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a/materials/tutorial_04/tests_tutorial_04.R b/materials/tutorial_04/tests_tutorial_04.R new file mode 100644 index 0000000..bb524b2 --- /dev/null +++ b/materials/tutorial_04/tests_tutorial_04.R @@ -0,0 +1,416 @@ +library(digest) +library(testthat) + +# + +#abstraction templates + +check_TF <- function(answerX.X, expectedHash) { + var_name <- deparse(substitute(answerX.X)) + test_that(paste('Did not assign answer to an object called ', var_name), { + expect_true(exists(var_name)) + }) + + + test_that('Solution should be "true" or "false"', { + expect_match(answerX.X, "true|false", ignore.case = TRUE) + }) + + answer_hash <- digest(tolower(answerX.X)) + #if (answer_hash == "HASH_HERE") { + # print("HINT_HERE") + #} + + test_that("Solution is incorrect", { + expect_equal(answer_hash, expectedHash) + }) + + print("Success!") +} + +check_MC <- function(answerX.X, choiceList, expectedHash) { + var_name <- deparse(substitute(answerX.X)) + test_that(paste('Did not assign answer to an object called ', var_name), { + expect_true(exists(var_name)) + }) + + + test_that(paste('Solution should be a single character ', toString(choiceList)), { + expect_true(tolower(answerX.X) %in% tolower(choiceList)) + }) + + answer_hash <- digest(tolower(answerX.X)) + #if (answer_hash == "HASH_HERE") { + # print("HINT_HERE") + #} else if (answer_hash == "HASH_HERE") { + # print("HINT_HERE") + #} else if (answer_hash == "HASH_HERE") { + # print("HINT_HERE") + #} + + test_that("Solution is incorrect", { + expect_equal(answer_hash, expectedHash) + }) + + print("Success!") +} + + + +# dataCheckTuples is data.frame(c(colnames), c(scale factor), c(expectedHash)) +check_DF <- function(answerX.X, expected_colnames, hashNRows, cols_to_check, precision_list, expectedHashes) { + dataCheckTuples <- data.frame(cols_to_check, precision_list, expectedHashes) + var_name <- deparse(substitute(answerX.X)) + test_that(paste('Did not assign answer to an object called ', var_name), { + expect_true(exists(var_name)) + }) + + test_that("Solution should be a data frame", { + expect_true("data.frame" %in% class(answerX.X)) + }) + + given_colnames <- colnames(answerX.X) + test_that("Data frame does not have the correct columns", { + expect_equal(length(setdiff( + union(expected_colnames, given_colnames), + intersect(expected_colnames, given_colnames) + )), 0) + }) + + test_that("Data frame does not contain the correct number of rows", { + expect_equal(digest(as.integer(nrow(answerX.X))), hashNRows) + }) + + + + apply(dataCheckTuples, 1, function(tuple) { + test_that(paste(tuple[[1]], " does not contain the correct data"), { + expect_equal(digest(as.integer(sum(answerX.X[tuple[[1]]]) * as.double(tuple[[2]]))), + tuple[[3]]) + }) + }) + + + + + print("Success!") +} + + + + +check_numeric <- function(answerX.X, precision, expectedHash) { + var_name <- deparse(substitute(answerX.X)) + test_that(paste('Did not assign answer to an object called ', var_name), { + expect_true(exists(var_name)) + }) + + answer_as_numeric <- as.numeric(answerX.X) + test_that(paste(var_name, " should be a number"), { + expect_false(is.na(answer_as_numeric)) + }) + + test_that(paste(var_name, " value is incorrect"), { + expect_equal(digest(as.integer(answer_as_numeric * precision)), expectedHash) + }) + + print("Success!") +} + + + +check_numeric_element <- function(answerX.X, precision, expectedHash) { + var_name <- deparse(substitute(answerX.X)) + + answer_as_numeric <- as.numeric(answerX.X) + test_that(paste(var_name, " should be a number"), { + expect_false(is.na(answer_as_numeric)) + }) + + test_that(paste(var_name, " value is incorrect"), { + expect_equal(digest(as.integer(answer_as_numeric * precision)), expectedHash) + }) + + print("Success!") +} + + + + +check_plot <- function(answerX.X, x_axis_var, geom_type, hasVline, bin_width_hash, nrow_hash, x_axis_var_hash, hasTitle) { + var_name <- deparse(substitute(answerX.X)) + test_that(paste('Did not assign answer to an object called ', var_name), { + expect_true(exists(var_name)) + }) + + + test_that("Solution should be a ggplot object", { + expect_true(is.ggplot(answerX.X)) + }) + + properties <- c(answerX.X$layers[[1]]$mapping, answerX.X$mapping) + + test_that(paste("Plot should have ", x_axis_var," on the x-axis"), { + expect_true(x_axis_var == rlang::get_expr(properties$x)) + }) + + test_that("Plot does not have the correct layers", { + expect_true(geom_type %in% class(answerX.X$layers[[1]]$geom)) + + if(hasVline) { + expect_true("GeomVline" %in% class(answerX.X$layers[[2]]$geom)) + } + }) + + test_that("Plot does not have the correct bin width", { + expect_equal( + digest(as.integer(mget("stat_params", answerX.X$layers[[1]])[["stat_params"]][["binwidth"]])), + bin_width_hash) + }) + + test_that("Plot does not use the correct data", { + expect_equal(digest(nrow(answerX.X$data)), nrow_hash) + expect_equal(digest(round(sum(answerX.X$data[x_axis_var]))), x_axis_var_hash) + + # If X_AXIS_VAR is not known: + # expect_equal(digest(round(sum(pull(answerX.X$data, rlang::get_expr(properties$x))))), "HASH_HERE") + }) + + test_that("x-axis label should be descriptive and human readable", { + expect_false(answerX.X$labels$x == toString(rlang::get_expr(properties$x))) + }) + + if(hasTitle){ + + test_that("Plot should have a title", { + expect_true("title" %in% names(answerX.X$labels)) + }) + } + + + print("Success!") +} + + +getPermutations <- function(vec) { + rsf <- c() + for (i in 1:length(vec)) { + for (j in i:length(vec)) { + temp <- vec[i:j] + rsf <- c(rsf, paste(temp, collapse= '')) + if (i < j) { + for (k in i:j) { + rsf <- c(rsf, paste(temp[-k], collapse='')) + } + } + } + } + return(unique(rsf)) +} + + + + + +# + +# Question 1.0 + +test_1.0 <- function() { + check_MC(answer1.0, LETTERS[1:3], '127a2ec00989b9f7faf671ed470be7f8') +} + +# + +# Question 1.1 + +test_1.1 <- function() { + check_MC(answer1.1, LETTERS[1:4], '127a2ec00989b9f7faf671ed470be7f8') +} + +# + +# Question 1.2 + +test_1.2 <- function() { + check_MC(answer1.2, LETTERS[1:2], '127a2ec00989b9f7faf671ed470be7f8') +} + +# + +# Question 1.3 + +test_1.3 <- function() { + check_MC(answer1.3, LETTERS[1:6], 'ddf100612805359cd81fdc5ce3b9fbba') +} + +# + +# Question 1.4 + +test_1.4.0 <- function() { + check_numeric_element(caschools_MLR_add$coefficients[1],1e4,"7d5fdc4b1617f1213563cf12b0be1c68") +} + +test_1.4.1 <- function() { + check_numeric_element(caschools_MLR_add$coefficients[2],1e4,"1cf3a32c120bd3f6faddc6ae470fd2b8") +} + +test_1.4.2 <- function() { + check_numeric_element(caschools_MLR_add$coefficients[3],1e4,"8873eb87d376c1c05700be1435ff22dc") +} + + +# + +# Question 1.5 + +test_1.5 <- function() { + check_plot(caschools_MLR_add_plot, + "income", + "GeomPoint" , + FALSE, + "3e2e4a08c44d0224de5b7e668c75ace3", + "d6af036ffbdd7ccfc34dc7862b0e50d3", + "13742f581e47f00fd8beeade76db838c", + TRUE) +} + +# + +# Question 1.6 + +test_1.6 <- function() { + check_DF(caschools_MLR_add_results, + c("term","estimate", "std.error", "statistic", "p.value", "conf.low", "conf.high"), + "11946e7a3ed5e1776e81c0f0ecd383d0", + c("estimate", "std.error", "statistic", "p.value", "conf.low", "conf.high"), + c(100, 100, 100, 100, 100, 100), + c("3f2caceee58bc5e5092ab875c8066a9b", + "d3c5ba4fef4e46e63e649dc573977aad", + "6e4a7f58d3c649fe8d8313435565c283", + "569ddf8dcb5af0cbc7177be6a8b9700d", + "fd34f0720893972017cb2261e9353fb2", + "ee86da303eb6b2854286c84802788768")) +} + +# + +# Question 1.7 + +# manual + +# + +# Question 1.8 + +test_1.8 <- function() { + check_MC(answer1.8, getPermutations(LETTERS[1:4]), "6e7a8c1c098e8817e3df3fd1b21149d1") +} + +# + +# Question 2.0 + +test_2.0 <- function() { + check_MC(answer2.0, LETTERS[1:6], 'd110f00cfb1b248e835137025804a23b') +} + +# + +# Question 2.1 + +test_2.1.0 <- function() { + check_numeric_element(caschools_MLR_int$coefficients[1], 1e4, "080bbbf3c10c028f53b1901022933269") +} +test_2.1.1 <- function() { + check_numeric_element(caschools_MLR_int$coefficients[2], 1e4, "6750c14599866d62ee03d881a88d4737") +} +test_2.1.2 <- function() { + check_numeric_element(caschools_MLR_int$coefficients[3], 1e4, "9c3c926f355b55c26682a59a66d621e3") +} +test_2.1.3 <- function() { + check_numeric_element(caschools_MLR_int$coefficients[4], 1e4, "491174b285abb2888e9e602eecfb6037") +} + + +# + +# Question 2.2 + +test_2.2 <- function() { + check_plot(caschools_MLR_int_plot, + "income", + "GeomPoint", + FALSE, + "3e2e4a08c44d0224de5b7e668c75ace3", + "d6af036ffbdd7ccfc34dc7862b0e50d3", + "13742f581e47f00fd8beeade76db838c", + TRUE) +} + +# + +# Question 2.3 + +test_2.3 <- function() { + check_DF(caschools_MLR_int_results, + c("term","estimate", "std.error", "statistic", "p.value", "conf.low", "conf.high"), + "234a2a5581872457b9fe1187d1616b13", + c("estimate", "std.error", "statistic", "p.value", "conf.low", "conf.high"), + c(100, 100, 100, 100, 100, 100), + c("8adf1c6033759946124174b1ffecc9d1", + "2109c9c0db840505d06b32da37f3261e", + "6f11355413a4aa7c96bf7412868a7e7f", + "242f3fe311473815db79235ff6708bde", + "ec9d7c4ea6c09c65a368c4865e500886", + "8fcc24b94746de0d011202126d17c4e0")) +} + +# + +# Question 2.4 + +test_2.4 <- function() { + check_MC(answer2.4, getPermutations(LETTERS[1:5]), '8310e591706d1e38cdbfd4e26f17a274') +} + +# + +# Question 2.5 + +# manual + +# + +# Quesiton 2.6 + + +test_2.6.0 <- function() { + check_DF(caschools_SLR_kk06_results, + c("term","estimate", "std.error", "statistic", "p.value"), + "c01f179e4b57ab8bd9de309e6d576c48", + c("estimate", "std.error", "statistic", "p.value"), + c(100, 100, 100, 100), + c("82798d4574cf47d5cb838e4aca470ed8", + "9a1e47f252c2f2aa62cab1323c75885b", + "878fe51e9e4a668776d114d06fd00cc9", + "1473d70e5646a26de3c52aa1abd85b1f")) +} + + + +test_2.6.1 <- function() { + check_DF(caschools_SLR_kk08_results, + c("term","estimate", "std.error", "statistic", "p.value"), + "c01f179e4b57ab8bd9de309e6d576c48", + c("estimate", "std.error", "statistic", "p.value"), + c(100, 100, 100, 100), + c("8adf1c6033759946124174b1ffecc9d1", + "525d73b4c5528794642ceb4dd9f987c2", + "eda26e24431618557efc7037b20d0568", + "1473d70e5646a26de3c52aa1abd85b1f")) +} + + +test_2.6.2 <- function() { + check_DF(caschools_MLR_int_results, + c("term","estimate", "std.error", "statistic", "p.value", "conf.low", "conf.high"), + "234a2a5581872457b9fe1187d1616b13", + c("estimate", "std.error", "statistic", "p.value", "conf.low", "conf.high"), + c(100, 100, 100, 100, 100, 100), + c("8adf1c6033759946124174b1ffecc9d1", + "2109c9c0db840505d06b32da37f3261e", + "6f11355413a4aa7c96bf7412868a7e7f", + "242f3fe311473815db79235ff6708bde", + "ec9d7c4ea6c09c65a368c4865e500886", + "8fcc24b94746de0d011202126d17c4e0")) +} + +# + +# Question 2.7 + +# manual diff --git a/materials/tutorial_04/tutorial_04.ipynb b/materials/tutorial_04/tutorial_04.ipynb new file mode 100644 index 0000000..f842418 --- /dev/null +++ b/materials/tutorial_04/tutorial_04.ipynb @@ -0,0 +1,1613 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "f97f65e4d6b4c1d4d999d0c2ae225fc5", + "grade": false, + "grade_id": "cell-f1e1d845873036f4", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "# Tutorial 4: MLR with different types of input variables" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "1c57f899f006691c0cb0f40be06bb51e", + "grade": false, + "grade_id": "cell-82d9926086d47a80", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "#### Lecture and Tutorial Learning Goals:\n", + "After completing this week's lecture and tutorial work, you will be able to:\n", + "\n", + "1. Give an example of a real problem that that could be answered by a multiple linear regression.\n", + "2. Interpret the coefficients and $p$-values of different types of input variables, including categorical input variables.\n", + "3. Define interactions in the context of linear regression.\n", + "4. Write a computer script to perform linear regression when input variables are continuous or discrete, and when there are interactions between some of these variables." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "7fc505b9da3ba24a646a8a35b69f517d", + "grade": false, + "grade_id": "cell-a2a153352bc44a68", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# Run this cell before continuing.\n", + "library(tidyverse)\n", + "library(repr)\n", + "library(infer)\n", + "library(cowplot)\n", + "library(broom)\n", + "library(AER)\n", + "source(\"tests_tutorial_04.R\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "ef63ebcfe8716aad38a2bf893e613b02", + "grade": false, + "grade_id": "cell-9be71f65643c5906", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "## The data\n", + "\n", + "In this tutorial, we will continue using the `CASchools` real world dataset from 420 K-6 and K-8 districts in California. The California School data set comes with an R package called `AER`, an acronym for Applied Econometrics with R (by Christian Kleiber & Zeileis, 2017). \n", + "\n", + "The dataset contains data on test performance, school characteristics and student demographic backgrounds for school districts in California. Among many variables available we will use the following:\n", + "\n", + "- `grades`: factor indicating grade span of district.\n", + "\n", + "- `income`: District average income (in USD 1,000).\n", + "\n", + "- `english`: Percent of English learners.\n", + "\n", + "- `read`: Average reading score.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "e46acff06f2da23622a95dcad738046c", + "grade": false, + "grade_id": "cell-751a3a4db77146a7", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "#run this cell\n", + "\n", + "data(CASchools)\n", + "\n", + "caschools <- CASchools %>%\n", + " select(grades, income, english, read) %>%\n", + " mutate_if(is.numeric, round, 2)\n", + "\n", + "head(caschools)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "491d42046529205e254c52113200e55a", + "grade": false, + "grade_id": "cell-3dfb99accf2154a8", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "#### Important: Note that if the categorical variable is not a factor, `lm` won't create a dummy variable!! \n", + "\n", + "> Make sure that categorical variables in your model are factors. If they are not, then **set them as factors**!!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "f058fbba73a9a4936f333e50270d5d74", + "grade": false, + "grade_id": "cell-a7382e79e72c9703", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "## 1. MLR: additive\n", + "\n", + "As discussed in the lecture, R will create dummy variables to include categorical variables in the model. In this example, `grades` is a categorical variable with 2 levels. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "9367815b59f44875ddc3b3cedffd41a2", + "grade": false, + "grade_id": "cell-18576173209dcbfe", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.0**\n", + "
{points: 1}\n", + "\n", + "Since the input variable `grades` is a discrete and nominal variable with 2 levels, KK-06 and KK-08. Since this variable is a factor in the dataset, `lm` selects one level as a baseline to create a dummy variable. Which level of `grades` is selected, by default, as a baseline?\n", + "\n", + "**A.** `KK-06`\n", + "\n", + "**B.** `KK-08`\n", + "\n", + "*Assign your answer to an object called `answer1.0`. Your answer should be one of `\"A\"` or `\"B\"` surrounded by quotes.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "cd4bd2ff4058b85570033044f5e731a9", + "grade": false, + "grade_id": "cell-f073f90a4398375f", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# answer1.0 <- ...\n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "d6f3723f0f8ef72f8cbfa6906e42b426", + "grade": true, + "grade_id": "cell-b6ce784a5466648d", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_1.0()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "dc00d710ccdb843088fd0cd32e7120bc", + "grade": false, + "grade_id": "cell-3e16a0eb1d1251a6", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.1**\n", + "
{points: 1}\n", + "\n", + "How many dummy variables does `lm` create to fit a linear regression with the categorical variable `grades`?\n", + "\n", + "**A.** 1\n", + "\n", + "**B.** 2\n", + "\n", + "**C.** 3\n", + "\n", + "**D.** 4\n", + "\n", + "*Assign your answer to an object called `answer1.1`. Your answer should be one of `\"A\"`, `\"B\"`, `\"C\"`, or `\"D\"` surrounded by quotes.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "c3a74807a9fd10b0a98bf7040df5d7ca", + "grade": false, + "grade_id": "cell-49fd43204dbbbe64", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# answer1.1 <- \n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "aab29ab12d9f21578b4e0bb9fb243b26", + "grade": true, + "grade_id": "cell-8a6966bb42e5995c", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_1.1()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "accc4ebe5b88ec809ed324f02192458c", + "grade": false, + "grade_id": "cell-75a9578496bd6d9c", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.2**\n", + "
{points: 1}\n", + "\n", + "In the previous tutorial, you used a simple linear regression (SLR) to study the relation between `read` and `income`, on average for all type of schools. Suppose you want to examine if there is any difference in this relation depending on the grade span of the school (i.e.,KK-06 vs KK-08). \n", + "\n", + "If for all types of school (i.e., for all levels of `grades`) you expect the same change in reading score per unit change in the average income, which MLR will you fit in `R` using the `lm` function?\n", + "\n", + "**A.** `lm(read ~ income + grades, data = caschools)`\n", + "\n", + "**B.** `lm(read ~ income * grades, data = caschools)`\n", + "\n", + "*Assign your answer to an object called `answer1.2`. Your answer should be one of `\"A\"` or `\"B\"` surrounded by quotes.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "e97fed2fc79c181b9447e6caafaa4b18", + "grade": false, + "grade_id": "cell-f6b2d0e8025cf80e", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# answer1.2 <- \n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "d810fcc6f81a8afc5987ec10316adfb0", + "grade": true, + "grade_id": "cell-645245eaf0a415b6", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_1.2()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "12af6ed36232289caa83e3518b468b98", + "grade": false, + "grade_id": "cell-37a0395078a18c50", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.3**\n", + "
{points: 1}\n", + "\n", + "Which of the following descriptions will best describe a visualization of the MLR considered in **Question 1.2**? \n", + "\n", + "**A.** one line through a cloud of data points\n", + "\n", + "**B.** two lines with equal slopes but different intercepts\n", + "\n", + "**C.** two lines with different slopes and different intercepts\n", + "\n", + "**D.** a smooth concave curve through a cloud of data points\n", + "\n", + "**E.** two boxplots for different levels of `grades`\n", + "\n", + "*Assign your answer to an object called `answer1.3`. Your answer should be one of `\"A\"`, `\"B\"`, `\"C\"`, `\"D\"`, or `\"E\"` surrounded by quotes.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "a44f499620bcd84405a2c6bd2a8a9d73", + "grade": false, + "grade_id": "cell-fd274734aed6b6c7", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# answer1.3 <- \n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "35393769c0469b8c86febb09350aee54", + "grade": true, + "grade_id": "cell-905c24ed72606cd0", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_1.3()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "b0960d461c3ee4f2a8374e801249aa6e", + "grade": false, + "grade_id": "cell-e905a3e604e8750e", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.4**\n", + "
{points: 1}\n", + "\n", + "Using `caschools`, estimate the MLR proposed in **Question 1.2** and called it `caschools_MLR_add`.\n", + "\n", + "*Fill out those parts indicated with `...`, uncomment the corresponding code in the cell below, and run it.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "50c8eb2ff60b12ebb21f9c86ca8d4190", + "grade": false, + "grade_id": "cell-537a5de8c45b73fd", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# caschools_MLR_add <- ...(...,\n", + "# ...\n", + "# )\n", + "# caschools_MLR_add\n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "1024a6c0ac471806ff34ea856ddcbc0a", + "grade": true, + "grade_id": "cell-c955967bb20ade73", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_1.4.0()\n", + "test_1.4.1()\n", + "test_1.4.2()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "1b032d1a200038ebfb0c9418863f77a5", + "grade": false, + "grade_id": "cell-8a3de76c80df5397", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.5**\n", + "
{points: 1}\n", + "\n", + "Create a plot of the data in `caschools` (using `geom_point()`) along with the estimated regression lines coming from the additive regression model `caschools_MLR_add`. Use different colours for the points and regression lines of each type of school (levels of `grades`). Include a legend indicating what colour corresponds to each level with proper axis labels. The `ggplot()` object's name will be `caschools_MLR_add_plot`.\n", + "\n", + "*Fill out those parts indicated with `...`, uncomment the corresponding code in the cell below, and run it.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "3a291e10325632cc6dbe54e29fbd0a5b", + "grade": false, + "grade_id": "cell-9dcae296b8566967", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "options(repr.plot.width = 15, repr.plot.height = 7) # Adjust these numbers so the plot looks good in your desktop.\n", + "\n", + "# caschools$pred_MLR_Add <- predict(caschools_MLR_add) # Using predict() to create estimated regression lines.\n", + "\n", + "# caschools_MLR_add_plot <- ggplot(..., aes(\n", + "# ...,\n", + "# ...,\n", + "# color = ...\n", + "# )) +\n", + "# ...() +\n", + "# geom_line(aes(y = pred_MLR_Add), size = 1) +\n", + "# labs(\n", + "# title = ...,\n", + "# x = ...,\n", + "# y = ...\n", + "# ) +\n", + "# theme(\n", + "# text = element_text(size = 16.5),\n", + "# plot.title = element_text(face = \"bold\"),\n", + "# axis.title = element_text(face = \"bold\"),\n", + "# legend.title = element_text(face = \"bold\"),\n", + "# ) +\n", + "# labs(color = \"grades\")\n", + "# caschools_MLR_add_plot\n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "125d765392989a6f948357a6cc048d01", + "grade": true, + "grade_id": "cell-60b4784943979e31", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_1.5()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "806f32d510d22cb6fee3cde12b870e5f", + "grade": false, + "grade_id": "cell-5a6b3d5e566adacc", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.6**\n", + "
{points: 1}\n", + "\n", + "Find the estimated coefficients of `caschools_MLR_add` using `tidy()`. Report the estimated coefficients, their standard errors and corresponding $p$-values. Include the corresponding asymptotic **90% confidence intervals**. Store the results in the variable `caschools_MLR_add_results`.\n", + "\n", + "*Fill out those parts indicated with `...`, uncomment the corresponding code in the cell below, and run it.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "d35aa6dc891e12999af8ebac83a3f01d", + "grade": false, + "grade_id": "cell-253df594cc213305", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# caschools_MLR_add_results <- ...(..., ..., ....) %>% mutate_if(is.numeric, round, 2)\n", + "# caschools_MLR_add_results\n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "182cc3fee5a4319bbefb8dee3139a641", + "grade": true, + "grade_id": "cell-2e20842d0ef2e18c", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_1.6()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "99fa41618949973ba0ef9a3898cfcdac", + "grade": false, + "grade_id": "cell-045d79b6d3e4e227", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.7**\n", + "
{points: 1}\n", + "\n", + "Using the results in `caschools_MLR_add_results` from **Question 1.6**, how would you interpret the estimated coefficient of the continuous variable `income` ?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "885cf006afa42b04df3d244c08372d30", + "grade": true, + "grade_id": "cell-c4f0c10f52097476", + "locked": false, + "points": 1, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "source": [ + "> *Your answer goes here.*\n", + "\n", + "DOUBLE CLICK TO EDIT **THIS CELL** AND REPLACE THIS TEXT WITH YOUR ANSWER." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "29524df0c431f38b0c86393221e632ae", + "grade": false, + "grade_id": "cell-2c547503213abacd", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 1.8**\n", + "
{points: 1}\n", + "\n", + "Using a **significance level $\\alpha = 0.10$**, which of the following claims are correct?\n", + "\n", + "\n", + "**A.** for any average income, the expected reading score is the same for schools with KK-06 and schools with KK-08 grades. \n", + "\n", + "**B.** there is enough evidence to reject the hypothesis that, for any average income, the expected reading score is the same for schools with KK-06 and schools with KK-08 grades.\n", + "\n", + "**C.** for any type of school, the change in `read` per unit change in `income` is statistically significant.\n", + "\n", + "**D.** there is enough evidence to believe that the association between `income` and `read` varies depending on the grade span of the school.\n", + "\n", + "\n", + "*Assign your answers to the object `answer1.8`. Your answers have to be included in a single string indicating the correct options **in alphabetical order** and surrounded by quotes (e.g., `\"ABCD\"` indicates you are selecting the four options).*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "e77708faa194004e77f8a89d1d0fa38c", + "grade": false, + "grade_id": "cell-7ded1cd632f3869e", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# answer1.8 <- \n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "041fdc33a657af0a6e2e3f9dbd1d9fb7", + "grade": true, + "grade_id": "cell-51e7b8a61bab24c9", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_1.8()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "66e67b9204bf0f10fb51ab869301f118", + "grade": false, + "grade_id": "cell-e9994b034ba662aa", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "source": [ + "**Question 1.9**\n", + "
{points: 1}\n", + "\n", + "In one or two sentence explain what \"statistically significant\" mean in the following sentence and how it is different from \"practical significant\".\n", + "\n", + "> \"for any type of school, the change in `read` per unit change in `income` is statistically significant\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "a810e419b66aa68785aac7a6f64b97e0", + "grade": true, + "grade_id": "cell-66c583a8d25d2564", + "locked": false, + "points": 1, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "source": [ + "> *Your answer goes here.*\n", + "\n", + "DOUBLE CLICK TO EDIT **THIS CELL** AND REPLACE THIS TEXT WITH YOUR ANSWER." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "2a9dc9062fbfdf7e4d6b107eacc71562", + "grade": false, + "grade_id": "cell-873ce5c231e18f2c", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "source": [ + "## 2. MLR: with interactions\n", + "\n", + "In this section we will explore if the relation between `read` and `income` is the same for all types of schools. We can do this using **interactions** between the input variables!\n", + "\n", + "> **Note** that interactions can be used, in general, when the relation between an input and the response depends on another input variable (not necessarily categorical!)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "4fa6f32f5ed0f62df4758f88422b5fcd", + "grade": false, + "grade_id": "cell-004da4c289bb7b52", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 2.0**\n", + "
{points: 1}\n", + "\n", + "We can use `lm` to fit the MLR with interactions between the continuous variable `income` and the categorical variable `grades` (with 2 levels) defined above.\n", + "\n", + "How many regression coefficients will be estimated by `lm`?\n", + "\n", + "**A.** 1\n", + "\n", + "**B.** 2\n", + "\n", + "**C.** 3\n", + "\n", + "**D.** 4\n", + "\n", + "\n", + "*Assign your answer to an object called `answer2.0`. Your answer should be one of `\"A\"`, `\"B\"`, `\"C\"`, `\"D\"`, `\"E\"`, or `\"F\"` surrounded by quotes.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "c879ea7b9e4c78544e35bad40039dbff", + "grade": false, + "grade_id": "cell-598588b1701bd38d", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# answer2.0 <- \n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "7392fce520cd1b366107f36865b48507", + "grade": true, + "grade_id": "cell-632b241ba713f5aa", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_2.0()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "38550478a20bfdac1e3007e1eeaa8707", + "grade": false, + "grade_id": "cell-d67f4a30fbd6b249", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 2.1**\n", + "
{points: 1}\n", + "\n", + "Using `caschools`, estimate the MLR with interaction described above and called it `caschools_MLR_int`.\n", + "\n", + "> **Hint:** Interaction terms can be easily specified in `lm()` using the notation `*`.\n", + "\n", + "*Fill out those parts indicated with `...`, uncomment the corresponding code in the cell below, and run it.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "3f7cd83f01098924b263228b29661d5e", + "grade": false, + "grade_id": "cell-d99a7bc9a1759fac", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# caschools_MLR_int <- ...(...,\n", + "# ...\n", + "# )\n", + "# caschools_MLR_int\n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "2fdb37752dd73b167cb7c10e09747df9", + "grade": true, + "grade_id": "cell-a2d3def81c3ee729", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_2.1.0()\n", + "test_2.1.1()\n", + "test_2.1.2()\n", + "test_2.1.3()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "cf9923865860d6e214047d8d307a97e2", + "grade": false, + "grade_id": "cell-1fc6d7f5ba4c6352", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 2.2**\n", + "
{points: 1}\n", + "\n", + "Create a plot of the data in `caschools` (using `geom_point()`) along with the estimated regression lines coming from the interaction regression model `caschools_MLR_int` (note that your plot should have two regression lines, one for each `grades`). Use different colours for the points and regression lines of each type of school (levels of `grades`). Include a legend indicating what colour corresponds to each level with proper axis labels. The `ggplot()` object's name will be `caschools_MLR_int_plot`.\n", + "\n", + "*Fill out those parts indicated with `...`, uncomment the corresponding code in the cell below, and run it.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "f174d5a9cf49023348e6d142454b81c4", + "grade": false, + "grade_id": "cell-0264d31dfcee946e", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# caschools$pred_MLR_int <- predict(caschools_MLR_int) # Using predict() to create estimated regression lines.\n", + "\n", + "# caschools_MLR_int_plot <- ggplot(..., aes(\n", + "# ...,\n", + "# ...,\n", + "# color = ...\n", + "# )) +\n", + "# ...() +\n", + "# geom_line(aes(y = pred_MLR_int), size = 1) +\n", + "# labs(\n", + "# title = ...,\n", + "# x = ...,\n", + "# y = ...\n", + "# ) +\n", + "# theme(\n", + "# text = element_text(size = 16.5),\n", + "# plot.title = element_text(face = \"bold\"),\n", + "# axis.title = element_text(face = \"bold\"),\n", + "# legend.title = element_text(face = \"bold\"),\n", + "# ) +\n", + "# labs(color = \"grades\")\n", + "# caschools_MLR_int_plot\n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "a0895f6f2f13d7ce6a6805aa3ca750a7", + "grade": true, + "grade_id": "cell-1de4883ebac641a7", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_2.2()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "766e5717f264eef3dd6af79a62b04deb", + "grade": false, + "grade_id": "cell-e850e2f516d793c9", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 2.3**\n", + "
{points: 1}\n", + "\n", + "Find the estimated coefficients of `caschools_MLR_int` using `tidy()`. Report the estimated coefficients, their standard errors and corresponding $p$-values. Include the corresponding asymptotic 90% confidence intervals. Store the results in the variable `caschools_MLR_int_results`.\n", + "\n", + "*Fill out those parts indicated with `...`, uncomment the corresponding code in the cell below, and run it.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "41ef5655a7cbfe3e5ae00bdddcae0a2a", + "grade": false, + "grade_id": "cell-b8a3711ac0aa9e78", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# caschools_MLR_int_results <- ...(..., ..., ....) %>% mutate_if(is.numeric, round, 2)\n", + "# caschools_MLR_int_results\n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "243d015f2afebda5db3917619f72d6fd", + "grade": true, + "grade_id": "cell-db1c5162e30c84bd", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_2.3()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "08d7282803f182d6211ed4dbf302b04c", + "grade": false, + "grade_id": "cell-3867f871a7af4b28", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 2.4**\n", + "
{points: 1}\n", + "\n", + "Using a **significance level $\\alpha = 0.10$**, which of the following claims are correct?\n", + "\n", + "\n", + "**A.** There is enough evidence to reject the hypothesis that, for any average income, the expected reading score is the same for schools with KK-06 and schools with KK-08 grades.\n", + "\n", + "**B.** For any type of school, the change in `read` per unit change in `income` is statistically significant.\n", + "\n", + "**C.** There is enough evidence to reject the hypothesis that the change in `read` per unit change in `income` is the same for schools with KK-06 and schools with KK-08 grades.\n", + "\n", + "**D.** There is not enough evidence to reject the hypothesis that the change in `read` per unit change in `income` is the same for schools with KK-06 and schools with KK-08 grades.\n", + "\n", + "**E.** For schools with KK-06 grade span, the change in `read` per unit change in `income` is statistically significant.\n", + "\n", + "*Assign your answers to the object `answer2.4`. Your answers have to be included in a single string indicating the correct options **in alphabetical order** and surrounded by quotes (e.g., `\"ABCDEFG\"` indicates you are selecting the seven options).*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "feef0f6cf6e41f07ab507be043fcd7fa", + "grade": false, + "grade_id": "cell-8040936e931b0c26", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# answer2.4 <- \n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "3e0e9dc82c3cc0b9ec220187142156a4", + "grade": true, + "grade_id": "cell-1873e4d29d602968", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_2.4()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "3f41bec2efe1206490c1b9db22847a4e", + "grade": false, + "grade_id": "cell-a4830b2233d003de", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 2.5**\n", + "
{points: 1}\n", + "\n", + "A common practice is not to interpret coefficients that are not statistically significant, since what you observe is not significantly different from 0 and reflects just noise in the data. Alternatively, you can provide an interpretation but with the caveat that the result is not statistically significant. \n", + "\n", + "Following the second approach, what would be a correct interpretation of estimated coefficient of the interaction term `income:gradesKK-08` from `caschools_MLR_int_results` in **Question 2.3**? (remember to comment on the significance of the result)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "af5ae4b1617c5eb5fa76f953cc7fc90d", + "grade": true, + "grade_id": "cell-94b5d3fd08f12a3f", + "locked": false, + "points": 1, + "schema_version": 3, + "solution": true, + "task": false + } + }, + "source": [ + "> *Your answer goes here.*\n", + "\n", + "DOUBLE CLICK TO EDIT **THIS CELL** AND REPLACE THIS TEXT WITH YOUR ANSWER." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "fec03cccfbc7e114c21bfd7fceaf1439", + "grade": false, + "grade_id": "cell-ad8a6bbdaf066526", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 2.6**\n", + "
{points: 1}\n", + "\n", + "Fit the following 3 models as indicated:\n", + "\n", + "**A.** a SLR with `read` as the response and `income` as the *only* input variable using only KK-06 schools in `caschools`. Use `tidy` to get estimated parameters and standard errors. Call the results `caschools_SLR_kk06_results`\n", + "\n", + "**B.** a SLR with `read` as the response and `income` as the *only* input variable using only KK-08 schools in `caschools`. Use `tidy` to get estimated parameters and standard errors. Call the results `caschools_SLR_kk08_results`\n", + "\n", + "**C.** a MLR with `read` as the response and `income` and `grades` as input variables, *including their interaction*, using `caschools`. Note that you already have the estimated parameters and standard errors in `caschools_MLR_int_results`. Uncomment the line to get the results again here.\n", + "\n", + "*Fill out those parts indicated with `...`, uncomment the corresponding code in the cell below, and run it.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "0162042f6abfbd87251fe0c24ba68add", + "grade": false, + "grade_id": "cell-6e18beb71a4fb71f", + "locked": false, + "schema_version": 3, + "solution": true, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# caschools_SLR_kk06_results <- tidy(lm(... ~ ... , \n", + "# data= subset(...,... == ...))) %>% mutate_if(is.numeric, round, 2)\n", + "# caschools_SLR_kk06_results\n", + "\n", + "# caschools_SLR_kk08_results <- tidy(lm(... ~ ... , \n", + "# data= subset(...,... == ...))) %>% mutate_if(is.numeric, round, 2)\n", + "# caschools_SLR_kk08_results\n", + "\n", + "# caschools_MLR_int_results\n", + "\n", + "\n", + "# your code here\n", + "fail() # No Answer - remove if you provide an answer" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "code", + "checksum": "3588b0c0ddca3eaaa2cfe7eb68472928", + "grade": true, + "grade_id": "cell-7211318468890365", + "locked": true, + "points": 1, + "schema_version": 3, + "solution": false, + "task": false + }, + "tags": [] + }, + "outputs": [], + "source": [ + "test_2.6.0()\n", + "test_2.6.1()\n", + "test_2.6.2()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "editable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "7607e9621ddc4c26db6df310297f81dc", + "grade": false, + "grade_id": "cell-22795bb3ed88a300", + "locked": true, + "schema_version": 3, + "solution": false, + "task": false + } + }, + "source": [ + "**Question 2.7**\n", + "
{points: 1}\n", + "\n", + "**2.7.0** Using the results from `caschools_SLR_kk06_results` and `caschools_MLR_int_results` in **Question 2.6**, explain why the estimated coefficients of `income` are the same in both models\n", + "\n", + "**2.7.1** Using the results from `caschools_SLR_kk08_results` and `caschools_MLR_int_results` in **Question 2.6**, explain why the estimated coefficients of `income` are *not* the same in both models. \n", + "\n", + "**2.7.2** Explain why the estimated coefficients of `income` in `caschools_SLR_kk08_results` is *not* the same as that of `income:gradesKK-08` in `caschools_MLR_int_results` using the results from **Question 2.6**." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "deletable": false, + "nbgrader": { + "cell_type": "markdown", + "checksum": "8c6973a0f022fe93f2585f89c5365adb", + "grade": true, + "grade_id": "cell-1bc7a024f2ac0de4", + "locked": false, + "points": 1, + "schema_version": 3, + "solution": true, + "task": false + } + }, + "source": [ + "> *Your answer goes here.*\n", + "\n", + "DOUBLE CLICK TO EDIT **THIS CELL** AND REPLACE THIS TEXT WITH YOUR ANSWER." + ] + } + ], + "metadata": { + "jupytext": { + "formats": "ipynb,Rmd" + }, + "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": "4.2.3" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}