[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657304-105":59,"doc-detail-657304-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","scatter-diagrams-and-correlation-correlation-lesson","Scatter diagrams and correlation - correlation lesson","","Scatter diagrams and correlation explain how to analyze bivariate data using three types of linear correlation: positive, negative, and no correlation. The correlation coefficient r quantifies the strength and direction of linear association on a scale from −1 to 1, linking r = 1, r = −1, and r = 0 to specific patterns on the scatter diagram. The regression line y = a + bx supports prediction, while interpolation and extrapolation are contrasted, including cautions about unreliable extrapolation. Correlation is also distinguished from causation and unrelated relationships.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/scatter-diagrams-and-correlation-correlation-lesson/657304/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/scatter-diagrams-and-correlation-correlation-lesson/657304.png","ImageObject",300,407,{"name":92,"@type":93},"Syukur Setiap Hari","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is a scatter diagram used for?","Question",{"text":112,"@type":113},"A scatter diagram is used to explore relationships between two variables by showing how their paired data points behave.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do positive, negative, and no correlation differ?",{"text":117,"@type":113},"Positive correlation shows a best-fit line with a positive gradient, negative correlation shows a negative gradient, and no correlation shows no pattern between the variables.",{"name":119,"@type":110,"acceptedAnswer":120},"What does the correlation coefficient r tell you?",{"text":121,"@type":113},"The correlation coefficient r measures how closely related the two variables are, with values between −1 and 1; r = 1 and r = −1 represent perfect positive or negative linear correlation.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657304,1793141457,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":39},962093541965,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Scatter diagrams and correlation  \nStarter  \n1. (Review of last lesson) Find the mean and standard deviation for this data using a suitable method of coding and only the basic functions of your calculator  \nWeights of students (kg)  \n4  \n5  \n6  \n7  \n8  \n6  \n2  \n4  \n7  \n5  \n7  \n7  \n8  \n7  \nKey: 4 | 3 means 43  \nNotes  \nCorrelation  \nCorrelation is about whether there is a relationship between bivariate data i.e. data with two variables. There are three types of linear correlation: positive, negative and no correlation.  \nPositive correlation: the line of best ﬁt has a positive gradient  \n(i.e. as x increases, y also increases) .  \nNegative correlation: the line of best ﬁt has a negative gradient  \n(i.e. as x increases, y decreases) .  \nNo correlation: there is no pattern between the variables  \n(see diagram)  \nCorrelation coefﬁcient  \nThe correlation coefﬁcient, r, is a measure of how closely related the two variables are. It takes a value between −1 and 1 i.e. −1 ≤ r ≤ 1.  \nr = 1 ⇒ perfect positive linear correlation, all data points lie on the line of best ﬁt. r = − 1 ⇒ perfect negative linear correlation, all data points lie on the line of best ﬁt.  \nr = 0 ⇒ no linear correlation, the variables may be correlated in another way (e.g. a quadratic relation)  \nIf there is linear correlation, a line of best ﬁt can be drawn on the scatter diagram —this line is called the regression line.  \nThe regression line is of the form y = a + bx where a is the y−intercept and b is the gradient of the line.  \n[www.mathspanda.com](www.mathspanda.com)  \n\n| GRAPHS | Positive correlation | Negative correlation |\n| --- | --- | --- |\n| Strong\u003Cbr>|r| ≥ 0.8 | | |\n| Weak\u003Cbr>0.4 ≤ |r| ≤ 0.6 | | |\n\nInterpolation vs. extrapolation  \nThe line of best ﬁt, or regression line, can be used to predict values.  \nInterpolation predicts values that are within the range of data given.  \nExtrapolation predicts values that are outside the range of data given.  \nIt can be dangerous to extrapolate values as they may not be accurate (e.g. age vs. height)  \nCorrelation vs. causation vs. unrelated  \nTwo variables may seem to be correlated but instead there may be a causal relationship. (E.g. increased temperature leads to an increase in sales of ice cream. Alternatively, two variables may appear correlated but in fact are unrelated (e.g. sales of cameras and sales of computers) .  \nVideo:  Correlation  \nVideo:  Regression  \nVideo:  Interpreting regression lines  \nVideo:  Making predictions and reliability of predicted values  \nSolutions to Starter and E.g.s  \nExercise  \np345 16D Qu 1-10  \nSummary  \nPositive correlation: the line of best ﬁt has a positive gradient  \nNegative correlation: the line of best ﬁt has a negative gradient  \nNo correlation: there is no pattern between the variables  \n[www.mathspanda.com](www.mathspanda.com)  \nCorrelation coefﬁcient  \nThe correlation coefﬁcient, r, is a measure of how closely related the two variables are. It takes a value between −1 and 1 i.e. −1 ≤ r ≤ 1.  \nr = 1 ⇒ perfect positive linear correlation, all data points lie on the line of best ﬁt.  \nr = − 1 ⇒ perfect negative linear correlation, all data points lie on the line of best ﬁt.  \nr = 0 ⇒ no linear correlation, the variables may be correlated in another way (e.g. a quadratic relation)  \nIf there is linear correlation, a line of best ﬁt can be drawn on the scatter diagram —this line is called the regression line.  \nInterpolation predicts values that are within the range of data given.  \nExtrapolation predicts values that are outside the range of data given.  \nTwo variables may seem to be correlated but instead there may be a causal relationship. (E.g. temperature and sales of ice cream) . Alternatively, two variables may appear correlated but in fact are unrelated (e.g. sales of cameras and sales of computers) .","cbCaidun7hvPrUnd","https://ap.wps.com/l/cbCaidun7hvPrUnd","pdf",362743,"English","# Correlation basics\n## Positive, negative, and no correlation\n# Correlation coefficient (r)\n## Strength of correlation using |r|\n# Regression line and prediction\n## Interpolation vs extrapolation\n# Correlation vs causation vs unrelated","[{\"question\":\"What is a scatter diagram used for?\",\"answer\":\"A scatter diagram is used to explore relationships between two variables by showing how their paired data points behave.\"},{\"question\":\"How do positive, negative, and no correlation differ?\",\"answer\":\"Positive correlation shows a best-fit line with a positive gradient, negative correlation shows a negative gradient, and no correlation shows no pattern between the variables.\"},{\"question\":\"What does the correlation coefficient r tell you?\",\"answer\":\"The correlation coefficient r measures how closely related the two variables are, with values between −1 and 1; r = 1 and r = −1 represent perfect positive or negative linear correlation.\"}]","Scatter diagrams and correlation - correlation lesson | PDF",1792977080]