import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

import seaborn as sns

from sklearn.preprocessing import StandardScaler

from sklearn.decomposition import FactorAnalysis

from sklearn.impute import SimpleImputer

# Load the dataset

# Assuming you have the dataset in CSV format named 'data.csv$\text{'}$

df $=$ pd$.$read$\_$csv$(\text{'}$data$.$csv$\text{'})$

# Selecting only numerical columns for factor analysis

numerical$\_$columns $=$ df$.$select$\_$dtypes$($include$=[$np$.$number$]).$columns.tolist$()$

df$\_$numerical $=$ df$[$numerical$\_$columns$]$

# Handling missing values by imputing with the mean

imputer $=$ SimpleImputer$($strategy$=$'mean'$)$

df$\_$numerical$\_$imputed $=$ imputer.fit$\_$transform$($df$\_$numerical$)$

# Standardizing the data

scaler $=$ StandardScaler$()$

df$\_$numerical$\_$scaled $=$ scaler.fit$\_$transform$($df$\_$numerical$\_$imputed$)$

# Performing factor analysis

fa $=$ FactorAnalysis$($n$\_$components$=5,$ random$\_$state$=0)$

fa$\_$components $=$ fa$.$fit$\_$transform$($df$\_$numerical$\_$scaled$)$

# Creating a DataFrame with the factor analysis components

fa$\_$df $=$ pd$.$DataFrame$($fa$\_$components, columns$=[$f$\text{'}$Factor$\{$i$+1\}\text{'}$ for i in range$($fa$.$n$\_$components$)])$

# Plotting the factor analysis results

plt$.$figure$($figsize$=(10,7))$

sns$.$heatmap$($pd$.$DataFrame$($fa$.$components$\_,$ columns$=$numerical$\_$columns$),$ annot$=$True, cmap$=$'coolwarm'$)$

plt$.$title$(\text{'}$Factor Analysis Components'$)$

plt$.$xlabel$(\text{'}$Features$\text{'})$

plt$.$ylabel$(\text{'}$Factors$\text{'})$

plt$.$show$()$

# Output the factor analysis components

print$("$Factor Analysis Components:"$)$

print$($fa$\_$df$.$head$())$

As for the above code, please add:

plt$.$xlabel$(\text{'}$Variables$\text{'})$

plt$.$ylabel$(\text{'}$Loadings$\text{'})$

plt$.$title$(\text{'}$Factor Loadings Before Rotation'$)$

plt$.$xticks$($np$.$arange$($len$($X$\_$factor.columns$)),$ X$\_$factor.columns, rotation$=45,$ ha$=$"right"$)$

plt$.$legend$()$

plt$.$tight$\_$layout$()$

plt$.$show$()$

# Bar plot for factor loadings after rotation

plt$.$xlabel$(\text{'}$Variables$\text{'})$

plt$.$ylabel$(\text{'}$Loadings$\text{'})$

plt$.$title$(\text{'}$Factor Loadings After Rotation'$)$

plt$.$xticks$($np$.$arange$($len$($X$\_$factor.columns$)),$ X$\_$factor.columns, rotation$=45,$ ha$=$"right"$)$

plt$.$legend$()$

plt$.$tight$\_$layout$()$

plt$.$show$()$

Please scale the data, and add some formulas to the code to plot the Factor Loadings Before Rotation and Factor Loadings After Rotation. Thank you very much!:$)$