[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-398900-105":59,"doc-detail-398900-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","srm-formula-sheet-introduction-to-terminology-and-notation","SRM Formula Sheet - Introduction to Terminology and Notation","","Concise SRM formula sheet summarizing core concepts in introductory regression analysis. Defines key terminology for variables, including response and explanatory variables, and distinguishes quantitative and qualitative variable types such as nominal and ordinal. Provides notation for indices and sample sizes, then covers descriptive data analysis with sample mean, variance, covariance, correlation, and common visualization tools like scatterplots, box plots, and quantile plots. Introduces linear models through simple and multiple linear regression, including OLS parameter estimates, SSR/SSE/RSS relationships, and diagnostic linear model assumptions with remedies for misspecification, residual issues, heteroscedasticity, dependence, non-normal errors, and multicollinearity.",{"@graph":69,"@context":123},[70,84,106],{"@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/srm-formula-sheet-introduction-to-terminology-and-notation/398900/",{"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/srm-formula-sheet-introduction-to-terminology-and-notation/398900.png","ImageObject",300,407,{"name":92,"@type":93},"jayni","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the difference between a response variable and an explanatory variable?","Question",{"text":113,"@type":114},"The response variable is the primary variable of interest to predict, also called the output, dependent, or target variable. The explanatory variable is used to explain or predict the response, also called the input, independent, predictor, or feature variable.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do sample covariance and sample correlation relate to descriptive analysis?",{"text":118,"@type":114},"Sample covariance quantifies how two variables vary together, while sample correlation measures the strength of their linear relationship using standardized form derived from covariance.",{"name":120,"@type":111,"acceptedAnswer":121},"What diagnostics and solutions are used for heteroscedasticity in linear regression?",{"text":122,"@type":114},"Heteroscedasticity is identified by inconsistent residual spread across predictions and can be tested using the Breusch-Pagan test. Solutions include transforming the response with a concave function, using weighted least squares, and adjusting standard errors with heteroscedasticity-consistent methods.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},398900,1790554706,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},3985747859343,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","SRM  \nUpdated 09/18/26  \nIntroductory Concepts  \nIntroduction to Terminology and Notation  \nData Terminology  \n• A response variable is the variable of primary interest that we aim to predictor understand. Other names include output variable, dependent variable, and target variable.  \n• An explanatory variable is a variable used to explain or predict the response variable. Other names include input variable, independent variable, predictor, and feature.  \n• A quantitative variable is a numeric variable that can be either a count variable or a continuous variable.  \n• A qualitative variable is a categorical variable that takes values as categories (levels or classes) .  \n• A nominal variable is a qualitative variable with no meaningful order.  \n• An ordinal variable is a qualitative variable with a meaningful order.  \n• The classification of a variable may depend on context and interpretation.  \n• An observation is a single data point, typically represented as a row.  \n• A variable is a measured characteristic, typically represented as a column.  \nNotation  \n􀁶, 􀁝􀁵, 􀁜 Subscript 􀁦  \n􀁫  \nSubscript 􀁧  \n􀁭  \nResponse variable Explanatory variable Index for observations  \nNo. of observations Index for variables except response No. of variables except response  \nDescriptive Data Analysis  \nNumerical Summaries Sample mean =  = ∑\"!~~ ~~$~~ ~~􀁵!  \n& ∑\"! \\# $(􀁵! − )& Sample variance = 􀁰% =  􀁫 − 1  Sample covariance = 􀁠􀁬􀁳%,(  \n∑\"! \\# $ (􀁵! − )(􀁶! − )  \n=  \n􀁫 − 1  \nSample correlation = 􀁯%,( = 􀁠􀁰􀁬%􀁳⋅~~ ~~%􀁰,((  ∑\"! \\# $ (􀁵! − )(􀁶! − )   \n=  \nE∑\"! \\# $ (􀁵! − )& ⋅ ∑\"! \\# $ (􀁶! − )&  \nScatterplots  \nPlots values of two variables to investigate their relationship.  \nBox Plots  \nCaptures a variable’s distribution using its median, 1st and 3rd quartiles, and distribution tails.  \n􀁮􀁮 Plots  \nPlots sample quantiles against theoretical quantiles to determine whether the sample and theoretical distributions have  \nsimilar shapes.  \nLinear Models  \nSimple Linear Regression (SLR)  \nSpecial case of MLR where 􀁭 = 1  \nParameter Estimates  \n∑\"! \\# $ (􀁵! − )(􀁶! − ) 􀁰(  \n􀁟 = ~~ ~~ = 􀁯 ⋅ ~~ ~~$ ∑\"! \\# $ (􀁵! − )& %,( 􀁰%  \n􀁟 ) =  − 􀁟$  \nOther Numerical Results 􀁘 & = 􀁯%&,(  \nSSR = 􀁟&$ ∑\"! \\# $ (􀁵! − )&  \nMultiple Linear Regression (MLR)  \n􀁝 = 􀁹) + 􀁹$􀁵$ + ⋯ + 􀁹*􀁵* + 􀁼  \nNotation 􀁹+  \n􀁟+  \n&􀂂  \nMSE  \nRSE  \n􀁢  \nSST/TSSSSR  \nSSE/RSS  \nThe 􀁧th regression coefficient Estimate of 􀁹+  \nVariance of response Estimate of 􀂂 &  \nResidual standard error Residual  \nTotal sum of squares Regression sum of squares Error sum of squares  \nParameter Estimates – Ordinary Least Squares (OLS)  \n = 􀁟 ) + 􀁟$􀁵$ + ⋯ + 􀁟*􀁵* MSE = SSE⁄(􀁫 − 􀁭 − 1)  \nRSE = √MSE  \nOther Numerical Results  \nP  \n􀁢 = 􀁶 − 􀁶  \nSST = ∑\"! \\# $ (􀁶! − )& = total variability SSR = ∑\"! \\# $ (! − )& = explained SSE = ∑\"! \\# $ (􀁶! − ! )& = unexplained SST = SSR + SSE  \n􀁘 & = SSR⁄SST = 􀁯&(,(,   \n© 2026 Coaching Actuaries. All Rights Reserved [www.coachingactuaries.com](www.coachingactuaries.com) SRM Formula Sheet 1  \nLinear Model Assumptions  \nMisspecified Model Equation Problem  \n• Incorrectly assuming the model equation or failing to include suitable predictors.  \n• Can invalidate all regression results.  \nDiagnosis  \n• Discernible trends in 􀁢 versus  plot  \nSolutions  \n• Add missing higher order term.  \n• Construct an added variable plot for potential new predictors.  \n• Calculate the partial correlation coefficient for the new variable.  \nWell-Behaved Residuals in 􀁢 Versus  Plot  \n• Points appear to be randomly scattered  \n• Residuals seem to average to 0  \n• Spread of residuals does not change  \nAdded Variable Plot  \nAssess the effect of adding a new explanatory variable to an existing regression model.  \nPartial Correlation Coefficient  􀁱+   \ni􀁱+& + 􀁫 − 􀁭 − 1  \nResiduals with Non-Zero Averages Problem  \n• Residuals should have an average that is close to zero.  \n• Typically a symptom of a larger problem.  \nDiagnosis  \n• Consistently positive or negative residuals in certain ranges in 􀁢 versus  plot.  \nHeteroscedasticity ","cbCaijrHOGG6J37C","https://ap.wps.com/l/cbCaijrHOGG6J37C","pdf",2047346,17,"English","# Introductory Concepts\n## Introduction to Terminology and Notation\n## Descriptive Data Analysis\n## Scatterplots and Box Plots\n## Linear Models\n## Simple Linear Regression (SLR)\n## Multiple Linear Regression (MLR)\n## Parameter Estimates – Ordinary Least Squares (OLS)\n## Linear Model Assumptions\n## Common Diagnostic Problems and Solutions","[{\"question\":\"What is the difference between a response variable and an explanatory variable?\",\"answer\":\"The response variable is the primary variable of interest to predict, also called the output, dependent, or target variable. The explanatory variable is used to explain or predict the response, also called the input, independent, predictor, or feature variable.\"},{\"question\":\"How do sample covariance and sample correlation relate to descriptive analysis?\",\"answer\":\"Sample covariance quantifies how two variables vary together, while sample correlation measures the strength of their linear relationship using standardized form derived from covariance.\"},{\"question\":\"What diagnostics and solutions are used for heteroscedasticity in linear regression?\",\"answer\":\"Heteroscedasticity is identified by inconsistent residual spread across predictions and can be tested using the Breusch-Pagan test. Solutions include transforming the response with a concave function, using weighted least squares, and adjusting standard errors with heteroscedasticity-consistent methods.\"}]","SRM Formula Sheet - Introduction to Terminology and Notation | PDF",1790489954,43]