Add app demo

index.qmd

@@ -2,22 +2,137 @@
 
 ## Welcome {.unnumbered}
 
-Welcome splash page! Provide an overview of the book.
+Welcome splash page!
 
-Sample evaluation of R and Python in a side-by-side manner:
+Sample shinylive app inside the textbook.
 
-::: {layout-ncol=2}
-#### R
+```{shinylive-r}
+#| standalone: true
+# Load the shiny and ggplot2 packages
+library(shiny)
+library(ggplot2)
 
-```{r}
-my_list = list(1, 2, 3)
-typeof(my_list)
-```
+# Define the UI
+ui <- fluidPage(
+  titlePanel("Interactive Graph with Linear Regression"),
+  
+  fluidRow(
+    column(
+      # Two sliders to adjust the x and y axis ranges
+      sliderInput("xrange", "X-axis range", min = -10, max = 10, value = c(-5, 5)),
+      sliderInput("yrange", "Y-axis range", min = -10, max = 10, value = c(-5, 5)),
+      # A button to reset the data
+      actionButton("reset", "Reset Data"),
+      width = 3
+    ),
+    column(
+      # A plot output to display the graph
+      plotOutput("plot", click = "plot_click"),
+      width = 6),
+    column(
+      # A table output to display the statistics
+      tableOutput("stats"),
+      # A text output to display the model equation
+      textOutput("model"), width = 3)
+  )
+)
 
-#### Python
+# Define the server
+server <- function(input, output, session) {
+  
+  # A reactive value to store the data frame
+  values <- reactiveValues(data = NULL)
+  
+  empty_dataframe <- function() { data.frame(x = numeric(), y = numeric()) }
+  # Initialize an empty data frame 
+  observe({
+    values$data <- empty_dataframe()
+  })
+  
+  # Update the data frame when the user clicks on the plot
+  observeEvent(input$plot_click, {
+    # Get the coordinates of the click
+    x <- input$plot_click$x
+    y <- input$plot_click$y
+    # Add a new row to the data frame
+    values$data <- rbind(values$data, data.frame(x = x, y = y))
+  })
+  
+  # Reset the data frame when the user clicks on the reset button
+  observeEvent(input$reset, {
+    values$data <- empty_dataframe()
+  })
+  
+  # Render the plot output
+  output$plot <- renderPlot({
+    # Create a ggplot object with the data
+    p <- ggplot(values$data, aes(x = x, y = y)) +
+      geom_point(size = 3) +
+      xlim(input$xrange[1], input$xrange[2]) +
+      ylim(input$yrange[1], input$yrange[2]) +
+      labs(x = "X", y = "Y")
+    # If there is more than one point, add a linear regression line
+    if (nrow(values$data) > 1) {
+      p <- p + geom_smooth(method = "lm", se = FALSE)
+    }
+    # Return the plot object
+    p
+  })
+  
+  # Render the table output
+  output$stats <- renderTable({
+    # If there is more than one point, calculate the statistics
+    if (nrow(values$data) > 1) {
+      # Fit a linear model
+      model <- lm(y ~ x, data = values$data)
+      # Get the correlation coefficient
+      rho <- cor(values$data$x, values$data$y)
+      # Get the sum of squared residuals
+      ssr <- sum(residuals(model)^2)
+      # Get the number of points
+      n <- nrow(values$data)
+      # Get the mean of x and y
+      xbar <- mean(values$data$x)
+      ybar <- mean(values$data$y)
+      # Get the covariance between x and y
+      covxy <- cov(values$data$x, values$data$y)
+      # Create a data frame with the statistics
+      stats <- data.frame(
+        Statistic = c("Number of Points", "Mean of X", "Mean of Y", "Covariance between X and Y", "Correlation", "Sum of Squared Residuals"),
+        Value = c(n, xbar, ybar, covxy, rho, ssr)
+      )
+      # Return the data frame
+      stats
+    } else {
+      # Return an empty data frame
+      data.frame()
+    }
+  })
+  
+  # Render the text output
+  output$model <- renderText({
+    # If there is more than one point, display the model equation
+    if (nrow(values$data) > 1) {
+      # Fit a linear model
+      model <- lm(y ~ x, data = values$data)
+      # Get the coefficients
+      a <- coef(model)[1]
+      b <- coef(model)[2]
+      # Get the R-squared
+      r2 <- summary(model)$r.squared
+      # Format the equation
+      equation <- paste0("y = ", round(a, 2), " + ", round(b, 2), "x")
+      # Format the R-squared
+      rsquared <- paste0("R^2 = ", round(r2, 2))
+      # Return the text
+      paste0("Model Equation:\n", equation, "\n\n", "Coefficient of Determination:\n", rsquared)
+    } else {
+      # Return an empty text
+      ""
+    }
+  })
+}
 
-```{python}
-my_list = [1, 2, 3]
-type(my_list)
-```
-:::
+# Run the app
+shinyApp(ui = ui, server = server)
+```