{"id":3874,"date":"2022-03-15T23:23:56","date_gmt":"2022-03-15T23:23:56","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=3874"},"modified":"2022-06-02T01:29:19","modified_gmt":"2022-06-02T01:29:19","slug":"corequisite-support-activity-for-6-e","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/corequisite-support-activity-for-6-e\/","title":{"raw":"Corequisite Support Activity for 6.E: Calculating Predicted Values of the Response Variable","rendered":"Corequisite Support Activity for 6.E: Calculating Predicted Values of the Response Variable"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>What you'll need to know<\/h3>\r\nIn this support activity you\u2019ll become familiar with the following:\r\n<ul>\r\n \t<li>Use technology to explore a linear relationship in bivariate data.<\/li>\r\n \t<li>Use technology to determine whether the line of best fit is an appropriate fit for the data.<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the upcoming material and activity, you will need to be able to use technology to make scatterplots to visualize bivariate relationships, calculate a line of best fit, and interpret the slope and intercept for the line. You should be familiar with these skills after having completed the previous sections in this module. Use this corequisite activity to assess\u00a0 your own understanding and get help with the skills as needed.\r\n\r\nIn this activity, we'll use data collected during a study of the use of a hiking trail. You'll use a data analysis tool to practice making a scatterplot, calculating a line of best fit, and interpreting its slope and intercept.\r\n<h2>Users of Massachusetts Trail<\/h2>\r\nThe objective of this analysis is to explore the relationship between the daily high temperature and the number of users on a trail in Florence, Massachusetts. The information in the dataset was collected over 90 days between April 5, 2005 to November 15, 2005 by the Pioneer Valley Planning Commission (PVPC). The number of trail users was collected by a laser sensor set up at a data collection station. A user was recorded each time there was a break in the laser beam.\r\n<h3>Linear Relationships<\/h3>\r\nThe dataset is called \u201cRail Trail\u201d and is available in the <em>DCMP Linear Regression<\/em> tool at\u00a0 <a href=\"https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/\">https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/<\/a>.\r\n\r\nWe will use the following variables in this corequisite support activity:\r\n<ul>\r\n \t<li><em>hightemp:<\/em> Daily high temperature in degrees Fahrenheit<\/li>\r\n \t<li><em>volume:<\/em> Estimated number of trail users that day (calculated as number of breaks recorded)<\/li>\r\n<\/ul>\r\nWe would like to use a line of best fit that can be used to predict the number of trail users on a given day based on the high temperature.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 1<\/h3>\r\nWhat is the response variable? Explain.\r\n\r\n[reveal-answer q=\"93890\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"93890\"]Of the two variables, <em>hightemp<\/em> and\u00a0<em>volume<\/em> which is the explanatory variable and which records the response data?[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 2<\/h3>\r\nLet\u2019s explore the relationship between the high temperature and the number of trail users.\r\n\r\n&nbsp;\r\n\r\nPart A: Use the tool to make a scatterplot and describe the relationship between the two variables.\r\n\r\n[reveal-answer q=\"389990\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"389990\"]Use the tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/\">https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/<\/a>\u00a0and choose the data set Rail Trail. What do you know about how to describe possible linear relationships in bivariate data? [\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart B: Use the tool to calculate a line of best fit for the data. Write the equation of the line using customized names for the variables (e.g., no x and y).\r\n\r\n[reveal-answer q=\"106068\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"106068\"]Find the selection to toggle on the line of best fit and choose your own descriptive variable words or letters when writing the equation.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart C: Interpret the slope in the context of the data.\r\n\r\n[reveal-answer q=\"317969\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"317969\"]Use a sentence to interpret the rate of change.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nPart D: Does the intercept have a meaningful interpretation? If so, interpret the intercept in the context of the data. Otherwise, explain why not.\r\n\r\n[reveal-answer q=\"633758\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"633758\"]What do <em>you\u00a0<\/em>think?\u00a0[\/hidden-answer]\r\n\r\nPart E: Suppose the high temperature tomorrow is expected to be 60 degrees Fahrenheit. What would be your best guess for the number of users to expect on the trail tomorrow? Explain your response using the line of best fit.\r\n\r\n[reveal-answer q=\"276873\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"276873\"]Either calculate the predictions by hand using the equation of the line of best fit or use the Find Predicted Value option in the sidebar of the tool.[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3>Evaluate the Line of Best Fit<\/h3>\r\nLet\u2019s evaluate if the line is an appropriate fit for the data. Use the <strong>Fitted Values and Residual Analysis<\/strong> tab to make a scatterplot of the residuals versus predicted or \u201cFitted\u201d values.\r\n\r\nUse the tab at the top of the tool to change your view to Fitted Values and Residual Analysis. Choose \"Versus Fitted Values\" under Plot Residuals. Use the resulting residual plot to determine if the line is appropriate for the data.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>question 3<\/h3>\r\nIs the line an appropriate fit for the data?\r\n\r\n[reveal-answer q=\"887490\"]Hint[\/reveal-answer]\r\n[hidden-answer a=\"887490\"] Does the line generally provide a meaningful prediction for the situation? Is any non-linear shape suggested by either the scatterplot or the residual plot? [\/hidden-answer]\r\n\r\n<\/div>\r\nHopefully this activity provided you a good opportunity to assess your skills using the technology to explore bivariate data.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>What you&#8217;ll need to know<\/h3>\n<p>In this support activity you\u2019ll become familiar with the following:<\/p>\n<ul>\n<li>Use technology to explore a linear relationship in bivariate data.<\/li>\n<li>Use technology to determine whether the line of best fit is an appropriate fit for the data.<\/li>\n<\/ul>\n<\/div>\n<p>In the upcoming material and activity, you will need to be able to use technology to make scatterplots to visualize bivariate relationships, calculate a line of best fit, and interpret the slope and intercept for the line. You should be familiar with these skills after having completed the previous sections in this module. Use this corequisite activity to assess\u00a0 your own understanding and get help with the skills as needed.<\/p>\n<p>In this activity, we&#8217;ll use data collected during a study of the use of a hiking trail. You&#8217;ll use a data analysis tool to practice making a scatterplot, calculating a line of best fit, and interpreting its slope and intercept.<\/p>\n<h2>Users of Massachusetts Trail<\/h2>\n<p>The objective of this analysis is to explore the relationship between the daily high temperature and the number of users on a trail in Florence, Massachusetts. The information in the dataset was collected over 90 days between April 5, 2005 to November 15, 2005 by the Pioneer Valley Planning Commission (PVPC). The number of trail users was collected by a laser sensor set up at a data collection station. A user was recorded each time there was a break in the laser beam.<\/p>\n<h3>Linear Relationships<\/h3>\n<p>The dataset is called \u201cRail Trail\u201d and is available in the <em>DCMP Linear Regression<\/em> tool at\u00a0 <a href=\"https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/\">https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/<\/a>.<\/p>\n<p>We will use the following variables in this corequisite support activity:<\/p>\n<ul>\n<li><em>hightemp:<\/em> Daily high temperature in degrees Fahrenheit<\/li>\n<li><em>volume:<\/em> Estimated number of trail users that day (calculated as number of breaks recorded)<\/li>\n<\/ul>\n<p>We would like to use a line of best fit that can be used to predict the number of trail users on a given day based on the high temperature.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 1<\/h3>\n<p>What is the response variable? Explain.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q93890\">Hint<\/span><\/p>\n<div id=\"q93890\" class=\"hidden-answer\" style=\"display: none\">Of the two variables, <em>hightemp<\/em> and\u00a0<em>volume<\/em> which is the explanatory variable and which records the response data?<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>question 2<\/h3>\n<p>Let\u2019s explore the relationship between the high temperature and the number of trail users.<\/p>\n<p>&nbsp;<\/p>\n<p>Part A: Use the tool to make a scatterplot and describe the relationship between the two variables.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q389990\">Hint<\/span><\/p>\n<div id=\"q389990\" class=\"hidden-answer\" style=\"display: none\">Use the tool at <a href=\"https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/\">https:\/\/dcmathpathways.shinyapps.io\/LinearRegression\/<\/a>\u00a0and choose the data set Rail Trail. What do you know about how to describe possible linear relationships in bivariate data? <\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part B: Use the tool to calculate a line of best fit for the data. Write the equation of the line using customized names for the variables (e.g., no x and y).<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q106068\">Hint<\/span><\/p>\n<div id=\"q106068\" class=\"hidden-answer\" style=\"display: none\">Find the selection to toggle on the line of best fit and choose your own descriptive variable words or letters when writing the equation.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part C: Interpret the slope in the context of the data.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q317969\">Hint<\/span><\/p>\n<div id=\"q317969\" class=\"hidden-answer\" style=\"display: none\">Use a sentence to interpret the rate of change.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Part D: Does the intercept have a meaningful interpretation? If so, interpret the intercept in the context of the data. Otherwise, explain why not.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q633758\">Hint<\/span><\/p>\n<div id=\"q633758\" class=\"hidden-answer\" style=\"display: none\">What do <em>you\u00a0<\/em>think?\u00a0<\/div>\n<\/div>\n<p>Part E: Suppose the high temperature tomorrow is expected to be 60 degrees Fahrenheit. What would be your best guess for the number of users to expect on the trail tomorrow? Explain your response using the line of best fit.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q276873\">Hint<\/span><\/p>\n<div id=\"q276873\" class=\"hidden-answer\" style=\"display: none\">Either calculate the predictions by hand using the equation of the line of best fit or use the Find Predicted Value option in the sidebar of the tool.<\/div>\n<\/div>\n<\/div>\n<h3>Evaluate the Line of Best Fit<\/h3>\n<p>Let\u2019s evaluate if the line is an appropriate fit for the data. Use the <strong>Fitted Values and Residual Analysis<\/strong> tab to make a scatterplot of the residuals versus predicted or \u201cFitted\u201d values.<\/p>\n<p>Use the tab at the top of the tool to change your view to Fitted Values and Residual Analysis. Choose &#8220;Versus Fitted Values&#8221; under Plot Residuals. Use the resulting residual plot to determine if the line is appropriate for the data.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>question 3<\/h3>\n<p>Is the line an appropriate fit for the data?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q887490\">Hint<\/span><\/p>\n<div id=\"q887490\" class=\"hidden-answer\" style=\"display: none\"> Does the line generally provide a meaningful prediction for the situation? Is any non-linear shape suggested by either the scatterplot or the residual plot? <\/div>\n<\/div>\n<\/div>\n<p>Hopefully this activity provided you a good opportunity to assess your skills using the technology to explore bivariate data.<\/p>\n","protected":false},"author":428269,"menu_order":22,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3874","chapter","type-chapter","status-publish","hentry"],"part":4241,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3874","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/428269"}],"version-history":[{"count":8,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3874\/revisions"}],"predecessor-version":[{"id":4813,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3874\/revisions\/4813"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4241"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/3874\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=3874"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=3874"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=3874"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=3874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}