{mis.presentation.vis.jpg?500}} {{what.is.wrong.vis.jpg?500}} * the same data * different axis ====== Pie Chart ====== {{good.pie.chart.jpg}} Good to go with * frequency data for categories which should add up to 100 percent ---- Better {{better.pie.chart.jpg}} * side note for actual numbers and * table ---- Bad {{bad.pie.chart.jpg?350}} * 각 게임 장르별 사용자의 만족도 퍼센티지를 모아 놓은 파이차트는 유용하지 않다. ====== Bar chart ====== {{good.bar.chart.jpg?600}} * region 별 sales * 대륙 별 sales * 분기 별 수익률 * 카테고리화한 종류 별 숫자기록 (일반화) {{good.bar.chart.2.png?600}} * 장르 별 만족도 * (우리 회사) 부서별 성취도 ====== 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 | {{:b:head_first_statistics:pasted:20240904-082648.png}} 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) {{:b:head_first_statistics:pasted:20240904-082258.png}} ====== 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 {{:c:ps1-1:2019:pasted:20190909-103341.png}} # Simple Scatterplot attach(mtcars) plot(wt, mpg, main="Scatterplot Example", xlab="Car Weight ", ylab="Miles Per Gallon ", pch=19) {{:b:head_first_statistics:pasted:20240904-083016.png}} 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) {{:b:head_first_statistics:pasted:20240904-083157.png}} Outlier에 대한 주의 [{{:pearson-6.png? |}}] ====== 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$estimate["shape2"] # 3. curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), add = TRUE, col = "red", lwd = 2) {{:b:head_first_statistics:pasted:20250903-074821.png}} set.seed(1) data <- rbeta(500, shape1 = 10, shape2 = 10) hist(data, probability = TRUE, main = "Histogram with Normal Distribution Data", xlab = "Value", ylab = "Density", col = "lightblue", border = "white") # 2. # install.packages("fitdistrplus") library(fitdistrplus) fit <- fitdist(data, "beta") alpha_est <- fit$estimate["shape1"] beta_est <- fit$estimate["shape2"] # 3. curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), add = TRUE, col = "red", lwd = 2) {{:b:head_first_statistics:pasted:20250903-074830.png}} ## # right-skewed distribution # 1. set.seed(1) data <- rbeta(500, shape1 = 2, shape2 = 10) hist(data, probability = TRUE, main = "Histogram with Right-skewed Distribution", xlab = "Value", ylab = "Density", col = "lightblue", border = "white") # install.packages("fitdistrplus") library(fitdistrplus) fit <- fitdist(data, "beta") alpha_est <- fit$estimate["shape1"] beta_est <- fit$estimate["shape2"] # curve(dbeta(x, shape1 = alpha_est, shape2 = beta_est), add = TRUE, col = "red", lwd = 2) {{:b:head_first_statistics:pasted:20250903-082513.png}} ====== 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) {{:b:head_first_statistics:pasted:20250903-083409.png}} 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) {{:b:head_first_statistics:pasted:20250903-083524.png}} ### 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) {{:b:head_first_statistics:pasted:20250903-082247.png}} ====== 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") {{:c:ps1-1:2019:pasted:20190909-111438.png}} ====== see also ====== https://r-graph-gallery.com/