{"id":1462,"date":"2023-06-22T02:28:54","date_gmt":"2023-06-22T02:28:54","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-and-prediction-interval-apply-it-1\/"},"modified":"2025-05-17T02:37:20","modified_gmt":"2025-05-17T02:37:20","slug":"confidence-interval-and-prediction-interval-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-and-prediction-interval-apply-it-1\/","title":{"raw":"Confidence Interval and Prediction Interval - Apply It 1","rendered":"Confidence Interval and Prediction Interval &#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;Find and interpret the confidence interval for the mean response&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;}\">Find and interpret the confidence interval for the mean response<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and interpret the prediction interval for the mean response&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;}\">Find and interpret the prediction interval for an individual response<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem&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;}\">Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2><strong>Capital Bikeshare Rentals<\/strong><\/h2>\r\n<p><img class=\"aligncenter wp-image-2145 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193847\/Picture1-1-2.jpg\" alt=\"Person riding a bike outdoors.\" width=\"300\" height=\"200\" \/><\/p>\r\n<p>Suppose you are a data scientist for <em>Capital Bikeshare<\/em> in Washington, D.C., and your job is to develop a linear regression model to predict the number of bike rentals based on the temperature. These predictions will be used to help determine the number of bikes to make available across the city each day.<\/p>\r\n<p>Previously, you\u2019ve used the regression model to calculate a predicted value of the response given a particular value of the explanatory variable. This time, you decide to include an interval with your predictions, so you report a plausible range of values the number of bike rentals might take, given a particular value of temperature.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3186[\/ohm2_question]<\/section>\r\n<p>Data set: <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Data+Set+Files\/dcbikeshare_winter_sample_FINAL.xlsx\">Capital Bikeshare<\/a> in Washington, D.C.<\/p>\r\n<p>It contains daily information about the number of bike rentals, weather, day of the week, and other details for days in 2011 and 2012. Your primary objective in this activity is to predict the number of daily bike rentals during the winter months (December [latex]21[\/latex] to March [latex]20[\/latex]). To do so, you\u2019ll use data from [latex]50[\/latex] randomly selected winter days in 2011 and 2012. The variables of interest for this activity are:<\/p>\r\n<ul>\r\n\t<li><em>count<\/em>: Total number of bikes rented<\/li>\r\n\t<li><em>temperature<\/em>: Approximate high temperature in degrees Fahrenheit<\/li>\r\n<\/ul>\r\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Access the spreadsheet <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Data+Set+Files\/dcbikeshare_winter_sample_FINAL.xlsx\">Capital Bikeshare<\/a>.<br \/>\r\n<strong>Step 2: <\/strong>Under \u201cEnter Data,\u201d select \u201cEnter Own.\u201d<strong><br \/>\r\nStep 3: <\/strong>Select the appropriate explanatory variable ([latex]x[\/latex]) and response variable ([latex]y[\/latex]).<br \/>\r\n<strong>Step 4: <\/strong>Enter the data.<\/section>\r\n<section><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"1050\" frameborder=\"no\"><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3187[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3188[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and interpret the confidence interval for the mean response&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;}\">Find and interpret the confidence interval for the mean response<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find and interpret the prediction interval for the mean response&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;}\">Find and interpret the prediction interval for an individual response<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem&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;}\">Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem<\/span><\/li>\n<\/ul>\n<\/section>\n<h2><strong>Capital Bikeshare Rentals<\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2145 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193847\/Picture1-1-2.jpg\" alt=\"Person riding a bike outdoors.\" width=\"300\" height=\"200\" \/><\/p>\n<p>Suppose you are a data scientist for <em>Capital Bikeshare<\/em> in Washington, D.C., and your job is to develop a linear regression model to predict the number of bike rentals based on the temperature. These predictions will be used to help determine the number of bikes to make available across the city each day.<\/p>\n<p>Previously, you\u2019ve used the regression model to calculate a predicted value of the response given a particular value of the explanatory variable. This time, you decide to include an interval with your predictions, so you report a plausible range of values the number of bike rentals might take, given a particular value of temperature.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3186\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3186&theme=lumen&iframe_resize_id=ohm3186&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Data set: <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Data+Set+Files\/dcbikeshare_winter_sample_FINAL.xlsx\">Capital Bikeshare<\/a> in Washington, D.C.<\/p>\n<p>It contains daily information about the number of bike rentals, weather, day of the week, and other details for days in 2011 and 2012. Your primary objective in this activity is to predict the number of daily bike rentals during the winter months (December [latex]21[\/latex] to March [latex]20[\/latex]). To do so, you\u2019ll use data from [latex]50[\/latex] randomly selected winter days in 2011 and 2012. The variables of interest for this activity are:<\/p>\n<ul>\n<li><em>count<\/em>: Total number of bikes rented<\/li>\n<li><em>temperature<\/em>: Approximate high temperature in degrees Fahrenheit<\/li>\n<\/ul>\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Access the spreadsheet <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Statistics+Exemplar\/Data+Set+Files\/dcbikeshare_winter_sample_FINAL.xlsx\">Capital Bikeshare<\/a>.<br \/>\n<strong>Step 2: <\/strong>Under \u201cEnter Data,\u201d select \u201cEnter Own.\u201d<strong><br \/>\nStep 3: <\/strong>Select the appropriate explanatory variable ([latex]x[\/latex]) and response variable ([latex]y[\/latex]).<br \/>\n<strong>Step 4: <\/strong>Enter the data.<\/section>\n<section><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" width=\"100%\" height=\"1050\" frameborder=\"no\"><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/linear_regression\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3187\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3187&theme=lumen&iframe_resize_id=ohm3187&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3188\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3188&theme=lumen&iframe_resize_id=ohm3188&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":22,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1438,"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\/1462"}],"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":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1462\/revisions"}],"predecessor-version":[{"id":6899,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1462\/revisions\/6899"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1438"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1462\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1462"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1462"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1462"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1462"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}