BMA is the best method to estimate the most powerful model in multiple linear regression by using BIC method

library(readxl)
## Warning: package 'readxl' was built under R version 4.0.3
Data <- read_excel("C:/Users/Admin/Desktop/R/Data.xlsx", 
     sheet = "MBA", col_types = c("text", 
        "text", "text", "numeric", "numeric", 
         "numeric", "numeric", "numeric", 
         "numeric"))
attach(Data)
library(BMA)
X=cbind(Viscera,Fillet,`Abd. fat`,Liver,`Weight gain`)
Y=Data$`Body Weight`
David=bicreg(X,Y,strict = FALSE,OR=20)
summary(David)
## 
## Call:
## bicreg(x = X, y = Y, strict = FALSE, OR = 20)
## 
## 
##   9  models were selected
##  Best  5  models (cumulative posterior probability =  0.8803 ): 
## 
##              p!=0    EV       SD        model 1   model 2   model 3   model 4 
## Intercept    100.0  487.3367  187.7807  463.2453  567.0210  494.3460  452.7882
## Viscera       16.8    0.3088    1.6673      .         .         .       0.6159
## Fillet       100.0    2.3921    0.4077    2.4153    2.3874    2.6329    2.3135
## Abd..fat      15.4   -0.2804    3.0526      .         .         .         .   
## Liver         12.7   -0.4356    4.3880      .         .      -4.1359      .   
## Weight.gain   20.7   -0.1254    0.4670      .      -0.5030      .         .   
##                                                                               
## nVar                                        1         2         2         2   
## r2                                        0.807     0.811     0.808     0.808 
## BIC                                     -36.3097  -33.6052  -33.2827  -33.2339
## post prob                                 0.464     0.120     0.102     0.100 
##              model 5 
## Intercept    463.3482
## Viscera          .   
## Fillet         2.4222
## Abd..fat      -0.1631
## Liver            .   
## Weight.gain      .   
##                      
## nVar             2   
## r2             0.807 
## BIC          -33.1342
## post prob      0.095
imageplot.bma(David)

Read the result

  1. p! is the probability of Xp when Xp different with 0
  2. EV: Expected value
  3. Post prob: the probability of model appearing

Inconclusion

Model 1 shows that Fillet accouting for 80.7% of contribution (R^2=0.870) The probability of model 1 is 46.4%