Logistic Function Visualization

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#| standalone: true
#| viewerHeight: 600

# Load necessary libraries
library(shiny)
library(ggplot2)

# Define UI for application
ui <- fluidPage(
  titlePanel("Logistic Function Visualization"),
  sidebarLayout(
    sidebarPanel(
      sliderInput("beta", "Beta Coefficient", min = -5, max = 5, value = 1, step = 0.1),
      sliderInput("intercept", "Intercept (Log Odds at x=0)", min = -5, max = 5, value = 0, step = 0.1)
    ),
    mainPanel(
      plotOutput("log_odds_plot"),
      plotOutput("probability_plot")
    )
  )
)

# Define server logic
server <- function(input, output) {
  # Calculate logistic function
  logistic_function <- function(x, beta, intercept) {
    return(1 / (1 + exp(-(intercept + beta * x))))
  }
  
  # Generate x values
  x_values <- seq(-10, 10, length.out = 100)
  
  # Create log odds plot
  output$log_odds_plot <- renderPlot({
    log_odds <- input$intercept + input$beta * x_values
    
    ggplot() +
      geom_line(aes(x = x_values, y = log_odds), color = "blue") +
      labs(title = "Log Odds Plot", x = "X", y = "Log Odds") + theme_bw()
  })
  
  # Create probability plot
  output$probability_plot <- renderPlot({
    probabilities <- logistic_function(x_values, input$beta, input$intercept)
    
    ggplot() +
      geom_line(aes(x = x_values, y = probabilities), color = "red") +
      labs(title = "Probability Plot", x = "X", y = "Probability") + 
      theme_bw()
  })
}

# Run the application
shinyApp(ui = ui, server = server)