简单线性回归方程R中的设计环问题

Question

方程的一般形式是

Sector ~ Beta_0 + Beta_1*absMkt + Beta_2*sqMkt

这些部门是12个部门的每日股票回报率，即汽车、IT、房地产、银行、能源、金融服务、快速消费品、基础设施、服务、媒体、金属和制药。

Beta_0是截距；Beta_1是绝对市场回报系数；Beta_2是平方市场回报系数。

对于每个扇区，我想运行线性回归，其中我想提取系数Beta_1和Beta_2，如果对应的p值小于0.0 5，并存储它。

样本数据说明如下。

它也可从我的google驱动器位置下载。

https://drive.google.com/drive/folders/16XUq8_lXXtD2BSlUdDAAWeHiWIznf--c?usp=share_link

文件名: Week_1_CSV.csv

​

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我试过的代码，但没有得到结果

# Reading the data
Returns <- read.csv("Week_1_CSV.CSV", header = TRUE, stringsAsFactors = FALSE)

# Splitting the Data into Sector and Market Returns
Sector_Returns <- Returns[,2:13]
Market_Returns <- Returns[,14:15]

# Defining the number of sectors
nc <- ncol(Sector_Returns)

# Creating a matrix with zero value to store the coefficient values and their corresponding p-values

Beta_1 <- Beta_2 <- p_1 <- p_2 <- matrix(0, 1, nc)  # coefs and p values

# Converting the Sectoral Returns into a Matrix named "Sect_Ret_Mat"

Sect_Ret_Mat <- as.matrix(Sector_Returns)
head(Sect_Ret_Mat)

# Converting the Market Returns into a Matrix named "Mkt_Ret_Mat"

Mkt_Ret_Mat <- as.matrix(Market_Returns)
head(Mkt_Ret_Mat)

#### Without Loop ##############

mode1_lm <- lm(Sect_Ret_Mat[,1] ~ Mkt_Ret_Mat[,1] + Mkt_Ret_Mat[,2] )
summary(mode1_lm)

 # Extracting the p-value

coef(summary(mode1_lm))[2, 4] ## p-value corresponding to Beta_1
coef(summary(mode1_lm))[3, 4] ## p-value corresponding to Beta_2

# Extracting the Coefficient

coef(mode1_lm)[[2]] ## Coeficient corresponding to Beta_1
coef(mode1_lm)[[3]] ## Coeficient corresponding to Beta_2

##############################################################################

#### WithLoop ##############

for (i in 1:nc) {
  for (j in 1:nc) {
    if (i != j) {
      mode1_lm <- lm(Sect_Ret_Mat[,i] ~ Mkt_Ret_Mat[,1] + Mkt_Ret_Mat[,2] )
      p_0[i,j] <- coef(summary(mode1_lm))[2, 4]
      p_1[i,j] <- coef(summary(mode1_lm))[3, 4]
      if 
      (p_0[i, j] < 0.05) 
        Beta_0[i,j] <- coef(mode1_lm)[[2]]
     if
      (p_1[i, j] < 0.05) 
        Beta_1[i,j] <- coef(mode1_lm)[[3]]
    
    }
  }
}

Beta_0

Beta_1

Answer 1

一般情况下，我不从链接下载数据集。你应该试着做一个很容易在任何人的电脑上运行的小例子。在为不同的组运行大量的回归时，我发现最容易的方法是将所有数据保存在一个数据帧中，并避免循环。一般的工作流程是: 1)按组嵌套数据，2)对各组进行回归，3)使用broom将系数生成一个良好的表，4)将模型系数分解为表。下面是一个使用mtcars的示例。我展示了如何对每一组cyl运行回归。

library(tidyverse)

mtcars |>
  nest(data = -cyl) |>
  mutate(mod = map(data, ~lm(mpg~wt + hp, data = .x)),
         summ = map(mod, broom::tidy)) |>
  select(-data, -mod) |>
  unnest(summ)
#> # A tibble: 9 x 6
#>     cyl term        estimate std.error statistic   p.value
#>   <dbl> <chr>          <dbl>     <dbl>     <dbl>     <dbl>
#> 1     6 (Intercept)  32.6       5.57        5.84 0.00428  
#> 2     6 wt           -3.24      1.37       -2.36 0.0776   
#> 3     6 hp           -0.0222    0.0202     -1.10 0.333    
#> 4     4 (Intercept)  45.8       4.79        9.58 0.0000117
#> 5     4 wt           -5.12      1.60       -3.19 0.0128   
#> 6     4 hp           -0.0905    0.0436     -2.08 0.0715   
#> 7     8 (Intercept)  26.7       3.66        7.28 0.0000158
#> 8     8 wt           -2.18      0.721      -3.02 0.0117   
#> 9     8 hp           -0.0137    0.0107     -1.27 0.229

Answer 2

将您的数据融化很长时间，并在每个扇区应用一个辅助函数：

1. 将dataframe wk1设置为data.table，并融化了long

library(data.table)
setDT(wk1)


wk1 = melt(
  data = wk1[, id:=.I],
  id = c("id", "Date", "ABSOLUTE MARKLET RETURN", "SQUARED MARKET RETURN"),
  variable.name = "sector"
)

1. 编写助手函数，该函数运行模型并在列表

中返回beta和p.value

f <- function(v,a,s) {
  cf = summary(lm(v~a+s))$coefficients[-1,]
  list(est = cf[,1],pvalue=cf[,4])
}

1. 将f应用于每个扇区

wk1[, f(value, `ABSOLUTE MARKLET RETURN`, `SQUARED MARKET RETURN`), sector]

输出：

                sector         beta       pvalue
 1:               AUTO   0.71847599 1.837679e-02
 2:               AUTO  -7.44556841 3.921574e-01
 3:                 IT   0.33384211 2.878851e-02
 4:                 IT  -1.69884185 6.970822e-01
 5:             REALTY   0.19224293 3.128459e-01
 6:             REALTY   0.63655626 9.084056e-01
 7:               BANK   0.72886921 4.544867e-06
 8:               BANK -15.07590018 6.835331e-04
 9:             ENERGY   0.30568300 5.611571e-01
10:             ENERGY  -0.42252869 9.780039e-01
11: FINANCIAL SERVICES   0.46149507 1.940130e-04
12: FINANCIAL SERVICES  -2.72192333 4.238560e-01
13:               FMCG   0.38259697 1.398654e-02
14:               FMCG  -0.45504587 9.180342e-01
15:     INFRASTRUCTURE   0.28891493 1.845572e-01
16:     INFRASTRUCTURE   0.03244222 9.958937e-01
17:           SERVICES   0.49497910 2.098375e-06
18:           SERVICES  -6.52723131 2.036243e-02
19:              MEDIA   0.10040065 7.554367e-01
20:              MEDIA   0.26014494 9.779231e-01
21:              METAL   0.45139509 1.576446e-02
22:              METAL  -6.87462275 1.991497e-01
23:             PHARMA   0.39993847 1.781434e-02
24:             PHARMA  -0.74201727 8.772388e-01