R Notebook

Introduction

Gabriel Gencsi

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# Load necessary library
library(ggplot2)

# Hypothetical dataset
set.seed(123)
data <- data.frame(
  robotization = runif(100, 0, 10),
  productivity = runif(100, 50, 150)
)

# Fit a linear regression model
model <- lm(productivity ~ robotization, data = data)

# Summary of the model
summary(model)

Call:
lm(formula = productivity ~ robotization, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-51.061 -21.159  -0.986  17.769  48.695 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  105.4495     5.3420  19.740   <2e-16 ***
robotization  -0.8077     0.9314  -0.867    0.388    
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 26.41 on 98 degrees of freedom
Multiple R-squared:  0.007616,  Adjusted R-squared:  -0.00251 
F-statistic: 0.7521 on 1 and 98 DF,  p-value: 0.3879

# Extracting coefficients and p-values
coefficients <- summary(model)$coefficients

# Interpretation of coefficients
cat("Intercept (beta_0):", coefficients[1, 1], "\n")

Intercept (beta_0): 105.4495 

cat("Slope (beta_1):", coefficients[2, 1], "\n")

Slope (beta_1): -0.8077256 

cat("p-value for robotization:", coefficients[2, 4], "\n")

p-value for robotization: 0.3879265 

if (coefficients[2, 4] < 0.05) {
  cat("The coefficient for robotization is statistically significant.\n")
} else {
  cat("The coefficient for robotization is not statistically significant.\n")
}

The coefficient for robotization is not statistically significant.

cat("Interpretation: For each unit increase in robotization, productivity is expected to change by", coefficients[2, 1], "units, holding all else constant.\n")

Interpretation: For each unit increase in robotization, productivity is expected to change by -0.8077256 units, holding all else constant.

# Residual diagnostics
par(mfrow = c(2, 2))
plot(model)

Error in plot.new() : figure margins too large

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