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108 changes: 99 additions & 9 deletions exercises.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,6 @@
"execution_count": 1,
"metadata": {
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"ein.hycell": false,
"ein.tags": "worksheet-0",
"slideshow": {
Expand Down Expand Up @@ -39,7 +38,6 @@
"execution_count": null,
"metadata": {
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"ein.tags": "worksheet-0",
"slideshow": {
Expand All @@ -60,7 +58,6 @@
"execution_count": null,
"metadata": {
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"slideshow": {
Expand All @@ -77,16 +74,100 @@
"# 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\") "
]
},
{
"cell_type": "code",
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"slideshow": {
Expand All @@ -104,7 +185,6 @@
"execution_count": null,
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"ein.tags": "worksheet-0",
"slideshow": {
Expand All @@ -122,7 +202,6 @@
"execution_count": null,
"metadata": {
"autoscroll": false,
"collapsed": false,
"ein.hycell": false,
"ein.tags": "worksheet-0",
"slideshow": {
Expand All @@ -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"
]
}
],
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"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,
Expand Down