R&D Expenditure Analysis

Load Libraries

library(ggplot2)
library(MASS)
library(lmtest)

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

library(tseries)

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

Simulate Data

set.seed(42)

n <- 200
firm_size <- runif(n, 10, 500)

error <- rnorm(n, mean = 0, sd = 0.5)
rd_expenditure <- exp(1.5 + 0.6 * log(firm_size) + error)

df_firms <- data.frame(
  Firm_ID = 1:n,
  Total_Assets = firm_size,
  RD_Expenditure = rd_expenditure
)

head(df_firms)

##   Firm_ID Total_Assets RD_Expenditure
## 1       1     458.2550      322.76939
## 2       2     469.1670      302.76313
## 3       3     150.2084       54.90529
## 4       4     416.9193      421.56611
## 5       5     324.4553      103.12089
## 6       6     264.3570      134.17397

1. Visualize the Relationship

ggplot(df_firms, aes(x = Total_Assets, y = RD_Expenditure)) +
  geom_point(alpha = 0.6) +
  labs(title = "R&D Expenditure vs Total Assets",
       x = "Total Assets (Millions)",
       y = "R&D Expenditure") +
  theme_minimal()

2. OLS Regression

model1 <- lm(RD_Expenditure ~ Total_Assets, data = df_firms)
summary(model1)

## 
## Call:
## lm(formula = RD_Expenditure ~ Total_Assets, data = df_firms)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -135.79  -42.06  -12.37   25.08  404.97 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  40.50788   11.25914   3.598 0.000405 ***
## Total_Assets  0.35091    0.03731   9.405  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 75.31 on 198 degrees of freedom
## Multiple R-squared:  0.3088, Adjusted R-squared:  0.3053 
## F-statistic: 88.46 on 1 and 198 DF,  p-value: < 2.2e-16

3. Residual Diagnostics

par(mfrow = c(2, 2))
plot(model1)

jarque.bera.test(residuals(model1))

## 
##  Jarque Bera Test
## 
## data:  residuals(model1)
## X-squared = 332.83, df = 2, p-value < 2.2e-16

bptest(model1)

## 
##  studentized Breusch-Pagan test
## 
## data:  model1
## BP = 13.298, df = 1, p-value = 0.0002657

4. Box-Cox Transformation

boxcox(model1, lambda = seq(-2, 2, by = 0.1))

5. Transform Dependent Variable

df_firms$log_RD <- log(df_firms$RD_Expenditure)

model2 <- lm(log_RD ~ Total_Assets, data = df_firms)
summary(model2)

## 
## Call:
## lm(formula = log_RD ~ Total_Assets, data = df_firms)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.47221 -0.39713  0.02358  0.35362  1.37330 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.7787315  0.0798760   47.31   <2e-16 ***
## Total_Assets 0.0033566  0.0002647   12.68   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5343 on 198 degrees of freedom
## Multiple R-squared:  0.4482, Adjusted R-squared:  0.4454 
## F-statistic: 160.8 on 1 and 198 DF,  p-value: < 2.2e-16

6. Diagnostics for New Model

par(mfrow = c(2, 2))
plot(model2)

7. Compare Models

AIC(model1, model2)

##        df       AIC
## model1  3 2300.2201
## model2  3  320.8362