{"id":5282,"date":"2021-01-04T23:36:55","date_gmt":"2021-01-05T07:36:55","guid":{"rendered":"https:\/\/portasftpserver.com\/?p=5282"},"modified":"2022-03-15T11:34:57","modified_gmt":"2022-03-15T18:34:57","slug":"linear-regression-model-part-iii","status":"publish","type":"post","link":"https:\/\/portasftpserver.com\/linear-regression-model-part-iii\/","title":{"rendered":"Linear Regression Model &#8211; Part III"},"content":{"rendered":"\n<p class=\"sera-block-paragraph\">Sometimes in our data, we want to see the effectiveness of other variables or the impact of multiple data for the sales. <\/p>\n\n\n\n<p class=\"sera-block-paragraph\">\\(\\widehat{Y} = 3.337+168.582x_{1}+ 67.151x_{2} \\)<\/p>\n\n\n\n<p class=\"sera-block-paragraph\">The given equation use for the&nbsp;<strong>multiple linear regression<\/strong>.<\/p>\n\n\n\n<p class=\"sera-block-paragraph\">Based on our data from the previous lesson in <strong>part II<\/strong>, we only have one predictor which is the online <strong>advertising cost. <\/strong>Now, as for experimentations, we want to add the variable <strong>Free Shipping<\/strong>. With that said, we want to see if adding free shipping will give a big impact on the Monthly E-commerce Sales as well.<\/p>\n\n\n\n<figure class=\"sera-block-table is-style-stripes\"><table><thead><tr><th>Store<\/th><th class=\"has-text-align-center\" data-align=\"center\">Monthly E-commerce Sales<br>(in $1000)<\/th><th class=\"has-text-align-center\" data-align=\"center\">Online Advertising Cost<br>(in $1000)<\/th><th class=\"has-text-align-center\" data-align=\"center\">Free Shipping<\/th><\/tr><\/thead><tbody><tr><td>1<\/td><td class=\"has-text-align-center\" data-align=\"center\">370<\/td><td class=\"has-text-align-center\" data-align=\"center\">2.3<\/td><td class=\"has-text-align-center\" data-align=\"center\">No<\/td><\/tr><tr><td>2<\/td><td class=\"has-text-align-center\" data-align=\"center\">311<\/td><td class=\"has-text-align-center\" data-align=\"center\">1.7<\/td><td class=\"has-text-align-center\" data-align=\"center\">No<\/td><\/tr><tr><td>3<\/td><td class=\"has-text-align-center\" data-align=\"center\">620<\/td><td class=\"has-text-align-center\" data-align=\"center\">3.0<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><tr><td>4<\/td><td class=\"has-text-align-center\" data-align=\"center\">910<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><tr><td>5<\/td><td class=\"has-text-align-center\" data-align=\"center\">500<\/td><td class=\"has-text-align-center\" data-align=\"center\">2.9<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><tr><td>6<\/td><td class=\"has-text-align-center\" data-align=\"center\">520<\/td><td class=\"has-text-align-center\" data-align=\"center\">2.5<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><tr><td>7<\/td><td class=\"has-text-align-center\" data-align=\"center\">600<\/td><td class=\"has-text-align-center\" data-align=\"center\">3.4<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><tr><td>8<\/td><td class=\"has-text-align-center\" data-align=\"center\">830<\/td><td class=\"has-text-align-center\" data-align=\"center\">4.3<\/td><td class=\"has-text-align-center\" data-align=\"center\">Yes<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<pre class=\"sera-block-code\"><code lang=\"python\" class=\"language-python\"> library(\"car\") #You need to install the package\n Sales&lt;-c(370, 311, 620, 910, 500, 520, 600, 830)\n Advertising.Cost&lt;-c(2.3, 1.7, 3.0, 5, 2.9, 2.5, 3.4, 4.3)\n Free.Shipping&lt;-c(0,0,1,1,1,1,1,1)\n mod&lt;-lm(Sales~Advertising.Cost + as.factor(Free.Shipping))\n summary(mod)<\/code><\/pre>\n\n\n\n<p class=\"sera-block-paragraph\">Now let&#8217;s see the significance of the <strong>free shipping<\/strong>. As you can see, the free shipping seems not to really impact the overall monthly e-commerce sales since its p-value is greater than 0.05. This is because if you see our datasets, the sales really actually affected (driven) by the increases in advertising costs.<\/p>\n\n\n\n<p class=\"sera-block-paragraph\">Note: In reality, free shipping should attract more customers which means more sales but for the sake of this lesson I showed you the opposite result :-).<\/p>\n\n\n\n<figure class=\"sera-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"809\" height=\"273\" src=\"https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-24.png\" alt=\"\" class=\"sera-image-6463\" srcset=\"https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-24.png 809w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-24-585x197.png 585w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-24-768x259.png 768w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-24-100x34.png 100w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-24-600x202.png 600w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-24-178x60.png 178w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-24-267x90.png 267w\" sizes=\"auto, (max-width: 809px) 100vw, 809px\" \/><\/figure>\n\n\n\n<p class=\"sera-block-paragraph\">\\(\\widehat{Y} = 3.337+sax_{1}+ 67.151x_{2} \\)<\/p>\n\n\n\n<p class=\"sera-block-paragraph\">Above is the equation for multiple linear regression<\/p>\n\n\n\n<p class=\"sera-block-paragraph\">Now, let see the 3d plot using scatter3d() function<\/p>\n\n\n\n<pre class=\"sera-block-code\"><code lang=\"python\" class=\"language-python\"> scatter3d(x=Free.Shipping, y=Advertising.Cost,z = Sales)<\/code><\/pre>\n\n\n\n<figure class=\"sera-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"832\" height=\"670\" src=\"https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-26.png\" alt=\"\" class=\"sera-image-6497\" srcset=\"https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-26.png 832w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-26-585x471.png 585w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-26-768x618.png 768w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-26-100x81.png 100w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-26-600x483.png 600w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-26-75x60.png 75w, https:\/\/portasftpserver.com\/sera-uploads\/2021\/01\/image-26-112x90.png 112w\" sizes=\"auto, (max-width: 832px) 100vw, 832px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Sometimes in our data, we want to see the effectiveness of other variables or the impact of multiple data for the sales. The given equation use for the&nbsp;multiple linear regression. Based on our data from the previous lesson in part II, we only have one predictor which is the online advertising cost. Now, as for [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":7749,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5282","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-programming-software"],"_links":{"self":[{"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/posts\/5282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/comments?post=5282"}],"version-history":[{"count":0,"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/posts\/5282\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/media\/7749"}],"wp:attachment":[{"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/media?parent=5282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/categories?post=5282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portasftpserver.com\/sera-json\/wp\/v2\/tags?post=5282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}