{"id":1485,"date":"2023-06-22T02:36:52","date_gmt":"2023-06-22T02:36:52","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/multiple-linear-regression-apply-it-1\/"},"modified":"2024-03-01T20:13:58","modified_gmt":"2024-03-01T20:13:58","slug":"multiple-linear-regression-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/multiple-linear-regression-apply-it-1\/","title":{"raw":"Multiple Linear Regression - Apply It 1","rendered":"Multiple Linear Regression &#8211; Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write and describe a multiple linear regression model equation&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Write and describe a multiple linear regression model equation<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate and describe the unadjusted coefficient of determination&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate and describe the unadjusted coefficient of determination<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Assess the model assumptions with a residual or a predicted values plot&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Assess the model assumptions with a residual or a predicted values plot<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Students in an introductory statistics class at The University of Queensland participated in a simple experiment.[footnote]Wilson, R. J. (n.d.). Pulse rates before and after exercise. StatSci.org. http:\/\/www.statsci.org\/data\/oz\/ms212.html[\/footnote] The students took their own pulse rates. They were then asked to flip a coin. If the coin came up heads, they were to run in place for one minute. Otherwise, they sat for one minute. Afterward, everyone took their pulse rates again. The pulse rates and other physiological and lifestyle data were recorded in a data set called \u201c<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Data+Set+Files\/PulseRate_FINAL.csv\">Pulse Rate<\/a>.\u201d There are a total of 110 observations and 11 variables about the experiment.<\/p>\r\n<p>[reveal-answer q=\"171997\"]Data Dictionary[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"171997\"]The variables in the data set are:<\/p>\r\n<div style=\"text-align: left;\" align=\"center\">\r\n<table style=\"width: 696px;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><strong>Variable<\/strong><\/td>\r\n<td style=\"width: 446.181px;\"><strong>Description<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>ID<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Identification number<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Height<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Height in centimeters (cm)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Weight<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Weight in kilograms (kg)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Age<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Age in years<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Sex<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Male\/female<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Smokes<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Are you a regular smoker? (yes\/no)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Alcohol<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Are you a regular drinker? (yes\/no)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Exercise<\/em><\/td>\r\n<td style=\"width: 446.181px;\">What is your frequency of exercise? (low, moderate, high)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>GroupAssignment<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Whether the student ran or sat between the first and second pulse measurements<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Pulse1<\/em><\/td>\r\n<td style=\"width: 446.181px;\">First pulse measurement (rate per minute)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Pulse2<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Second pulse measurement (rate per minute)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 167.587px;\"><em>Year<\/em><\/td>\r\n<td style=\"width: 446.181px;\">Year of class (1993\u20131998)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>[\/hidden-answer]<br \/>\r\nThe first research question we are interested in exploring is: \u201cWhat is the relationship between weight and first pulse measurement? Is weight a useful predictor of first pulse rate?\u201d<\/p>\r\n<\/div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3084[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3086[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3087[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3088[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3089[\/ohm2_question]<\/section>\r\n<p>The second research question that we are interested in exploring is: \u201cWhat is the relationship between weight and age on the first pulse measurement? Are weight and age useful predictors of the first pulse rate?\u201d<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3090[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3091[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3092[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write and describe a multiple linear regression model equation&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Write and describe a multiple linear regression model equation<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate and describe the unadjusted coefficient of determination&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate and describe the unadjusted coefficient of determination<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Assess the model assumptions with a residual or a predicted values plot&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Assess the model assumptions with a residual or a predicted values plot<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Students in an introductory statistics class at The University of Queensland participated in a simple experiment.<a class=\"footnote\" title=\"Wilson, R. J. (n.d.). Pulse rates before and after exercise. StatSci.org. http:\/\/www.statsci.org\/data\/oz\/ms212.html\" id=\"return-footnote-1485-1\" href=\"#footnote-1485-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> The students took their own pulse rates. They were then asked to flip a coin. If the coin came up heads, they were to run in place for one minute. Otherwise, they sat for one minute. Afterward, everyone took their pulse rates again. The pulse rates and other physiological and lifestyle data were recorded in a data set called \u201c<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Data+Set+Files\/PulseRate_FINAL.csv\">Pulse Rate<\/a>.\u201d There are a total of 110 observations and 11 variables about the experiment.<\/p>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q171997\">Data Dictionary<\/button><\/p>\n<div id=\"q171997\" class=\"hidden-answer\" style=\"display: none\">The variables in the data set are:<\/p>\n<div style=\"text-align: left; margin: auto;\">\n<table style=\"width: 696px;\">\n<tbody>\n<tr>\n<td style=\"width: 167.587px;\"><strong>Variable<\/strong><\/td>\n<td style=\"width: 446.181px;\"><strong>Description<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>ID<\/em><\/td>\n<td style=\"width: 446.181px;\">Identification number<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Height<\/em><\/td>\n<td style=\"width: 446.181px;\">Height in centimeters (cm)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Weight<\/em><\/td>\n<td style=\"width: 446.181px;\">Weight in kilograms (kg)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Age<\/em><\/td>\n<td style=\"width: 446.181px;\">Age in years<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Sex<\/em><\/td>\n<td style=\"width: 446.181px;\">Male\/female<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Smokes<\/em><\/td>\n<td style=\"width: 446.181px;\">Are you a regular smoker? (yes\/no)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Alcohol<\/em><\/td>\n<td style=\"width: 446.181px;\">Are you a regular drinker? (yes\/no)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Exercise<\/em><\/td>\n<td style=\"width: 446.181px;\">What is your frequency of exercise? (low, moderate, high)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>GroupAssignment<\/em><\/td>\n<td style=\"width: 446.181px;\">Whether the student ran or sat between the first and second pulse measurements<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Pulse1<\/em><\/td>\n<td style=\"width: 446.181px;\">First pulse measurement (rate per minute)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Pulse2<\/em><\/td>\n<td style=\"width: 446.181px;\">Second pulse measurement (rate per minute)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 167.587px;\"><em>Year<\/em><\/td>\n<td style=\"width: 446.181px;\">Year of class (1993\u20131998)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p>\nThe first research question we are interested in exploring is: \u201cWhat is the relationship between weight and first pulse measurement? Is weight a useful predictor of first pulse rate?\u201d<\/p>\n<\/div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3084\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3084&theme=lumen&iframe_resize_id=ohm3084&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3086\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3086&theme=lumen&iframe_resize_id=ohm3086&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3087\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3087&theme=lumen&iframe_resize_id=ohm3087&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3088\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3088&theme=lumen&iframe_resize_id=ohm3088&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3089\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3089&theme=lumen&iframe_resize_id=ohm3089&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>The second research question that we are interested in exploring is: \u201cWhat is the relationship between weight and age on the first pulse measurement? Are weight and age useful predictors of the first pulse rate?\u201d<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3090\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3090&theme=lumen&iframe_resize_id=ohm3090&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3091\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3091&theme=lumen&iframe_resize_id=ohm3091&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3092\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3092&theme=lumen&iframe_resize_id=ohm3092&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1485-1\">Wilson, R. J. (n.d.). Pulse rates before and after exercise. StatSci.org. http:\/\/www.statsci.org\/data\/oz\/ms212.html <a href=\"#return-footnote-1485-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":12,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1473,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1485"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1485\/revisions"}],"predecessor-version":[{"id":5866,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1485\/revisions\/5866"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1473"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1485\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1485"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1485"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1485"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}