{"id":251,"date":"2019-07-15T22:43:45","date_gmt":"2019-07-15T22:43:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebracorequisite\/chapter\/summary-modeling-with-linear-functions\/"},"modified":"2019-07-15T22:43:45","modified_gmt":"2019-07-15T22:43:45","slug":"summary-modeling-with-linear-functions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/chapter\/summary-modeling-with-linear-functions\/","title":{"raw":"Summary: Modeling With Linear Functions","rendered":"Summary: Modeling With Linear Functions"},"content":{"raw":"\n<h2>Key Concepts<\/h2>\n<ul id=\"fs-id1165137785014\">\n \t<li>Scatter plots show the relationship between two sets of data.<\/li>\n \t<li>Scatter plots may represent linear or non-linear models.<\/li>\n \t<li>The line of best fit may be estimated or calculated using a calculator or statistical software.<\/li>\n \t<li>Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data.<\/li>\n \t<li>The correlation coefficient, <span id=\"MathJax-Element-329-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-4867\" class=\"math\"><span id=\"MathJax-Span-4868\" class=\"mrow\"><span id=\"MathJax-Span-4869\" class=\"semantics\"><span id=\"MathJax-Span-4870\" class=\"mrow\"><span id=\"MathJax-Span-4871\" class=\"mrow\"><em><span id=\"MathJax-Span-4872\" class=\"mi\">r<\/span><\/em><span id=\"MathJax-Span-4873\" class=\"mo\">,<\/span><\/span><\/span><\/span><\/span><\/span><\/span> indicates the degree of linear relationship between data.<\/li>\n \t<li>A regression line best fits the data.<\/li>\n \t<li>The least squares regression line is found by minimizing the squares of the distances of points from a line passing through the data and may be used to make predictions regarding either of the variables.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165137705061\" class=\"definition\">\n \t<dt><strong>correlation coefficient<\/strong><\/dt>\n \t<dd id=\"fs-id1165135250649\">a value, <em>r<\/em>, between \u20131 and 1 that indicates the degree of linear correlation of variables or how closely a regression line fits a data set.<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137549428\" class=\"definition\">\n \t<dt><strong>extrapolation<\/strong><\/dt>\n \t<dd id=\"fs-id1165135485274\">predicting a value outside the domain and range of the data<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135485278\" class=\"definition\">\n \t<dt><strong>interpolation<\/strong><\/dt>\n \t<dd id=\"fs-id1165135184191\">predicting a value inside the domain and range of the data<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137761665\" class=\"definition\">\n \t<dt><strong>least squares regression<\/strong><\/dt>\n \t<dd id=\"fs-id1165135192379\">a statistical technique for fitting a line to data in a way that minimizes the differences between the line and data values<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137446440\" class=\"definition\">\n \t<dt><strong>model breakdown<\/strong><\/dt>\n \t<dd id=\"fs-id1165137446445\">when a model no longer applies after a certain point<\/dd>\n<\/dl>\n","rendered":"<h2>Key Concepts<\/h2>\n<ul id=\"fs-id1165137785014\">\n<li>Scatter plots show the relationship between two sets of data.<\/li>\n<li>Scatter plots may represent linear or non-linear models.<\/li>\n<li>The line of best fit may be estimated or calculated using a calculator or statistical software.<\/li>\n<li>Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data.<\/li>\n<li>The correlation coefficient, <span id=\"MathJax-Element-329-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-4867\" class=\"math\"><span id=\"MathJax-Span-4868\" class=\"mrow\"><span id=\"MathJax-Span-4869\" class=\"semantics\"><span id=\"MathJax-Span-4870\" class=\"mrow\"><span id=\"MathJax-Span-4871\" class=\"mrow\"><em><span id=\"MathJax-Span-4872\" class=\"mi\">r<\/span><\/em><span id=\"MathJax-Span-4873\" class=\"mo\">,<\/span><\/span><\/span><\/span><\/span><\/span><\/span> indicates the degree of linear relationship between data.<\/li>\n<li>A regression line best fits the data.<\/li>\n<li>The least squares regression line is found by minimizing the squares of the distances of points from a line passing through the data and may be used to make predictions regarding either of the variables.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165137705061\" class=\"definition\">\n<dt><strong>correlation coefficient<\/strong><\/dt>\n<dd id=\"fs-id1165135250649\">a value, <em>r<\/em>, between \u20131 and 1 that indicates the degree of linear correlation of variables or how closely a regression line fits a data set.<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137549428\" class=\"definition\">\n<dt><strong>extrapolation<\/strong><\/dt>\n<dd id=\"fs-id1165135485274\">predicting a value outside the domain and range of the data<\/dd>\n<\/dl>\n<dl id=\"fs-id1165135485278\" class=\"definition\">\n<dt><strong>interpolation<\/strong><\/dt>\n<dd id=\"fs-id1165135184191\">predicting a value inside the domain and range of the data<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137761665\" class=\"definition\">\n<dt><strong>least squares regression<\/strong><\/dt>\n<dd id=\"fs-id1165135192379\">a statistical technique for fitting a line to data in a way that minimizes the differences between the line and data values<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137446440\" class=\"definition\">\n<dt><strong>model breakdown<\/strong><\/dt>\n<dd id=\"fs-id1165137446445\">when a model no longer applies after a certain point<\/dd>\n<\/dl>\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-251\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/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":17533,"menu_order":19,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\"}]","CANDELA_OUTCOMES_GUID":"b27fb45b-0ddf-429b-beb2-ac9c996b3288","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-251","chapter","type-chapter","status-publish","hentry"],"part":232,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters\/251","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":0,"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters\/251\/revisions"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/parts\/232"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapters\/251\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/wp\/v2\/media?parent=251"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=251"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/wp\/v2\/contributor?post=251"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-collegealgebracorequisite\/wp-json\/wp\/v2\/license?post=251"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}