통계실습 I. 회귀분석, ARIMA 모형

# 통계실습 I. 회귀분석, ARIMA 모형
----
## **가천대 길병원 고급통계교육**
### 방태모
### 2022-06-14

---

# .brand-red[목차]

.font100[.content-box-red[1 회귀분석]]
  
  - 방법론 소개
  
  - 단순회귀모형
  
  - 실습: 단순회귀모형
  
  - 다중회귀모형
  
  - 실습: 다중회귀모형

]

.font100[.content-box-red[2 ARIMA 모형: 실제 사례 중심]]
 
 - 준비
 
 - 결측치 처리
 
 - 시계열 자료 다루기
 
 - 모형 적합
 
 - 예측
 
]

]

---

# 1 회귀분석

---

# .brand-red[방법론 소개]

- 데이터로부터 독립변수(또는 예측변수, `$x$`)들의 함수를 다음과 같이 추정하여 종속변수(또는 반응변수, `$y$`)를 예측하는 방법:

\begin{align} 
\hat{y} = f(x_1, x_2, \cdots, x_p). 
\end{align}

- 여기서 `$x = (x_1, x_2, \cdots, x_p)^{T}$`는 주어지는 값

- `$y$`는 주어진 `$x$`에서 측정되는 값으로 벡터로 주어질 수 있음

---

# .brand-red[단순회귀모형]

- 단순선형회귀(simple linear regression)는 예측변수와 종속변수가 모두 1개인 경우에 해당:

\begin{align} 
y = \beta_0 + \beta_1 x + \epsilon, \epsilon \sim N(0, \sigma^2). 
\end{align}

- 오차항 `$\epsilon_i \sim i.i.d \ N(0, \sigma^2)$` 에 관한 가정

- 정규성(Normality)
  
  - 독립성(Independent): `${\rm{Cov}}(\epsilon_{i}, \epsilon_{j}) = 0 (i \neq j)$`
  
  - 등분산성(Homoscedasticity): `${\rm{Var}}(\epsilon_{i}) = \sigma^2$`

---

# .brand-red[단순회귀모형]

]

<div class="figure">
<img src="./fig/simple.png" alt="fig 2. Simple linear regression" width="550" height="350" />
<p class="caption">fig 2. Simple linear regression</p>
</div>

]

\begin{align} 
\hat{y} = \hat{\beta}_0 + \hat{\beta}_1 x 
\end{align}

---

# .brand-red[실습: 단순회귀모형]

## 준비하기

- 패키지 설치

```r
install.packages("MASS")
install.packages("car")
install.packages("dplyr")
```

- 패키지 로딩

```r
library(MASS)
library(car)
library(dplyr)
```

---

# .brand-red[실습: 단순회귀모형]

## 데이터 소개

```r
head(cats, 4)
```
<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Sex </th>
   <th style="text-align:right;"> Bwt </th>
   <th style="text-align:right;"> Hwt </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> F </td>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:right;"> 7.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> F </td>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:right;"> 7.4 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> F </td>
   <td style="text-align:right;"> 2.0 </td>
   <td style="text-align:right;"> 9.5 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> F </td>
   <td style="text-align:right;"> 2.1 </td>
   <td style="text-align:right;"> 7.2 </td>
  </tr>
</tbody>
</table>

]

```r
glimpse(cats)
```

```
## Rows: 144
## Columns: 3
## $ Sex <fct> F, F, F, F, F, F, F, F, F, F, F, F, F, F, F, F, F, F, F, F, F, F, …
## $ Bwt <dbl> 2.0, 2.0, 2.0, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.2, 2…
## $ Hwt <dbl> 7.0, 7.4, 9.5, 7.2, 7.3, 7.6, 8.1, 8.2, 8.3, 8.5, 8.7, 9.8, 7.1, 8…
```
]

---

# .brand-red[실습: 단순회귀모형]

## 모형 적합

- {stats} 패키지의 `lm()`을 이용해 단순회귀모형 적합

```r
lm_mod <- lm(Hwt ~ Bwt, data = cats)
summary(lm_mod)
```

```
## 
## Call:
## lm(formula = Hwt ~ Bwt, data = cats)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5694 -0.9634 -0.0921  1.0426  5.1238 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -0.3567     0.6923  -0.515    0.607    
## Bwt           4.0341     0.2503  16.119   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.452 on 142 degrees of freedom
## Multiple R-squared:  0.6466,	Adjusted R-squared:  0.6441 
## F-statistic: 259.8 on 1 and 142 DF,  p-value: < 2.2e-16
```

]

---

# .brand-red[실습: 단순회귀모형]

## 회귀선 시각화

```r
plot(cats$Hwt ~ cats$Bwt, pch = 19, col = "darkgray")
abline(lm_mod, lwd = 2)
```

---

# .brand-red[실습: 단순회귀모형]

## 잔차분석: 등분산성, 정규성

- `$y$`와 `$x$` 간의 relationship에 관한 분석을 목적으로 선형회귀모형을 적합할 때는 잔차분석 필수

```r
par(mfrow = c(1, 2))
plot(lm_mod, 1)
plot(lm_mod, 2)
```

---

# .brand-red[실습: 단순회귀모형]

## 잔차분석: 이상점 체크

- 144번 자료에 대한 정보 확인

```r
cats[144, ]
```

```
##     Sex Bwt  Hwt
## 144   M 3.9 20.5
```
]

```r
lm_mod$fitted[144]
```

```
##      144 
## 15.37618
```

```r
lm_mod$residuals[144]
```

```
##      144 
## 5.123818
```
]

---

# .brand-red[실습: 단순회귀모형]

## 잔차분석: 독립성 검정

- Durbin-Watson Test를 이용한 잔차의 독립성 검정
  - 더빈-왓슨 테스트 통계량( `$d$` )는 `$0 < d < 4$` 사이의 값을 가짐
  - `$d \rightarrow 2$`: 자기상관이 존재하지 않음
  - `$d \rightarrow 0$` or `$d \rightarrow 4$`: 자기상관이 존재함

- {car} 패키지의 `durbinWatsonTest()`를 이용해 잔차에 대해 독립성 검정 수행

```r
residuals(lm_mod) |> 
    durbinWatsonTest()
```

```
## [1] 1.579896
```

---

# .brand-red[다중회귀모형]

- 다중선형회귀(multiple linear regression)는 단순선형회귀의 확장으로 독립변수의 수가 여러개인 경우에 해당:

\begin{align} 
y = \alpha + \beta_{1} x_1 + \beta_2 x_2 + \cdots + \beta_p x_p + \epsilon, \epsilon \sim N(0, \sigma^2) 
\end{align}

- 오차항에 대한 가정은 단순선형회귀의 경우와 같음

---

# .brand-red[다중회귀모형]

<div class="figure" style="text-align: center">
<img src="./fig/multiple.jpg" alt="fig 3. Multilple linear regression" width="500" height="350" />
<p class="caption">fig 3. Multilple linear regression</p>
</div>

\begin{align} 
\hat{y} = \hat{\beta}_0 + \hat{\beta}_1 x_1 + \hat{\beta}_2 x_2 
\end{align}

---

# .brand-red[다중회귀모형]

\begin{align} 
\boldsymbol{\beta} = (X^TX)^{-1}X^Ty 
\end{align}

- 다중공선성 문제
  - 다중선형회귀에서는 자료의 수( `$n$` )가 모수의 수( `$p$` )보다 필히 많아야 함( `$n \geq p+1$` )
  - `$p \geq n$` 인 경우 또는 다중공선성이 심한 경우 `$(X^TX)$`의 역행렬의 계산이 불가능해 짐 
  - 결과적으로 `$\boldsymbol{\beta}$` 추정량의 분산이 매우 커짐
  - 즉, 추정된 회귀계수를 신뢰하기 어려움

- 다중공선성의 징후
  - `$X$`들 간에 높은 상관계수가 존재할 때
  - 이론적으로 반응변수와 상관이 높을것으로 생각되는 변수임에도 회귀계수가 유의하지 않음
  - 이론적으로 `$X$`에 따라 반응변수가 증가해야 함에도 회귀계수가 음의 값을 가짐
  - 특정 변수 `$X$`를 추가하거나 제외하였을 때, 회귀계수의 변화가 크게 일어남

---

# .brand-red[다중회귀모형]

- 다중공선성 문제 해결 방법

- 상관된 예측변수 제거: 상관성이 높은 변수를 제거해 나가되, `$R^2$`가 높은 모형 선택
  
      - Variable selection: Forward Selection, Backward elimination, Stepwise selection
      
      - Best subset regression
      
  - 벌점회귀(Penalized regression) 이용
  
      - Lasso regression
      
---

# .brand-red[실습: 다중회귀모형]

## 데이터 소개

-   미국 50개 주에서 여러 변수값(인구, 수입, 문맹비율, 기대수명, 살인율, 고졸비율, 연평균영하기온일수, 면적)을 측정한 자료
 
 - 이 중 기대수명(`Life exp`)을 반응변수로 다중회귀분석 실시

```r
head(state.x77, 3)
```
<table>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Population </th>
   <th style="text-align:right;"> Income </th>
   <th style="text-align:right;"> Illiteracy </th>
   <th style="text-align:right;"> Life Exp </th>
   <th style="text-align:right;"> Murder </th>
   <th style="text-align:right;"> HS Grad </th>
   <th style="text-align:right;"> Frost </th>
   <th style="text-align:right;"> Area </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Alabama </td>
   <td style="text-align:right;"> 3615 </td>
   <td style="text-align:right;"> 3624 </td>
   <td style="text-align:right;"> 2.1 </td>
   <td style="text-align:right;"> 69.05 </td>
   <td style="text-align:right;"> 15.1 </td>
   <td style="text-align:right;"> 41.3 </td>
   <td style="text-align:right;"> 20 </td>
   <td style="text-align:right;"> 50708 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Alaska </td>
   <td style="text-align:right;"> 365 </td>
   <td style="text-align:right;"> 6315 </td>
   <td style="text-align:right;"> 1.5 </td>
   <td style="text-align:right;"> 69.31 </td>
   <td style="text-align:right;"> 11.3 </td>
   <td style="text-align:right;"> 66.7 </td>
   <td style="text-align:right;"> 152 </td>
   <td style="text-align:right;"> 566432 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Arizona </td>
   <td style="text-align:right;"> 2212 </td>
   <td style="text-align:right;"> 4530 </td>
   <td style="text-align:right;"> 1.8 </td>
   <td style="text-align:right;"> 70.55 </td>
   <td style="text-align:right;"> 7.8 </td>
   <td style="text-align:right;"> 58.1 </td>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:right;"> 113417 </td>
  </tr>
</tbody>
</table>

---

# .brand-red[실습: 다중회귀모형]

## 데이터 소개

-   데이터 구조 확인

```r
glimpse(state.x77)
```

```
##  num [1:50, 1:8] 3615 365 2212 2110 21198 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:50] "Alabama" "Alaska" "Arizona" "Arkansas" ...
##   ..$ : chr [1:8] "Population" "Income" "Illiteracy" "Life Exp" ...
```

- 데이터프레임으로 변환 후, 변수명 빈칸 제외

```r
# install.packages("janitor")
state <- as.data.frame(state.x77) |> 
    janitor::clean_names()
glimpse(state)
```

```
## Rows: 50
## Columns: 8
## $ population <dbl> 3615, 365, 2212, 2110, 21198, 2541, 3100, 579, 8277, 4931, …
## $ income     <dbl> 3624, 6315, 4530, 3378, 5114, 4884, 5348, 4809, 4815, 4091,…
## $ illiteracy <dbl> 2.1, 1.5, 1.8, 1.9, 1.1, 0.7, 1.1, 0.9, 1.3, 2.0, 1.9, 0.6,…
## $ life_exp   <dbl> 69.05, 69.31, 70.55, 70.66, 71.71, 72.06, 72.48, 70.06, 70.…
## $ murder     <dbl> 15.1, 11.3, 7.8, 10.1, 10.3, 6.8, 3.1, 6.2, 10.7, 13.9, 6.2…
## $ hs_grad    <dbl> 41.3, 66.7, 58.1, 39.9, 62.6, 63.9, 56.0, 54.6, 52.6, 40.6,…
## $ frost      <dbl> 20, 152, 15, 65, 20, 166, 139, 103, 11, 60, 0, 126, 127, 12…
## $ area       <dbl> 50708, 566432, 113417, 51945, 156361, 103766, 4862, 1982, 5…
```

]

---

# .brand-red[실습: 다중회귀모형]

## 모형 적합

```r
lm_mod2 <- lm(life_exp ~ ., data = state)
summary(lm_mod2)
```

```
## 
## Call:
## lm(formula = life_exp ~ ., data = state)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.48895 -0.51232 -0.02747  0.57002  1.49447 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.094e+01  1.748e+00  40.586  < 2e-16 ***
## population   5.180e-05  2.919e-05   1.775   0.0832 .  
## income      -2.180e-05  2.444e-04  -0.089   0.9293    
## illiteracy   3.382e-02  3.663e-01   0.092   0.9269    
## murder      -3.011e-01  4.662e-02  -6.459 8.68e-08 ***
## hs_grad      4.893e-02  2.332e-02   2.098   0.0420 *  
## frost       -5.735e-03  3.143e-03  -1.825   0.0752 .  
## area        -7.383e-08  1.668e-06  -0.044   0.9649    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7448 on 42 degrees of freedom
## Multiple R-squared:  0.7362,	Adjusted R-squared:  0.6922 
## F-statistic: 16.74 on 7 and 42 DF,  p-value: 2.534e-10
```

]

---

# .brand-red[실습: 다중회귀모형]

## 다중공선성 검토: 분산팽창요인(VIF, Variance Inflation factor)

\begin{align} 
{\rm{VIF}}_j = \frac{1}{1-R_j^2}
\end{align}

- `$R_j^2$`는 `$j$`-번째 예측변수( `$x_j$` )를 나머지 ( `$p-1$` )개의 예측변수로 회귀를 수행하여 구해지는 결정계수

- 10보다 큰 경우 다중공선성을 야기하는 변수로 간주

]

- {car} 패키지의 `vif()`를 이용해 구할 수 있음

```r
vif(lm_mod2)
```

```
## population     income illiteracy     murder    hs_grad      frost       area 
##   1.499915   1.992680   4.403151   2.616472   3.134887   2.358206   1.789764
```

]

---

# .brand-red[실습: 다중회귀모형]

- Variable selection: Backward eliination
  
  - `step()` 이용

```r
lm_mod3 <- step(lm_mod2, direction = "backward", trace = FALSE)
summary(lm_mod3)
```

```
## 
## Call:
## lm(formula = life_exp ~ population + murder + hs_grad + frost, 
##     data = state)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.47095 -0.53464 -0.03701  0.57621  1.50683 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.103e+01  9.529e-01  74.542  < 2e-16 ***
## population   5.014e-05  2.512e-05   1.996  0.05201 .  
## murder      -3.001e-01  3.661e-02  -8.199 1.77e-10 ***
## hs_grad      4.658e-02  1.483e-02   3.142  0.00297 ** 
## frost       -5.943e-03  2.421e-03  -2.455  0.01802 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7197 on 45 degrees of freedom
## Multiple R-squared:  0.736,	Adjusted R-squared:  0.7126 
## F-statistic: 31.37 on 4 and 45 DF,  p-value: 1.696e-12
```

]

---

# .brand-red[실습: 다중회귀모형]

- 신뢰구간 구하기

```r
confint(lm_mod3)
```

```
##                     2.5 %        97.5 %
## (Intercept)  6.910798e+01 72.9462729104
## population  -4.543308e-07  0.0001007343
## murder      -3.738840e-01 -0.2264135705
## hs_grad      1.671901e-02  0.0764454870
## frost       -1.081918e-02 -0.0010673977
```

- 주어진 자료에 대한 예측값 구하기

```r
predict(lm_mod3, list(population = 4000, murder = 10.5, hs_grad = 48, frost = 100))
```

```
##        1 
## 69.71774
```

]
---
class: inverse, middle, center

# 2 ARIMA 모형: 실제 사례 중심

---

# .brand-red[준비]

- 패키지 설치

```r
install.packages("fpp3")
install.packages("readr")
install.packages("showtext")
install.packages("ggplot2")
install.packages("conflicted")
```

- 패키지 불러오기

```r
library(fpp3)
library(readr)
library(showtext)
library(ggplot2)
library(ggh4x)
font_add_google(name = "Nanum Gothic", family = "nanum")
showtext_auto(enable = TRUE)
conflicted::conflict_prefer("select", "dplyr")
ggplot2::theme_set(theme_bw())
```

]

---

# .brand-red[준비]

```r
disease <- read_csv("./data/example.csv")
disease
```

```
## # A tibble: 1,128 × 4
##    Sex    Group   Date         N
##    <chr>  <chr>   <chr>    <dbl>
##  1 Female 10_14세 2010 Jan   114
##  2 Female 10_14세 2010 Feb   121
##  3 Female 10_14세 2010 Mar   106
##  4 Female 10_14세 2010 Apr   120
##  5 Female 10_14세 2010 May   112
##  6 Female 10_14세 2010 Jun   122
##  7 Female 10_14세 2010 Jul   116
##  8 Female 10_14세 2010 Aug   138
##  9 Female 10_14세 2010 Sep   122
## 10 Female 10_14세 2010 Oct   112
## # … with 1,118 more rows
```
]

- 8개 그룹에 대해 모델링 필요

```r
disease |> 
    select(-Date, -N) |> 
    distinct()
```

```
## # A tibble: 8 × 2
##   Sex    Group  
##   <chr>  <chr>  
## 1 Female 10_14세
## 2 Female 15_19세
## 3 Female 5_9세  
## 4 Female 5세미만
## 5 Male   10_14세
## 6 Male   15_19세
## 7 Male   5_9세  
## 8 Male   5세미만
```
  
]

]

---

## 결측치 처리

- 결측이 존재하지 않는 데이터이지만 임의로 결측 처리(원자료 값 121)

```r
disease2 <- disease |> 
    slice(-2)
disease2
```

```
## # A tibble: 1,127 × 4
##    Sex    Group   Date         N
##    <chr>  <chr>   <chr>    <dbl>
##  1 Female 10_14세 2010 Jan   114
##  2 Female 10_14세 2010 Mar   106
##  3 Female 10_14세 2010 Apr   120
##  4 Female 10_14세 2010 May   112
##  5 Female 10_14세 2010 Jun   122
##  6 Female 10_14세 2010 Jul   116
##  7 Female 10_14세 2010 Aug   138
##  8 Female 10_14세 2010 Sep   122
##  9 Female 10_14세 2010 Oct   112
## 10 Female 10_14세 2010 Nov   104
## # … with 1,117 more rows
```

]

---

# .brand-red[시계열 자료 다루기]

- R에게 우리가 모델링할 시계열이 총 8개임을 알려줘야함

- `as_tsibble()`을 이용할 수 있음

```r
disease3 <- disease2 |> 
    mutate(Date = yearmonth(Date)) |> 
    as_tsibble(key = c(Sex, Group), index = Date)
disease3
```

```
## # A tsibble: 1,127 x 4 [1M]
## # Key:       Sex, Group [8]
##    Sex    Group       Date     N
##    <chr>  <chr>      <mth> <dbl>
##  1 Female 10_14세 2010 Jan   114
##  2 Female 10_14세 2010 Mar   106
##  3 Female 10_14세 2010 Apr   120
##  4 Female 10_14세 2010 May   112
##  5 Female 10_14세 2010 Jun   122
##  6 Female 10_14세 2010 Jul   116
##  7 Female 10_14세 2010 Aug   138
##  8 Female 10_14세 2010 Sep   122
##  9 Female 10_14세 2010 Oct   112
## 10 Female 10_14세 2010 Nov   104
## # … with 1,117 more rows
```

]

---

# .brand-red[시계열 자료 다루기]

- `fill_gaps()` 이용 결측치 대치

```r
disease4 <- disease3 |> 
    fill_gaps(N = 121L, .full = TRUE)
disease4
```

```
## # A tsibble: 1,128 x 4 [1M]
## # Key:       Sex, Group [8]
##    Sex    Group       Date     N
##    <chr>  <chr>      <mth> <dbl>
##  1 Female 10_14세 2010 Jan   114
##  2 Female 10_14세 2010 Feb   121
##  3 Female 10_14세 2010 Mar   106
##  4 Female 10_14세 2010 Apr   120
##  5 Female 10_14세 2010 May   112
##  6 Female 10_14세 2010 Jun   122
##  7 Female 10_14세 2010 Jul   116
##  8 Female 10_14세 2010 Aug   138
##  9 Female 10_14세 2010 Sep   122
## 10 Female 10_14세 2010 Oct   112
## # … with 1,118 more rows
```

]

---

# .brand-red[모형 적합]

- AICc를 기반으로 최적의 ARIMA 모형 적합

```r
mod <- disease4 |> 
    model(arima = ARIMA(N))
mod
```

```
## # A mable: 8 x 3
## # Key:     Sex, Group [8]
##   Sex    Group            arima
##   <chr>  <chr>          <model>
## 1 Female 10_14세 <ARIMA(0,1,1)>
## 2 Female 15_19세 <ARIMA(1,1,1)>
## 3 Female 5_9세   <ARIMA(0,1,1)>
## 4 Female 5세미만 <ARIMA(0,1,1)>
## 5 Male   10_14세 <ARIMA(0,1,1)>
## 6 Male   15_19세 <ARIMA(0,1,1)>
## 7 Male   5_9세   <ARIMA(0,1,1)>
## 8 Male   5세미만 <ARIMA(1,1,1)>
```

]

---

# .brand-red[예측]

- 향후 15개월 예측 후, 80% 및 95% 신뢰구간 추출

```r
f <- mod %>% 
    forecast(h = "15 months") %>% 
    hilo(level = c(80, 95)) %>% 
    unpack_hilo(c("80%", "95%"))   # 신뢰구간 값 열로 추출
head(f, 3)
```

<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Sex </th>
   <th style="text-align:left;"> Group </th>
   <th style="text-align:left;"> .model </th>
   <th style="text-align:left;"> Date </th>
   <th style="text-align:left;"> N </th>
   <th style="text-align:right;"> .mean </th>
   <th style="text-align:right;"> 80%_lower </th>
   <th style="text-align:right;"> 80%_upper </th>
   <th style="text-align:right;"> 95%_lower </th>
   <th style="text-align:right;"> 95%_upper </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Female </td>
   <td style="text-align:left;"> 10_14세 </td>
   <td style="text-align:left;"> arima </td>
   <td style="text-align:left;"> 2021 Oct </td>
   <td style="text-align:left;"> N(99, 133) </td>
   <td style="text-align:right;"> 99.20714 </td>
   <td style="text-align:right;"> 84.43298 </td>
   <td style="text-align:right;"> 113.9813 </td>
   <td style="text-align:right;"> 76.61202 </td>
   <td style="text-align:right;"> 121.8023 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Female </td>
   <td style="text-align:left;"> 10_14세 </td>
   <td style="text-align:left;"> arima </td>
   <td style="text-align:left;"> 2021 Nov </td>
   <td style="text-align:left;"> N(99, 133) </td>
   <td style="text-align:right;"> 99.20714 </td>
   <td style="text-align:right;"> 84.40289 </td>
   <td style="text-align:right;"> 114.0114 </td>
   <td style="text-align:right;"> 76.56600 </td>
   <td style="text-align:right;"> 121.8483 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Female </td>
   <td style="text-align:left;"> 10_14세 </td>
   <td style="text-align:left;"> arima </td>
   <td style="text-align:left;"> 2021 Dec </td>
   <td style="text-align:left;"> N(99, 134) </td>
   <td style="text-align:right;"> 99.20714 </td>
   <td style="text-align:right;"> 84.37286 </td>
   <td style="text-align:right;"> 114.0414 </td>
   <td style="text-align:right;"> 76.52007 </td>
   <td style="text-align:right;"> 121.8942 </td>
  </tr>
</tbody>
</table>

]

---

# .brand-red[시각화]

- 과거 시점(2010년 1월 - 2021년 9월)의 자료 만들기

```r
historic <- bind_rows(
    disease4 %>% 
        mutate(Type = "과거 실제값") %>%
        as_tibble(),
    mod %>% 
        fitted %>%  
        mutate(Type = "모형 적합값") %>% 
        as_tibble %>% 
        rename(N = .fitted) %>% 
        select(Date, Sex, Group, N, Type)
)
```

---

# .brand-red[시각화]

- 미래 시점(2021년 10월 - 2022년 12월)의 자료 만들기

```r
fore <- f %>% 
    mutate(Type = "모형 예측값", N = .mean) %>% 
    as_tibble %>% 
    select(Date, Sex, Group, N, Type)
```

---

# .brand-red[시각화]

- `{ggplot2}` 이용

```r
ggplot() +
    geom_line(data = historic,
              aes(x = Date, y = N, col = Type)) + # 과거 실제값, 모형 적합값
    geom_line(data = fore,
              aes(x = Date, y = N, col = Type)) + # 모형 예측값
    geom_ribbon(data = f, # 80% 신뢰구간
                aes(x = Date, ymin = `80%_lower`, ymax = `80%_upper`),
                fill = "skyblue", alpha = 0.25) +
    geom_ribbon(data = f, # 95% 신뢰구간
                aes(x = Date, ymin = `95%_lower`, ymax = `95%_upper`),
                fill = "skyblue", alpha = 0.25/2) +
    scale_color_manual(values = c("tomato", "blue", "paleturquoise3"), name = "") +
    theme(
        text = element_text(family = "nanum", size = 12),
        legend.position = "bottom") +
    labs(x = " ",
         y = "N") +
    facet_nested_wrap(vars(Sex, Group), scales = "free",
                      ncol = 4)
```

]

---

# .brand-red[시각화]

---

# .brand-red[책 추천]

## R 기본기

- 🔗[R for Data Science](https://bookdown.org/sulgi/r4ds/)

- 🔗[Do it! 쉽게 배우는 R 데이터 분석](http://www.yes24.com/Product/Goods/43868089)

## 회귀분석

- 🔗[예제를 통한 회귀분석 5판](http://www.kyobobook.co.kr/product/detailViewKor.laf?mallGb=KOR&ejkGb=KOR&barcode=9791158080105)

- 🔗[An Introduction to Statistical Learning, 2nd Edition](https://www.statlearning.com)

## 시계열 자료분석

- 🔗[Forecasting: principles and practice, 3rd edition](https://otexts.com/fpp3/)

---
class: inverse, middle, center

# References

---

## .brand-red[References]

[1] 나, 종화. R 시각화와 통계자료분석 2. 자유아카데미, 2016. http://www.yes24.com/Product/Goods/29643662.

[2] Breheny, Patrick. “High-Dimensional Data Analysis (BIOS 7600),” 2016. https://myweb.uiowa.edu/pbreheny/7600/s16/index.html.

---

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]]