From 510f095bf7c86f51658c9db93f569f71bfb5d75e Mon Sep 17 00:00:00 2001
From: Ubuntu <ubuntu@ip-172-31-47-100.eu-west-3.compute.internal>
Date: Wed, 19 Sep 2018 10:34:36 +0000
Subject: [PATCH] :(

---
 exercises.ipynb | 108 ++++++++++++++++++++++++++++++++++++++++++++----
 1 file changed, 99 insertions(+), 9 deletions(-)

diff --git a/exercises.ipynb b/exercises.ipynb
index 7196331..a811dfe 100644
--- a/exercises.ipynb
+++ b/exercises.ipynb
@@ -5,7 +5,6 @@
    "execution_count": 1,
    "metadata": {
     "autoscroll": false,
-    "collapsed": false,
     "ein.hycell": false,
     "ein.tags": "worksheet-0",
     "slideshow": {
@@ -39,7 +38,6 @@
    "execution_count": null,
    "metadata": {
     "autoscroll": false,
-    "collapsed": false,
     "ein.hycell": false,
     "ein.tags": "worksheet-0",
     "slideshow": {
@@ -60,7 +58,6 @@
    "execution_count": null,
    "metadata": {
     "autoscroll": false,
-    "collapsed": false,
     "ein.hycell": false,
     "ein.tags": "worksheet-0",
     "slideshow": {
@@ -77,8 +74,93 @@
     "# sd of X's should be c(.2,.5,.3)\n",
     "# noise sd should be .5\n",
     "\n",
-    "params <- list(???)\n",
-    "class(params) <- \"multivariate_params\""
+    "generate_data <- function (params) {\n",
+    "    UseMethod(\"generate_data\")\n",
+    "}\n",
+    "\n",
+    "generate_data.multivariate_params <- function(params) {\n",
+    "        \n",
+    "       N <- params$N\n",
+    "       beta <- params$beta\n",
+    "       params1 <- cbind(params$means, params$sd)\n",
+    "       sd <- params$noise \n",
+    "    \n",
+    "       x <- apply(params1, 1, function(x) rnorm(N, mean = x[1], sd = x[2]))\n",
+    "       x <- cbind(rep(1, N), x)\n",
+    "       eps <- rnorm(N, 0, sd)\n",
+    "       y <- x%*%beta + eps\n",
+    "       list(x = x, y = y)\n",
+    "       \n",
+    "}\n",
+    "                  \n",
+    "generate_data.univariate_params <- function (N, beta, sd) {\n",
+    "    \n",
+    "       N <- params$N\n",
+    "       beta <- params$beta\n",
+    "       sd <- params$noise\n",
+    "    \n",
+    "       x <- rnorm(N, 0, 1)\n",
+    "       eps <- rnorm(N, 0, sd)\n",
+    "       y <- beta*x + eps\n",
+    "       list(x = x, y = y)\n",
+    "}\n",
+    "                  \n",
+    "calc_coef <- function(y,x) {\n",
+    "  coef <- solve(t(x)%*%x, t(x)%*%y)\n",
+    "  coef\n",
+    "}\n",
+    "                  \n",
+    "calc_se <- function(y, x, coef) {\n",
+    "      \n",
+    "      eps <- y - x %*% coef\n",
+    "      sigma2 <- (t(eps) %*% eps) / (nrow(x) - ncol(x))\n",
+    "      varmatrix <- c(sigma2) * solve(t(x) %*% x)\n",
+    "      se<- sqrt(diag(varmatrix))\n",
+    "}\n",
+    "\n",
+    "run_regression <- function(y, x) {\n",
+    "    coef <- calc_coef(y, x)\n",
+    "    se <- calc_se(y, x, coef)\n",
+    "    model <- list(coef=coef, se=se)\n",
+    "    class(model) <- \"simple_model\"\n",
+    "    model\n",
+    "}\n",
+    "                  \n",
+    "                \n",
+    " eval_model <- function(model, beta, conf = 1.96) {\n",
+    "    UseMethod(\"eval_model\")\n",
+    "}\n",
+    "                \n",
+    "                  \n",
+    "eval_model.simple_model <- function(model, beta, conf = 1.96) {\n",
+    "    coef <- model$coef\n",
+    "    se <- model$se\n",
+    "    up <- coef + se*conf\n",
+    "    down <- coef - se*conf\n",
+    "    beta > down & beta < up\n",
+    "}\n",
+    "\n",
+    "                  \n",
+    "simulate <- function(N, beta, params, sd) {\n",
+    "       d <- generate_data(N, beta, params, sd)\n",
+    "       m <- run_regression(d$y, d$x)\n",
+    "       eval_model(m$coef, m$se, beta)\n",
+    "  }\n",
+    "\n",
+    "                  \n",
+    "avg_simulations <- function(M, N, beta, params, sd) {\n",
+    "       inside <- sapply(1:M, function (x) {\n",
+    "           simulate(N, beta, params, sd)\n",
+    "})\n",
+    "       sum(inside) / M\n",
+    "   }\n",
+    "                  \n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "params <- list(N = N, beta = beta, means = params1, sd = sd, noise = noise)\n",
+    "class(params) <- c(\"univariate\", \"multivariate_params\") "
    ]
   },
   {
@@ -86,7 +168,6 @@
    "execution_count": null,
    "metadata": {
     "autoscroll": false,
-    "collapsed": false,
     "ein.hycell": false,
     "ein.tags": "worksheet-0",
     "slideshow": {
@@ -104,7 +185,6 @@
    "execution_count": null,
    "metadata": {
     "autoscroll": false,
-    "collapsed": false,
     "ein.hycell": false,
     "ein.tags": "worksheet-0",
     "slideshow": {
@@ -122,7 +202,6 @@
    "execution_count": null,
    "metadata": {
     "autoscroll": false,
-    "collapsed": false,
     "ein.hycell": false,
     "ein.tags": "worksheet-0",
     "slideshow": {
@@ -145,15 +224,26 @@
     "\n",
     "# Note: be creative in your design! Add more classes if you think it helps!\n",
     "# Think about which functions you want to be class-agnostic and which to be\n",
-    "# class-aware! "
+    "# class-aware! \n",
+    "\n",
+    "\n"
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
    "display_name": "R",
+   "language": "R",
    "name": "ir"
   },
+  "language_info": {
+   "codemirror_mode": "r",
+   "file_extension": ".r",
+   "mimetype": "text/x-r-source",
+   "name": "R",
+   "pygments_lexer": "r",
+   "version": "3.4.1"
+  },
   "name": "Untitled.ipynb"
  },
  "nbformat": 4,