[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-573896-105":3,"detail-sidebar-cat-1-en-105":79,"doc-detail-573896-en":125},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":72,"head_meta":74,"extra_data":76,"updated_unix":78},105,"en","exam-srm-formula-review-sheet-linear-regression-page-2","Exam SRM Formula & Review Sheet - Linear Regression - Page 2","","Formula & Review Sheet for Exam SRM provides a quick-reference set of essential statistical learning and regression concepts. It summarizes supervised versus unsupervised learning, prediction and inference ideas, and bias–variance trade-offs including overfitting and underfitting. It includes key regression metrics such as training/test MSE, sums of squares (TSS, RSS, regression SS), and R², then presents linear regression fundamentals, model assumptions, parameter interpretations, and confidence and prediction interval forms.",{"@graph":14,"@context":71},[15,34,54],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/paper-templates/","Paper Templates",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/exam-srm-formula-review-sheet-linear-regression-page-2/573896/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":48,"encodingFormat":47,"isAccessibleForFree":49,"interactionStatistic":50},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/exam-srm-formula-review-sheet-linear-regression-page-2/573896.png","ImageObject",442,249,{"name":42,"@type":43},"aboduw","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-14",true,{"@type":51,"interactionType":52,"userInteractionCount":30},"InteractionCounter",{"@type":53},"ViewAction",{"@type":55,"mainEntity":56},"FAQPage",[57,63,67],{"name":58,"@type":59,"acceptedAnswer":60},"What is the role of training MSE and test MSE in model evaluation?","Question",{"text":61,"@type":62},"Training MSE measures average squared error on the training data, while test MSE reflects average squared error on new data. Test MSE typically shows a U-shape as model flexibility increases, decreasing at first and then increasing.","Answer",{"name":64,"@type":59,"acceptedAnswer":65},"How do bias and variance affect predictive performance?",{"text":66,"@type":62},"Bias measures the difference between the expected estimator value and the true value, while variance measures sensitivity of the estimator to different random samples. Increasing model complexity may reduce bias but increase variance.",{"name":68,"@type":59,"acceptedAnswer":69},"Which quantities are used to assess goodness of fit in linear regression?",{"text":70,"@type":62},"Goodness of fit uses partitioning of sums of squares into total sum of squares (TSS), residual sum of squares (RSS), and regression sum of squares (Reg SS). The coefficient of determination R² represents the proportion of variability explained by the regression.","https://schema.org",{"og:url":32,"og:type":73,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":75,"canonical":32},"index,follow",{"doc_id":77,"site_id":7},573896,1791978893,{"code":4,"msg":80,"data":81},"success",[82,87,92,97,102,107,112,117,121],{"id":83,"doc_module":22,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},11,"Presentations",90,"presentations",{"id":88,"doc_module":22,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},12,"Resumes",80,"resumes",{"id":93,"doc_module":22,"doc_module_name":25,"category_name":94,"show_sort_weight":95,"slug":96},14,"Invoices",70,"invoices",{"id":98,"doc_module":22,"doc_module_name":25,"category_name":99,"show_sort_weight":100,"slug":101},15,"Posters",60,"posters",{"id":103,"doc_module":22,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},16,"Social Media",50,"social-media",{"id":108,"doc_module":22,"doc_module_name":25,"category_name":109,"show_sort_weight":110,"slug":111},17,"Forms",40,"forms",{"id":113,"doc_module":22,"doc_module_name":25,"category_name":114,"show_sort_weight":115,"slug":116},18,"Letters",30,"letters",{"id":118,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":119,"slug":120},21,5,"papers-templates",{"id":122,"doc_module":22,"doc_module_name":25,"category_name":123,"show_sort_weight":4,"slug":124},158,"General","general-158",{"code":4,"msg":80,"data":126},{"doc_id":77,"user_id":127,"nickname":42,"user_avatar":128,"doc_module":22,"category_id":118,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":129,"file_id":130,"file_url":131,"file_type":132,"file_size":133,"view_count":30,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":134,"language":135,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":12,"update_tm":139,"read_time":140},3985747862266,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Formula & Review Sheet for Exam SRM  \nYour quick-reference guide for the most important formulas and concepts you need.  \nWant More Than Just the Formula Sheet?  \nThis free Formula & Review Sheet is just one part of the ACTEX Learning experience. Our complete study program is designed to help you  \nunderstand concepts, practice effectively, and pass with confidence. With the ACTEX Learning Bundle for Exam SRM, you get:  \n Comprehensive Study Manual  \n GOAL Practice Problems  \n Instructional Videos  \n Flashcards  \n Formula & Review Sheets  \n Learning Platform with a Study Planner and Topic Explorer  \nWant an Extra Edge?  \nTake your preparation even further with premium ACTEX resources designed to sharpen exam skills and boost confidence when it matters most.  \nPopular Upgrades:  \n Live Bootcamps  \nLearn More  \nOne-On-One Tutoring  \n Graded Mock Exams  \nClick anywhere on this page or scan the QR code to learn more about offerings for this exam. ~~ ~~  \nExam SRM Formula & Review Sheet  \n(updated 10/31/2024)  \nPrediction: Determining what the response will be for new sets of predictor values.  \nInference: Understanding how the explanatory variables influence the response.  \nParametric: Specifies a function, and statistics is used to fit the function’s parameters  \nNon-parametric: Without specify a functional form for the relationship.  \nSupervised learning: Has a response variable that is influenced by explanatory variables.  \nUnsupervised learning: Relates the observations to each other or finds patterns in the observations.  \nTraining MSE: ~~ ~~1n i1 hyi 􀀀 ^f(xi)i2 , the training MSE decreases monotonically when the model flexibility  \nincreases.  \nTest MSE: Average hy0 􀀀 ^f(x0 )i2 , the test MSE exhibits a U-shape,  \nfirst declining as flexibility increases, then starting to increase again.  \nBias: Measures the extent to which the expected value of the estimator differs from the true value  \nVariance: Measures how much the estimator varies with different random samples of data  \nBias-variance trade-off: Minimize Ey0 􀀔 􀀐y0 􀀀 ^f(x0 )􀀑 2􀀕 = Var h^f(x0 )i + hBias 􀀐 ^f(x0 )􀀑i 2 + Var(\")  \nIncreasing complexity/flexibility of a model may result in an increase in variance but a reduction in bias.  \nOverfitting:  \nUnderfitting:  \nn n  \nSum of squares: Sxy = P (xi 􀀀 ) (yi 􀀀 ) = P xi yi 􀀀 n  \ni=1 i=1  \nn n  \nSxx = P (xi 􀀀 )2 = P x2i 􀀀 n2  \ni=1 i=1  \nSample variance of x and y: s2x = nS1 s2y = nS1  \nSample covariance: cvxy = nS1  \nSample correlation between x and y: rxy = csvxxsyy  \nBASIC STATISTICAL LEARNING  \nThe model will replicate historical data very well but cannot predict future outcomes reliably.  \nThe model will predict future outcomes reliably but cannot explain what is driving the result.  \nNeed Help? Email [support@actuarialuniversity.com](support@actuarialuniversity.com) Copyright © ArchiMedia Advantage Inc. All Rights Reserved  \nACTEX Learning  \nExam SRM  \nPage 2  \nLinear Regression  \nSIMPLE LINEAR REGRESSION  \nModel equation: yi = 􀀌0 + 􀀌1 xi + \"i ;  \n􀀌0 (intercept) and 􀀌1 (slope parameter) are regression coefficients, \"i is the random error term.  \nModel assumptions: \"i are independent with E [\"i] = 0 and Var (\"i ) = 􀀛 2 : Fitted regression:  = 0n+(i1  ) (yi 􀀀 ) nP xi yi 􀀀 n  \n1 = i=1 i1 (xi 􀀀 )2 = i11 x2i 􀀀 n2 and 0 =  􀀀 1  Specialized formulas for 1 : 1 = rxy 􀀂 ssyx  \nProperties:  \nE h0i = 􀀌0 Var 􀀐0 􀀑 = 􀀛 2 􀀒 1n + x2x 􀀓 SE 􀀐0 􀀑 = ss2 􀀒 1n + x2x 􀀓 s2 is an unbiased estimator of 􀀛 2  \nE h1i = 􀀌1 Var 􀀐1 􀀑 = 􀀛 2 􀀒 S1xx 􀀓 SE 􀀐1 􀀑 = ss2 􀀒 S1xx 􀀓 Cov (􀀌0 ; 􀀌1 ) = 􀀀 􀀛Sx2x   \nv  \nE [i] = 􀀌0 + 􀀌1 xi Var (i ) = 􀀛 2 ~~ ~~1n + (xi)2 ! SE (i ) = tu s2 ~~ ~~1n + (xi)2 !   \nv  \nConfidence interval: 􀀃 􀀆 tn􀀀2;􀀋/2 􀀂 SE (E[y􀀃] 􀀀 􀀃 ) = 􀀃 􀀆 tn􀀀2;􀀋/2 tu s2 \" 1n +vu  (x􀀃S)2 \\# 􀀖 2  Prediction interval: 􀀃 􀀆 tn􀀀2;􀀋/2 􀀂 SE (y􀀃 􀀀 􀀃 ) = 􀀐0 + 1 x 􀀃􀀑 􀀆 tn􀀀2;􀀋/2 tu s2 \" 1 + 1n + (x􀀃Sx)~~ ~~\\#  \nResiSumd-utoa-lz(Rawerocresiduaonstrali:ts onei =resiydiuli: = obsvede ial0u; e fittedx ie il0ue  \ni=1 i=1  \nGOODNESS OF FIT OF A MODEL  \nPartition sum of squar","cbCaikktMIp51ziH","https://ap.wps.com/l/cbCaikktMIp51ziH","pdf",1474685,24,"English","# BASIC STATISTICAL LEARNING\n## Prediction, Inference, Parametric and Non-parametric Learning\n## Bias, Variance, and Bias-variance Trade-off\n## Overfitting and Underfitting\n# Linear Regression\n## Simple Linear Regression\n## Properties, Confidence Interval, and Prediction Interval\n## Goodness of Fit of a Model\n## Multiple Linear Regression\n## Model Fitting and Least Squares Estimation","[{\"question\":\"What is the role of training MSE and test MSE in model evaluation?\",\"answer\":\"Training MSE measures average squared error on the training data, while test MSE reflects average squared error on new data. Test MSE typically shows a U-shape as model flexibility increases, decreasing at first and then increasing.\"},{\"question\":\"How do bias and variance affect predictive performance?\",\"answer\":\"Bias measures the difference between the expected estimator value and the true value, while variance measures sensitivity of the estimator to different random samples. Increasing model complexity may reduce bias but increase variance.\"},{\"question\":\"Which quantities are used to assess goodness of fit in linear regression?\",\"answer\":\"Goodness of fit uses partitioning of sums of squares into total sum of squares (TSS), residual sum of squares (RSS), and regression sum of squares (Reg SS). The coefficient of determination R² represents the proportion of variability explained by the regression.\"}]","Exam SRM Formula & Review Sheet - Linear Regression - Page 2 | PDF",1791950618,8]