{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# R Graphics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## R Graphics Systems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are 3 different grpahcis systems widely used in R - base, `lattice` and `ggplot2`. We will focus on `ggplot2` because it provides the most logical approach to plot constructin using a *grammar of graphics*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Base" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "n <- 100\n", "x <- sort(runif(n))\n", "y <- x^2 + x + 1 + 0.2*rnorm(n)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "m <- lm(y ~ I(x^2))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "options.orig <- options(repr.plot.width=6, repr.plot.height=4)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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oVCafN3/OjRoxMSElqXNjTAr7+CtTWRbSQICk5UUbmmpcUikSQlJQHg4MGDffv2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\nAADiCBwAAEAcgQMAAIgjcAAAAHH/A7URBoo9d2/UAAAAAElFTkSuQmCC", "text/plain": [ "Plot with title “Base Graphics”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(x, y, main=\"Base Graphics\")\n", "lines(x, predict(m), col = \"red\", lwd = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `ggplot2`" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Registered S3 methods overwritten by 'ggplot2':\n", " method from \n", " [.quosures rlang\n", " c.quosures rlang\n", " print.quosures rlang\n", "── \u001b[1mAttaching packages\u001b[22m ─────────────────────────────────────── tidyverse 1.2.1 ──\n", "\u001b[32m✔\u001b[39m \u001b[34mggplot2\u001b[39m 3.1.1 \u001b[32m✔\u001b[39m \u001b[34mpurrr \u001b[39m 0.3.2\n", "\u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 2.1.2 \u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 0.8.1\n", "\u001b[32m✔\u001b[39m \u001b[34mtidyr \u001b[39m 0.8.3 \u001b[32m✔\u001b[39m \u001b[34mstringr\u001b[39m 1.4.0\n", "\u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 1.3.1 \u001b[32m✔\u001b[39m \u001b[34mforcats\u001b[39m 0.4.0\n", "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n", "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n", "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n" ] } ], "source": [ "library(tidyverse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### `ggplto2` only works on `data.frame` or similar objects" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "df <- tibble(x=x, y=y)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
| x | y |
|---|---|
| <dbl> | <dbl> |
| 0.02597720 | 0.8526721 |
| 0.03939677 | 0.9947642 |
| 0.04915126 | 0.9809143 |
| 0.04920200 | 1.1198401 |
| 0.05609914 | 1.0031721 |
| 0.06669788 | 1.3603442 |