{"id":244,"date":"2017-04-15T03:20:04","date_gmt":"2017-04-15T03:20:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/nonlinear-models-review\/"},"modified":"2017-05-29T00:20:27","modified_gmt":"2017-05-29T00:20:27","slug":"nonlinear-models-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/chapter\/nonlinear-models-review\/","title":{"raw":"Putting It Together: Nonlinear Models","rendered":"Putting It Together: Nonlinear Models"},"content":{"raw":"&nbsp;\r\n<h3><strong>Let\u2019s Summarize<\/strong><\/h3>\r\nThis is what we have learned about exponential models:\r\n\r\nThe general form of an <em>exponential model<\/em> is <em>y = C \u00b7 b<sup><em>x<\/em><\/sup><\/em>.\r\n<ul>\r\n \t<li>Exponential models are nonlinear. More specifically, exponential models predict that <em>y<\/em> increases or decreases by a constant percentage for each 1-unit increase in <em>x<\/em>.<\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li><em>C<\/em> is the <em>initial value<\/em>. It is the <em>y<\/em>-value when <em>x<\/em> = 0. It is also the <em>y<\/em>-intercept.<\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li><em>b<\/em> is the <em>growth factor<\/em> or <em>decay factor<\/em>. <em>b<\/em> is always positive.\r\n<ul>\r\n \t<li>If <em>b<\/em> is greater than 1, <em>b<\/em> is a growth factor. In this case, the association is positive, and <em>y<\/em> is increasing. This makes sense because multiplying by a number greater than 1 increases the initial value. From the growth factor, we can determine the percent increase in <em>y<\/em> for each additional 1-unit increase in <em>x<\/em>.<\/li>\r\n \t<li>Similarly, if <em>b<\/em> is greater than 0 and less than 1, <em>b<\/em> is a decay factor. In this case, the association is negative, and <em>y<\/em> is decreasing. From the decay factor, we can determine the <em>percentage decrease<\/em> in <em>y<\/em> for each additional 1-unit increase in <em>x<\/em>.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\nLet\u2019s compare the general form of an exponential model to the general form for a <em>linear model:<\/em> <em>y<\/em> = <em>a<\/em> + <em>bx<\/em>.\r\n<ul>\r\n \t<li>In the linear model, <em>a<\/em> is the <em>initial value<\/em>. It is the <em>y<\/em>-value when <em>x<\/em> = 0. It is also the <em>y<\/em>-intercept.<\/li>\r\n<\/ul>\r\n<ul>\r\n \t<li><em>b<\/em> is the <em>slope<\/em>. From the slope, we can determine the <em>amount<\/em> and <em>direction<\/em> the <em>y<\/em>-value changes for each additional 1-unit increase in <em>x<\/em>. When <em>b<\/em> is positive, there is a positive association, and <em>y<\/em> increases. When <em>b<\/em> is negative, there is a negative association, and <em>y<\/em> decreases.<\/li>\r\n<\/ul>","rendered":"<p>&nbsp;<\/p>\n<h3><strong>Let\u2019s Summarize<\/strong><\/h3>\n<p>This is what we have learned about exponential models:<\/p>\n<p>The general form of an <em>exponential model<\/em> is <em>y = C \u00b7 b<sup><em>x<\/em><\/sup><\/em>.<\/p>\n<ul>\n<li>Exponential models are nonlinear. More specifically, exponential models predict that <em>y<\/em> increases or decreases by a constant percentage for each 1-unit increase in <em>x<\/em>.<\/li>\n<\/ul>\n<ul>\n<li><em>C<\/em> is the <em>initial value<\/em>. It is the <em>y<\/em>-value when <em>x<\/em> = 0. It is also the <em>y<\/em>-intercept.<\/li>\n<\/ul>\n<ul>\n<li><em>b<\/em> is the <em>growth factor<\/em> or <em>decay factor<\/em>. <em>b<\/em> is always positive.\n<ul>\n<li>If <em>b<\/em> is greater than 1, <em>b<\/em> is a growth factor. In this case, the association is positive, and <em>y<\/em> is increasing. This makes sense because multiplying by a number greater than 1 increases the initial value. From the growth factor, we can determine the percent increase in <em>y<\/em> for each additional 1-unit increase in <em>x<\/em>.<\/li>\n<li>Similarly, if <em>b<\/em> is greater than 0 and less than 1, <em>b<\/em> is a decay factor. In this case, the association is negative, and <em>y<\/em> is decreasing. From the decay factor, we can determine the <em>percentage decrease<\/em> in <em>y<\/em> for each additional 1-unit increase in <em>x<\/em>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Let\u2019s compare the general form of an exponential model to the general form for a <em>linear model:<\/em> <em>y<\/em> = <em>a<\/em> + <em>bx<\/em>.<\/p>\n<ul>\n<li>In the linear model, <em>a<\/em> is the <em>initial value<\/em>. It is the <em>y<\/em>-value when <em>x<\/em> = 0. It is also the <em>y<\/em>-intercept.<\/li>\n<\/ul>\n<ul>\n<li><em>b<\/em> is the <em>slope<\/em>. From the slope, we can determine the <em>amount<\/em> and <em>direction<\/em> the <em>y<\/em>-value changes for each additional 1-unit increase in <em>x<\/em>. When <em>b<\/em> is positive, there is a positive association, and <em>y<\/em> increases. When <em>b<\/em> is negative, there is a negative association, and <em>y<\/em> decreases.<\/li>\n<\/ul>\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-244\">\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":8,"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":"d9502fab-febf-464a-8a6e-c780102b0539","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-244","chapter","type-chapter","status-publish","hentry"],"part":225,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/244","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":3,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/244\/revisions"}],"predecessor-version":[{"id":1008,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/244\/revisions\/1008"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/225"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/244\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/media?parent=244"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=244"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=244"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-wmopen-concepts-statistics\/wp-json\/wp\/v2\/license?post=244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}