{"id":4510,"date":"2022-04-13T14:04:48","date_gmt":"2022-04-13T14:04:48","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=4510"},"modified":"2022-05-17T18:32:36","modified_gmt":"2022-05-17T18:32:36","slug":"instructor-guide-6b-forming-connections","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/instructor-guide-6b-forming-connections\/","title":{"raw":"Instructor Guide 6B: Forming Connections","rendered":"Instructor Guide 6B: Forming Connections"},"content":{"raw":"<h2>Overview<\/h2>\r\n<ul>\r\n \t<li>This activity will focus on the interpretation of parameters in the context of the problems and on the reasonableness (or unreasonableness) associated with instances of extrapolation.<\/li>\r\n \t<li>Students will use data analysis tools to generate equations for lines of best fit and identify the estimated slope and y-intercept.<\/li>\r\n \t<li>This activity connects back to the correlation coefficient and the method of Least Squares\u00a0Regression and prepares students for using the least squares regression line to make predictions,\u00a0residual analysis, and multiple regression.<\/li>\r\n \t<li><span style=\"background-color: #ffff99;\">[a list of tags like S2, O1, B1, V3] \u2190 Link to EBTP descriptions\u00a0<\/span><\/li>\r\n<\/ul>\r\n<h3>Prerequisite assumptions<\/h3>\r\nStudents should be able to do each of the following after completing the <em>What to Know<\/em> assignment.\r\n<ul>\r\n \t<li>Identify the estimated y-intercept and estimated slope from the equation of the line.<\/li>\r\n \t<li>Interpret the estimated slope in context.<\/li>\r\n<\/ul>\r\n<h3>Intended goals for this activity<\/h3>\r\nAfter completing this activity, students should understand the definition of extrapolation and that the equation of the line of best fit is based on sample data and will change with new datasets.\r\n\r\nThey should be able\u00a0to identify the estimated slope and estimated y-intercept given the equation of the line of best fit and interpret the estimated y-intercept in the specific context of a problem.\r\n<h2>Synchronous Delivery and Activity Flow<\/h2>\r\nThe sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.\r\n<h3>Frame the activity (3 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Question 1 -- Think-Pair-Share\u00a0S2, C4, V1, V4, O3\r\n<ul>\r\n \t<li aria-level=\"1\">Use Part A to start a conversation about the importance of looking for\u00a0trends in quantitative data. If students do not see a connection\u00a0between the cricket example and the importance of identifying\u00a0trends, share other examples of situations in which we can identify\u00a0trends that help us make decisions. For example, a plot of carbon\u00a0emissions and changes in temperature show a positive trend.<\/li>\r\n \t<li aria-level=\"1\">Students should identify the explanatory and response variables in\u00a0Part B on their own. It is important that the students defend their\u00a0answers. One interpretation is that the researcher gets to choose.\u00a0Another answer is that it seems unnatural to have the chirps\u00a0determine the temperature. This could be a good time to plant a seed\u00a0for \u201cassociation does not mean causation.\u201d<\/li>\r\n \t<li aria-level=\"1\">Transition to the in-class activity by briefly discussing the Objectives\u00a0for the activity.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h3>Activity Flow (20 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Question 2 -- Working in Groups\r\n<ul>\r\n \t<li aria-level=\"1\">In Parts A through C, guide students to support their claims using\u00a0outputs from the Linear Regression tool.<\/li>\r\n \t<li aria-level=\"1\">Emphasize that every new dataset will generate a different linear\u00a0equation and that each equation offers different estimates of the\u00a0parameters, or true population values, of the slope and y-intercept.<\/li>\r\n \t<li aria-level=\"1\">In Part D, change in estimated temperature for every increase in one\u00a0chirp per second is estimated \u201con average,\u201d given all values of chirps\u00a0per second. This phrase is purposely included. Our least squares\u00a0regression line estimates the average temperature values for each\u00a0value of chirps per second. Therefore, the slope of the line tells us\u00a0how the average temperature changes for a change in the number of\u00a0chirps.<\/li>\r\n \t<li aria-level=\"1\">Generally speaking, the least squares regression line connects the\u00a0points that represent the mean value of temperature for each value\u00a0of chirps per second, assuming the trend is, in fact, linear. Use Part\u00a0E to emphasize that each time we repeat the experiment, the\u00a0observed values of temperature and chirps per second will naturally\u00a0vary.<\/li>\r\n \t<li aria-level=\"1\">Part F requires students to extrapolate. Ask them to locate the y-intercept on the graph. Students will notice that this value is not\u00a0anywhere close to the value on the graph and is consequently\u00a0outside the range of the [latex]x[\/latex] values that were used to create the linear\r\nmodel.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Debriefing Questions 2 and 3 -- Whole Class Discussion\u00a0S4, C3, V1, O1, B2, B4\r\n<ul>\r\n \t<li aria-level=\"1\">Ensure students understand the dangers involved in extrapolation.\u00a0Possible talking points:\r\n<ul>\r\n \t<li aria-level=\"1\">\u00a0Extrapolation is the prediction of a response value using an\u00a0explanatory variable value that is outside the range of the\u00a0original data. During the discussion, display this definition\r\nor write it on the board.<\/li>\r\n \t<li aria-level=\"1\">We should always be cautious regarding the validity of this\u00a0interpretation\u2014if the range of the explanatory variable, [latex]x[\/latex],\u00a0does not include or come close to 0, then we may get a\u00a0completely unreasonable interpretation of the y-intercept.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Question 4 -- Students continue in small groups to practice writing interpretations and answering question using statistical terminology. It could be completed for homework if time runs short.<\/li>\r\n<\/ul>\r\n<h3>Wrap-up\/transition (2 minutes)<\/h3>\r\n<ul>\r\n \t<li>If you did not complete Question 4, the discussion after Questions 2 and 3 will serve as the wrap-up. Otherwise, students could share answers to Question 4.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Have students refer back to the Objectives and check the ones they recognize.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Assign the homework or\u00a0<em>Practice<\/em>\u00a0and any <em>What to Know<\/em> pages for the <em>Forming Connections<\/em> activities you plan to complete in the next class meeting. <span style=\"background-color: #ffff99;\">C2<\/span><\/li>\r\n<\/ul>","rendered":"<h2>Overview<\/h2>\n<ul>\n<li>This activity will focus on the interpretation of parameters in the context of the problems and on the reasonableness (or unreasonableness) associated with instances of extrapolation.<\/li>\n<li>Students will use data analysis tools to generate equations for lines of best fit and identify the estimated slope and y-intercept.<\/li>\n<li>This activity connects back to the correlation coefficient and the method of Least Squares\u00a0Regression and prepares students for using the least squares regression line to make predictions,\u00a0residual analysis, and multiple regression.<\/li>\n<li><span style=\"background-color: #ffff99;\">[a list of tags like S2, O1, B1, V3] \u2190 Link to EBTP descriptions\u00a0<\/span><\/li>\n<\/ul>\n<h3>Prerequisite assumptions<\/h3>\n<p>Students should be able to do each of the following after completing the <em>What to Know<\/em> assignment.<\/p>\n<ul>\n<li>Identify the estimated y-intercept and estimated slope from the equation of the line.<\/li>\n<li>Interpret the estimated slope in context.<\/li>\n<\/ul>\n<h3>Intended goals for this activity<\/h3>\n<p>After completing this activity, students should understand the definition of extrapolation and that the equation of the line of best fit is based on sample data and will change with new datasets.<\/p>\n<p>They should be able\u00a0to identify the estimated slope and estimated y-intercept given the equation of the line of best fit and interpret the estimated y-intercept in the specific context of a problem.<\/p>\n<h2>Synchronous Delivery and Activity Flow<\/h2>\n<p>The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.<\/p>\n<h3>Frame the activity (3 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Question 1 &#8212; Think-Pair-Share\u00a0S2, C4, V1, V4, O3\n<ul>\n<li aria-level=\"1\">Use Part A to start a conversation about the importance of looking for\u00a0trends in quantitative data. If students do not see a connection\u00a0between the cricket example and the importance of identifying\u00a0trends, share other examples of situations in which we can identify\u00a0trends that help us make decisions. For example, a plot of carbon\u00a0emissions and changes in temperature show a positive trend.<\/li>\n<li aria-level=\"1\">Students should identify the explanatory and response variables in\u00a0Part B on their own. It is important that the students defend their\u00a0answers. One interpretation is that the researcher gets to choose.\u00a0Another answer is that it seems unnatural to have the chirps\u00a0determine the temperature. This could be a good time to plant a seed\u00a0for \u201cassociation does not mean causation.\u201d<\/li>\n<li aria-level=\"1\">Transition to the in-class activity by briefly discussing the Objectives\u00a0for the activity.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>Activity Flow (20 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Question 2 &#8212; Working in Groups\n<ul>\n<li aria-level=\"1\">In Parts A through C, guide students to support their claims using\u00a0outputs from the Linear Regression tool.<\/li>\n<li aria-level=\"1\">Emphasize that every new dataset will generate a different linear\u00a0equation and that each equation offers different estimates of the\u00a0parameters, or true population values, of the slope and y-intercept.<\/li>\n<li aria-level=\"1\">In Part D, change in estimated temperature for every increase in one\u00a0chirp per second is estimated \u201con average,\u201d given all values of chirps\u00a0per second. This phrase is purposely included. Our least squares\u00a0regression line estimates the average temperature values for each\u00a0value of chirps per second. Therefore, the slope of the line tells us\u00a0how the average temperature changes for a change in the number of\u00a0chirps.<\/li>\n<li aria-level=\"1\">Generally speaking, the least squares regression line connects the\u00a0points that represent the mean value of temperature for each value\u00a0of chirps per second, assuming the trend is, in fact, linear. Use Part\u00a0E to emphasize that each time we repeat the experiment, the\u00a0observed values of temperature and chirps per second will naturally\u00a0vary.<\/li>\n<li aria-level=\"1\">Part F requires students to extrapolate. Ask them to locate the y-intercept on the graph. Students will notice that this value is not\u00a0anywhere close to the value on the graph and is consequently\u00a0outside the range of the [latex]x[\/latex] values that were used to create the linear<br \/>\nmodel.<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Debriefing Questions 2 and 3 &#8212; Whole Class Discussion\u00a0S4, C3, V1, O1, B2, B4\n<ul>\n<li aria-level=\"1\">Ensure students understand the dangers involved in extrapolation.\u00a0Possible talking points:\n<ul>\n<li aria-level=\"1\">\u00a0Extrapolation is the prediction of a response value using an\u00a0explanatory variable value that is outside the range of the\u00a0original data. During the discussion, display this definition<br \/>\nor write it on the board.<\/li>\n<li aria-level=\"1\">We should always be cautious regarding the validity of this\u00a0interpretation\u2014if the range of the explanatory variable, [latex]x[\/latex],\u00a0does not include or come close to 0, then we may get a\u00a0completely unreasonable interpretation of the y-intercept.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Question 4 &#8212; Students continue in small groups to practice writing interpretations and answering question using statistical terminology. It could be completed for homework if time runs short.<\/li>\n<\/ul>\n<h3>Wrap-up\/transition (2 minutes)<\/h3>\n<ul>\n<li>If you did not complete Question 4, the discussion after Questions 2 and 3 will serve as the wrap-up. Otherwise, students could share answers to Question 4.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Have students refer back to the Objectives and check the ones they recognize.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Assign the homework or\u00a0<em>Practice<\/em>\u00a0and any <em>What to Know<\/em> pages for the <em>Forming Connections<\/em> activities you plan to complete in the next class meeting. <span style=\"background-color: #ffff99;\">C2<\/span><\/li>\n<\/ul>\n","protected":false},"author":25777,"menu_order":4,"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-4510","chapter","type-chapter","status-publish","hentry"],"part":4483,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4510","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\/25777"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4510\/revisions"}],"predecessor-version":[{"id":4919,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4510\/revisions\/4919"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4483"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4510\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4510"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4510"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4510"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}