{"id":179,"date":"2017-04-15T03:18:42","date_gmt":"2017-04-15T03:18:42","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/assignment-linear-relationships\/"},"modified":"2017-05-30T23:33:04","modified_gmt":"2017-05-30T23:33:04","slug":"assignment-linear-relationships","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/chapter\/assignment-linear-relationships\/","title":{"raw":"Assignment: Linear Relationships","rendered":"Assignment: Linear Relationships"},"content":{"raw":"&nbsp;\r\n\r\nIn this activity we will:\r\n<ul>\r\n \t<li>Learn how to compute the correlation.<\/li>\r\n \t<li>Practice interpreting the value of the correlation.<\/li>\r\n \t<li>See an example of how including an outlier can <em>increase<\/em> the correlation.<\/li>\r\n<\/ul>\r\nRecall the following example: The average gestation period, or time of pregnancy, of an animal is closely related to its longevity\u2014the length of its lifespan. Data on the average gestation period and longevity (in captivity) of 40 different species of animals have been recorded.\r\n\r\n&nbsp;\r\n<h3>Instructions<\/h3>\r\nClick on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_r0.html\" target=\"new\"> R <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_statcrunch0.html\" target=\"new\"> StatCrunch <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_minitab0.html\" target=\"new\"> Minitab <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_excel0.html\" target=\"new\"> Excel 2007 <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_ti0.html\" target=\"new\"> TI Calculator <\/a>\r\n\r\nRemember that the correlation is only an appropriate measure of the <strong>linear <\/strong>relationship between two quantitative variables. First produce a scatterplot to verify that gestation and longevity are nearly linear in their relationship.\r\n\r\n&nbsp;\r\n<h3>Instructions<\/h3>\r\nClick on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_r1.html\" target=\"new\"> R <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_statcrunch1.html\" target=\"new\"> StatCrunch <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_minitab1.html\" target=\"new\"> Minitab <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_excel1.html\" target=\"new\"> Excel 2007 <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_ti1.html\" target=\"new\"> TI Calculator <\/a>\r\n\r\nObserve that the relationship between gestation period and longevity is linear and positive. Now we will compute the correlation between gestation period and longevity.\r\n\r\n&nbsp;\r\n<h3>Instructions<\/h3>\r\nClick on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_r2.html\" target=\"new\"> R <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_statcrunch2.html\" target=\"new\"> StatCrunch <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_minitab2.html\" target=\"new\"> Minitab <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_excel2.html\" target=\"new\"> Excel 2007 <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_ti2.html\" target=\"new\"> TI Calculator <\/a>\r\n<h3>Question 1:<\/h3>\r\nReport the correlation between gestation and longevity and comment on the strength and direction of the relationship. Interpret your findings in context.\r\n\r\nNow return to the scatterplot that you created earlier. Notice that there is an outlier in both longevity (40 years) and gestation (645 days). Note: This outlier corresponds to the longevity and gestation period of the elephant.\r\n\r\nWhat do you think will happen to the correlation if we remove this outlier?\r\n<h3>Instructions<\/h3>\r\nClick on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_r3.html\" target=\"new\"> R <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_statcrunch3.html\" target=\"new\"> StatCrunch <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_minitab3.html\" target=\"new\"> Minitab <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_excel3.html\" target=\"new\"> Excel 2007 <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_ti3.html\" target=\"new\"> TI Calculator <\/a>\r\n<h3>Question 2:<\/h3>\r\nReport the new value for the correlation between gestation and longevity and compare it to the value you found earlier when the outlier was included. What is it about this outlier that results in the fact that its inclusion in the data causes the correlation to increase? (Hint: look at the scatterplot.)\r\n<h3>Comment<\/h3>\r\nIn the last activity, we saw an example where there was a positive linear relationship between the two variables, and including the outlier just \"strengthened\" it. Consider the hypothetical data displayed by the following scatterplot:\r\n\r\n<img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031841\/m3_examining_relationships_topic_3_1_scatter_linear_corr_linear22.gif\" alt=\"scatterplot where the dots are loosely clustered at the upper right part of the graph\" width=\"346\" height=\"193\" \/>\r\n\r\nIn this case, the low outlier gives an \"illusion\" of a positive linear relationship, whereas in reality, there is no linear relationship between X and Y.\r\n\r\n&nbsp;","rendered":"<p>&nbsp;<\/p>\n<p>In this activity we will:<\/p>\n<ul>\n<li>Learn how to compute the correlation.<\/li>\n<li>Practice interpreting the value of the correlation.<\/li>\n<li>See an example of how including an outlier can <em>increase<\/em> the correlation.<\/li>\n<\/ul>\n<p>Recall the following example: The average gestation period, or time of pregnancy, of an animal is closely related to its longevity\u2014the length of its lifespan. Data on the average gestation period and longevity (in captivity) of 40 different species of animals have been recorded.<\/p>\n<p>&nbsp;<\/p>\n<h3>Instructions<\/h3>\n<p>Click on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_r0.html\" target=\"new\"> R <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_statcrunch0.html\" target=\"new\"> StatCrunch <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_minitab0.html\" target=\"new\"> Minitab <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_excel0.html\" target=\"new\"> Excel 2007 <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_ti0.html\" target=\"new\"> TI Calculator <\/a><\/p>\n<p>Remember that the correlation is only an appropriate measure of the <strong>linear <\/strong>relationship between two quantitative variables. First produce a scatterplot to verify that gestation and longevity are nearly linear in their relationship.<\/p>\n<p>&nbsp;<\/p>\n<h3>Instructions<\/h3>\n<p>Click on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_r1.html\" target=\"new\"> R <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_statcrunch1.html\" target=\"new\"> StatCrunch <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_minitab1.html\" target=\"new\"> Minitab <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_excel1.html\" target=\"new\"> Excel 2007 <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_ti1.html\" target=\"new\"> TI Calculator <\/a><\/p>\n<p>Observe that the relationship between gestation period and longevity is linear and positive. Now we will compute the correlation between gestation period and longevity.<\/p>\n<p>&nbsp;<\/p>\n<h3>Instructions<\/h3>\n<p>Click on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_r2.html\" target=\"new\"> R <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_statcrunch2.html\" target=\"new\"> StatCrunch <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_minitab2.html\" target=\"new\"> Minitab <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_excel2.html\" target=\"new\"> Excel 2007 <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_ti2.html\" target=\"new\"> TI Calculator <\/a><\/p>\n<h3>Question 1:<\/h3>\n<p>Report the correlation between gestation and longevity and comment on the strength and direction of the relationship. Interpret your findings in context.<\/p>\n<p>Now return to the scatterplot that you created earlier. Notice that there is an outlier in both longevity (40 years) and gestation (645 days). Note: This outlier corresponds to the longevity and gestation period of the elephant.<\/p>\n<p>What do you think will happen to the correlation if we remove this outlier?<\/p>\n<h3>Instructions<\/h3>\n<p>Click on the link corresponding to your statistical package to see instructions for completing the activity, and then answer the questions below.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_r3.html\" target=\"new\"> R <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_statcrunch3.html\" target=\"new\"> StatCrunch <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_minitab3.html\" target=\"new\"> Minitab <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_excel3.html\" target=\"new\"> Excel 2007 <\/a> | <a href=\"https:\/\/s3-us-west-2.amazonaws.com\/oerfiles\/Concepts+in+Statistics\/assignments\/linear4lbd\/linear4lbd_ti3.html\" target=\"new\"> TI Calculator <\/a><\/p>\n<h3>Question 2:<\/h3>\n<p>Report the new value for the correlation between gestation and longevity and compare it to the value you found earlier when the outlier was included. What is it about this outlier that results in the fact that its inclusion in the data causes the correlation to increase? (Hint: look at the scatterplot.)<\/p>\n<h3>Comment<\/h3>\n<p>In the last activity, we saw an example where there was a positive linear relationship between the two variables, and including the outlier just &#8220;strengthened&#8221; it. Consider the hypothetical data displayed by the following scatterplot:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15031841\/m3_examining_relationships_topic_3_1_scatter_linear_corr_linear22.gif\" alt=\"scatterplot where the dots are loosely clustered at the upper right part of the graph\" width=\"346\" height=\"193\" \/><\/p>\n<p>In this case, the low outlier gives an &#8220;illusion&#8221; of a positive linear relationship, whereas in reality, there is no linear relationship between X and Y.<\/p>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-179\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\">http:\/\/oli.cmu.edu<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":163,"menu_order":24,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"e0d1cd59-dd08-4e5c-acfb-e9201a2668ee","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-179","chapter","type-chapter","status-publish","hentry"],"part":140,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/179","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/179\/revisions"}],"predecessor-version":[{"id":1390,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/179\/revisions\/1390"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/140"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/179\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/media?parent=179"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=179"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=179"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/license?post=179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}