{"id":4508,"date":"2022-04-13T14:04:27","date_gmt":"2022-04-13T14:04:27","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=4508"},"modified":"2022-05-17T18:32:27","modified_gmt":"2022-05-17T18:32:27","slug":"instructor-guide-6a-forming-connections","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/instructor-guide-6a-forming-connections\/","title":{"raw":"Instructor Guide 6A: Forming Connections","rendered":"Instructor Guide 6A: Forming Connections"},"content":{"raw":"<h2>Overview<\/h2>\r\n<ul>\r\n \t<li>In this activity, students practice identifying explanatory and response variables\u00a0within two different contexts and are introduced to Least Squares Regression (LSR)\u00a0analysis to develop their conceptual understanding of the line of best fit.<\/li>\r\n \t<li>Throughout the activity, students rely heavily on the <em>DCMP Data Analysis Tools<\/em> to\u00a0perform all calculations and generate graphs, and they explore a non-linear dataset to\u00a0demonstrate that not all bivariate datasets should be considered for linear regression\u00a0analysis.<\/li>\r\n \t<li>This activity connects back to the distinction between categorical and quantitative variables, as well as scatterplots and correlation, and prepares students for linear modeling, residuals, using linear regression to make predictions, and multiple linear 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 when a linear regression analysis might be appropriate.<\/li>\r\n \t<li>Identify the explanatory and response variables in a given scenario.<\/li>\r\n \t<li>Use technology to calculate the line of best fit and write it using proper notation.<\/li>\r\n<\/ul>\r\n<h3>Intended goals for this activity<\/h3>\r\nAfter completing this activity, students should understand the basic concepts underlying the line of best fit and the method of linear regression analysis on a given dataset. They should be able to identify the explanatory and response variables given the context of a study, decide when linear regression is and is not appropriate. They should be able to use data analysis tools to generate appropriate scatterplots and line of best fit as well as the equation of the line of best fit and the correlation coefficient [latex]r[\/latex].\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 (10 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Question 1 -- Think-Pair-Share\u00a0\u00a0S2, C4, V1, V4, O3\r\n<ul>\r\n \t<li aria-level=\"1\">Have each student share a scenario they made up for the\u00a0<em>What to Know<\/em> assignment. Ask them to quiz one another by identifying the explanatory and response variables.<\/li>\r\n \t<li aria-level=\"1\">Students work in pairs to sketch scatterplots of their scenarios. Encourage conversations about trend.<\/li>\r\n \t<li aria-level=\"1\">Have a few pairs share their explanatory and response variables and scatterplots.<\/li>\r\n \t<li aria-level=\"1\">Summarize the question by explaining the importance of clearly identifying the explanatory and response variables and plotting the data to identify trends when analyzing bivariate data.<\/li>\r\n \t<li aria-level=\"1\">Transition to the activity by briefly discussing the Objectives.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h3>Activity Flow (14 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Questions 2 - 5 -- Working in Groups V1, V4, O3, S2, C6\r\n<ul>\r\n \t<li aria-level=\"1\">As you circulate, ensure students are identifying variables correctly.<\/li>\r\n \t<li aria-level=\"1\">Students can copy and paste the data from the spreadsheet [<span style=\"background-color: #ffff99;\">DCMP_STAT_6A_Student_Scores_FINAL (link spreadsheet)<\/span>] to the linear regression tool.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Whole Class Discussion -- after Question 5.\u00a0S4, C3, V1, O1, B2, B4\r\n<ul>\r\n \t<li aria-level=\"1\">Once most students have finished Question 5, bring the class together. Have students clearly state and justify their conclusions (i.e., their answer to Question 5).<\/li>\r\n \t<li aria-level=\"1\">Display the line of best fit using a projector and ask students to visually predict George's final exam score.<\/li>\r\n \t<li aria-level=\"1\">Display the five steps of LSR analysis [<span style=\"background-color: #ffff99;\">link the document attached to the end of the DC instructor notes<\/span>] and connect the questions students just answered to the steps.<\/li>\r\n \t<li aria-level=\"1\">Discuss the need for anonymity and confidentiality in data collection. Hopefully, students will bring this up. For example, Kanye may not want people to know he is a good student. Ask what the teacher could have done differently to keep the data confidential.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Questions 6 - 8 -- Working in groups\u00a0V1, V4, O3, S2, C6\r\n<ul>\r\n \t<li aria-level=\"1\">Consider rearranging pairs to create new small groups (working with the same groups is fine).<\/li>\r\n \t<li aria-level=\"1\">Monitor Question 6, Part A carefully. This quesiton has the potnetial to derail the conversations within groups. Be ready to guide students to continue with their analyses regardless of the answers.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h3>Wrap-up\/transition (2 minutes)<\/h3>\r\n<ul>\r\n \t<li>Have students clearly state and justify their conclusions (i.e., their answer to Question 8).<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Display the scatterplot and discuss the trends. In this case, there is no\u00a0linear relationship.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Have students refer back to the Objectives for the activity and\u00a0check 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>In this activity, students practice identifying explanatory and response variables\u00a0within two different contexts and are introduced to Least Squares Regression (LSR)\u00a0analysis to develop their conceptual understanding of the line of best fit.<\/li>\n<li>Throughout the activity, students rely heavily on the <em>DCMP Data Analysis Tools<\/em> to\u00a0perform all calculations and generate graphs, and they explore a non-linear dataset to\u00a0demonstrate that not all bivariate datasets should be considered for linear regression\u00a0analysis.<\/li>\n<li>This activity connects back to the distinction between categorical and quantitative variables, as well as scatterplots and correlation, and prepares students for linear modeling, residuals, using linear regression to make predictions, and multiple linear 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 when a linear regression analysis might be appropriate.<\/li>\n<li>Identify the explanatory and response variables in a given scenario.<\/li>\n<li>Use technology to calculate the line of best fit and write it using proper notation.<\/li>\n<\/ul>\n<h3>Intended goals for this activity<\/h3>\n<p>After completing this activity, students should understand the basic concepts underlying the line of best fit and the method of linear regression analysis on a given dataset. They should be able to identify the explanatory and response variables given the context of a study, decide when linear regression is and is not appropriate. They should be able to use data analysis tools to generate appropriate scatterplots and line of best fit as well as the equation of the line of best fit and the correlation coefficient [latex]r[\/latex].<\/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 (10 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Question 1 &#8212; Think-Pair-Share\u00a0\u00a0S2, C4, V1, V4, O3\n<ul>\n<li aria-level=\"1\">Have each student share a scenario they made up for the\u00a0<em>What to Know<\/em> assignment. Ask them to quiz one another by identifying the explanatory and response variables.<\/li>\n<li aria-level=\"1\">Students work in pairs to sketch scatterplots of their scenarios. Encourage conversations about trend.<\/li>\n<li aria-level=\"1\">Have a few pairs share their explanatory and response variables and scatterplots.<\/li>\n<li aria-level=\"1\">Summarize the question by explaining the importance of clearly identifying the explanatory and response variables and plotting the data to identify trends when analyzing bivariate data.<\/li>\n<li aria-level=\"1\">Transition to the activity by briefly discussing the Objectives.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>Activity Flow (14 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Questions 2 &#8211; 5 &#8212; Working in Groups V1, V4, O3, S2, C6\n<ul>\n<li aria-level=\"1\">As you circulate, ensure students are identifying variables correctly.<\/li>\n<li aria-level=\"1\">Students can copy and paste the data from the spreadsheet [<span style=\"background-color: #ffff99;\">DCMP_STAT_6A_Student_Scores_FINAL (link spreadsheet)<\/span>] to the linear regression tool.<\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Whole Class Discussion &#8212; after Question 5.\u00a0S4, C3, V1, O1, B2, B4\n<ul>\n<li aria-level=\"1\">Once most students have finished Question 5, bring the class together. Have students clearly state and justify their conclusions (i.e., their answer to Question 5).<\/li>\n<li aria-level=\"1\">Display the line of best fit using a projector and ask students to visually predict George&#8217;s final exam score.<\/li>\n<li aria-level=\"1\">Display the five steps of LSR analysis [<span style=\"background-color: #ffff99;\">link the document attached to the end of the DC instructor notes<\/span>] and connect the questions students just answered to the steps.<\/li>\n<li aria-level=\"1\">Discuss the need for anonymity and confidentiality in data collection. Hopefully, students will bring this up. For example, Kanye may not want people to know he is a good student. Ask what the teacher could have done differently to keep the data confidential.<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Questions 6 &#8211; 8 &#8212; Working in groups\u00a0V1, V4, O3, S2, C6\n<ul>\n<li aria-level=\"1\">Consider rearranging pairs to create new small groups (working with the same groups is fine).<\/li>\n<li aria-level=\"1\">Monitor Question 6, Part A carefully. This quesiton has the potnetial to derail the conversations within groups. Be ready to guide students to continue with their analyses regardless of the answers.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>Wrap-up\/transition (2 minutes)<\/h3>\n<ul>\n<li>Have students clearly state and justify their conclusions (i.e., their answer to Question 8).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Display the scatterplot and discuss the trends. In this case, there is no\u00a0linear relationship.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Have students refer back to the Objectives for the activity and\u00a0check 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":2,"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-4508","chapter","type-chapter","status-publish","hentry"],"part":4483,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4508","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":5,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4508\/revisions"}],"predecessor-version":[{"id":4769,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4508\/revisions\/4769"}],"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\/4508\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4508"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4508"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4508"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}