Shiny app for simple linear regression by hand and in R. See more information at: https://antoinesoetewey.shinyapps.io/statistics-202/

statistics-202.R

library(shiny)
library(ggplot2)
library(plotly)
library(rmarkdown)
library(knitr)
library(pander)
set.seed(123)
n <- 100

# Define UI for application that draws a histogram
ui <- shiny::tagList(
  withMathJax(), 
  includeCSS(path = "www/css/styles.css"), 
  
  tags$head(
    tags$link(
      rel = "shortcut icon", 
      href = "https://antoinesoetewey.com/favicon.ico"
    )
  ), 
  
  tags$div(
    tags$div(
      class = "app_title", 
      
      titlePanel(
        title = "Statistics 202 - Simple linear regression", 
        windowTitle = "Simple linear regression"
      ),
      
      tags$h4(
        tags$a(
          href = "https://antoinesoetewey.com/", 
          target = "_blank", 
          "Antoine Soetewey"
        )
      )
    ),
    
    # Sidebar with a slider input for number of bins
    fluidPage(
      theme = shinythemes::shinytheme("flatly"),
      sidebarLayout(
        sidebarPanel(
          tags$b("Data:"),
          textInput("x", "x", value = "90, 100, 90, 80, 87, 75", placeholder = "Enter values separated by a comma with decimals as points, e.g. 4.2, 4.4, 5, 5.03, etc."),
          textInput("y", "y", value = "950, 1000, 850, 750, 950, 775", placeholder = "Enter values separated by a comma with decimals as points, e.g. 4.2, 4.4, 5, 5.03, etc."),
          hr(),
          tags$b("Plot:"),
          checkboxInput("se", "Add confidence interval around the regression line", TRUE),
          textInput("xlab", label = "Axis labels:", value = "x", placeholder = "x label"),
          textInput("ylab", label = NULL, value = "y", placeholder = "y label"),
          hr(),
          # textInput("pred", "Prediction of y when x = ", value = "100, 110, 100, 90, 97, 85", placeholder = "Enter values separated by a comma with decimals as points, e.g. 4.2, 4.4, 5, 5.03, etc."),
          # hr(),
          # radioButtons("format", "Download report:", c("HTML", "PDF", "Word"),
          #              inline = TRUE
          radioButtons("format", "Download report:", c("HTML"),
                       inline = TRUE             
          ),
          checkboxInput("echo", "Show code in report?", FALSE),
          downloadButton("downloadReport")
        ),
        
        mainPanel(
          br(),
          tags$b("Data:"),
          br(),
          br(),
          DT::dataTableOutput("tbl"),
          br(),
          uiOutput("data"),
          br(),
          tags$b("Compute parameters by hand:"),
          br(),
          br(),
          uiOutput("by_hand"),
          br(),
          tags$b("Compute parameters in R:"),
          br(),
          br(),
          verbatimTextOutput("summary"),
          br(),
          tags$b("Regression plot:"),
          br(),
          br(),
          uiOutput("results"),
          plotlyOutput("plot"),
          br(),
          tags$b("Interpretation:"),
          br(),
          br(),
          uiOutput("interpretation"),
          br(),
          tags$b("Assumptions:"),
          plotOutput("assumptions"),
          br(),
          br()
        )
      )
    )
  ), 
  
  tags$footer(
    tags$div(
      class = "footer_container", 
      
      includeHTML(path = "www/html/footer.html")
    )
  )
  
)

server <- function(input, output) {
  extract <- function(text) {
    text <- gsub(" ", "", text)
    split <- strsplit(text, ",", fixed = FALSE)[[1]]
    as.numeric(split)
  }

  # Data output
  output$tbl <- DT::renderDataTable({
    y <- extract(input$y)
    x <- extract(input$x)
    DT::datatable(data.frame(x, y),
      extensions = "Buttons",
      options = list(
        lengthChange = FALSE,
        dom = "Blfrtip",
        buttons = c("copy", "csv", "excel", "pdf", "print")
      )
    )
  })

  output$data <- renderUI({
    y <- extract(input$y)
    x <- extract(input$x)
    if (anyNA(x) | length(x) < 2 | anyNA(y) | length(y) < 2) {
      "Invalid input or not enough observations"
    } else if (length(x) != length(y)) {
      "Number of observations must be equal for x and y"
    } else {
      withMathJax(
        paste0("\\(\\bar{x} =\\) ", round(mean(x), 3)),
        br(),
        paste0("\\(\\bar{y} =\\) ", round(mean(y), 3)),
        br(),
        paste0("\\(n =\\) ", length(x))
      )
    }
  })

  output$by_hand <- renderUI({
    y <- extract(input$y)
    x <- extract(input$x)
    fit <- lm(y ~ x)
    withMathJax(
      paste0("\\(\\hat{\\beta}_1 = \\dfrac{\\big(\\sum^n_{i = 1} x_i y_i \\big) - n \\bar{x} \\bar{y}}{\\sum^n_{i = 1} (x_i - \\bar{x})^2} = \\) ", round(fit$coef[[2]], 3)),
      br(),
      paste0("\\(\\hat{\\beta}_0 = \\bar{y} - \\hat{\\beta}_1 \\bar{x} = \\) ", round(fit$coef[[1]], 3)),
      br(),
      br(),
      paste0("\\( \\Rightarrow y = \\hat{\\beta}_0 + \\hat{\\beta}_1 x = \\) ", round(fit$coef[[1]], 3), " + ", round(fit$coef[[2]], 3), "\\( x \\)")
    )
  })

  output$summary <- renderPrint({
    y <- extract(input$y)
    x <- extract(input$x)
    fit <- lm(y ~ x)
    summary(fit)
  })

  output$results <- renderUI({
    y <- extract(input$y)
    x <- extract(input$x)
    fit <- lm(y ~ x)
    withMathJax(
      paste0(
        "Adj. \\( R^2 = \\) ", round(summary(fit)$adj.r.squared, 3),
        ", \\( \\beta_0 = \\) ", round(fit$coef[[1]], 3),
        ", \\( \\beta_1 = \\) ", round(fit$coef[[2]], 3),
        ", P-value ", "\\( = \\) ", signif(summary(fit)$coef[2, 4], 3)
      )
    )
  })

  output$interpretation <- renderUI({
    y <- extract(input$y)
    x <- extract(input$x)
    fit <- lm(y ~ x)
    if (summary(fit)$coefficients[1, 4] < 0.05 & summary(fit)$coefficients[2, 4] < 0.05) {
      withMathJax(
        paste0("(Make sure the assumptions for linear regression (independance, linearity, homoscedasticity, outliers and normality) are met before interpreting the coefficients.)"),
        br(),
        paste0("For a (hypothetical) value of ", input$xlab, " = 0, the mean of ", input$ylab, " = ", round(fit$coef[[1]], 3), "."),
        br(),
        paste0("For an increase of one unit of ", input$xlab, ", ", input$ylab, ifelse(round(fit$coef[[2]], 3) >= 0, " increases (on average) by ", " decreases (on average) by "), abs(round(fit$coef[[2]], 3)), ifelse(abs(round(fit$coef[[2]], 3)) >= 2, " units", " unit"), ".")
      )
    } else if (summary(fit)$coefficients[1, 4] < 0.05 & summary(fit)$coefficients[2, 4] >= 0.05) {
      withMathJax(
        paste0("(Make sure the assumptions for linear regression (independance, linearity, homoscedasticity, outliers and normality) are met before interpreting the coefficients.)"),
        br(),
        paste0("For a (hypothetical) value of ", input$xlab, " = 0, the mean of ", input$ylab, " = ", round(fit$coef[[1]], 3), "."),
        br(),
        paste0("\\( \\beta_1 \\)", " is not significantly different from 0 (p-value = ", round(summary(fit)$coefficients[2, 4], 3), ") so there is no significant relationship between ", input$xlab, " and ", input$ylab, ".")
      )
    } else if (summary(fit)$coefficients[1, 4] >= 0.05 & summary(fit)$coefficients[2, 4] < 0.05) {
      withMathJax(
        paste0("(Make sure the assumptions for linear regression (independance, linearity, homoscedasticity, outliers and normality) are met before interpreting the coefficients.)"),
        br(),
        paste0("\\( \\beta_0 \\)", " is not significantly different from 0 (p-value = ", round(summary(fit)$coefficients[1, 4], 3), ") so when ", input$xlab, " = 0, the mean of ", input$ylab, " is not significantly different from 0."),
        br(),
        paste0("For an increase of one unit of ", input$xlab, ", ", input$ylab, ifelse(round(fit$coef[[2]], 3) >= 0, " increases (on average) by ", " decreases (on average) by "), abs(round(fit$coef[[2]], 3)), ifelse(abs(round(fit$coef[[2]], 3)) >= 2, " units", " unit"), ".")
      )
    } else {
      withMathJax(
        paste0("(Make sure the assumptions for linear regression (independance, linearity, homoscedasticity, outliers and normality) are met before interpreting the coefficients.)"),
        br(),
        paste0("\\( \\beta_0 \\)", " and ", "\\( \\beta_1 \\)", " are not significantly different from 0 (p-values = ", round(summary(fit)$coefficients[1, 4], 3), " and ", round(summary(fit)$coefficients[2, 4], 3), ", respectively) so the mean of ", input$ylab, " is not significantly different from 0.")
      )
    }
  })
  
  output$assumptions <- renderPlot({
    y <- extract(input$y)
    x <- extract(input$x)
    fit <- lm(y ~ x)
    par(mfrow = c(2, 2))
    plot(fit, which = c(1:3, 5))
  })

  output$plot <- renderPlotly({
    y <- extract(input$y)
    x <- extract(input$x)
    fit <- lm(y ~ x)
    dat <- data.frame(x, y)
    p <- ggplot(dat, aes(x = x, y = y)) +
      geom_point() +
      stat_smooth(method = "lm", se = input$se) +
      ylab(input$ylab) +
      xlab(input$xlab) +
      theme_minimal()
    ggplotly(p)
  })

  output$downloadReport <- downloadHandler(
    filename = function() {
      paste("my-report", sep = ".", switch(
        # input$format, PDF = "pdf", HTML = "html", Word = "docx"
        input$format, HTML = "html"
      ))
    },

    content = function(file) {
      src <- normalizePath("report.Rmd")

      # temporarily switch to the temp dir, in case you do not have write
      # permission to the current working directory
      owd <- setwd(tempdir())
      on.exit(setwd(owd))
      file.copy(src, "report.Rmd", overwrite = TRUE)

      library(rmarkdown)
      out <- render("report.Rmd", switch(
        input$format,
        # PDF = pdf_document(), HTML = html_document(), Word = word_document()
        HTML = html_document()
      ))
      file.rename(out, file)
    }
  )
}

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