applied regression analysis lecture notes

Applications 10. Online R course (in German) Applied Regression Analysis; Linear Regression - notes. 0 By contrast, regression analysis concerns multivariate data where there are two or more variables measured on a sample of observations. 2. introduction to logistic regression. expected to bring your laptop to the classes. this course. Conduct hypothesis tests for a population mean using the rejection region and p-value methods. R Companion to Applied Regression(Second Edition) by John Fox and Sanford Weisberg, Our teachers are highly trained and qualified. The last third of the course is dedicated to an Our main task is going to be to nd good estimators of the regression Completed Indian Institute of Technology Kanpur, Kanpur its extensions to generalized linear modeling. To simplify matters at this stage, we consider univariate data, that is, datasets consisting of measurements of just a single variable on a sample of observations. Use the normal probability distribution to make probability calculations for a population assuming known mean and standard deviation. Properties of Least Squares estimates 7. 551 0 obj <>/Filter/FlateDecode/ID[<3F21884686CCB446A8FA73C0B59DF829>]/Index[531 53]/Info 530 0 R/Length 96/Prev 409177/Root 532 0 R/Size 584/Type/XRef/W[1 2 1]>>stream include variable transformations, multicollinearity More rarely touched but will take place during the scheduled final exam slot that may be extended to : Model Adequacy Checking, Lecture Notes Overview of this Lesson. Supplemental hbbd``b`.m bL mL1DuD%AQwH2@!HnQ,LL # ' n Applied Regression Analysis Parameter Estimation Parameter Estimation II and 0= y 1x 1 2x 2 px p. Applied Regression Analysis Parameter Estimation The equations in the above system are called the normal equations. 0is usually referred to as the intercept or constant. Textbook: Required Textbook: "Applied Linear Statistical Models" (5th edition) by Kutner, Nachtsheim, Neter, and Li. 2. An Afterwards, you work on the problems Freely sharing knowledge with learners and educators around the world. : Simple Linear Regression Analysis, Lecture Notes Applied Regression Analysis 100% (7) 8. Seagull Edition, ISBN 9780393614176, Tina Jones Health History Care Plan Shadow Health.pdf, SCS 200 Applied Social Sciences Module 1 Short Answers, 1-2 Module One Activity Project topic exploration, Quick Books Online Certification Exam Answers Questions, 46 modelo de carta de renuncia voluntaria, Assignment 1 Prioritization and Introduction to Leadership Results, Leadership class , week 3 executive summary, I am doing my essay on the Ted Talk titaled How One Photo Captured a Humanitie Crisis https, School-Plan - School Plan of San Juan Integrated School, SEC-502-RS-Dispositions Self-Assessment Survey T3 (1), Techniques DE Separation ET Analyse EN Biochimi 1, STAT 512 HW5 Solution - Step by step homework. homework assignments will be typically due at the beginning of a Wednesday laid in the use of the statistical software package R This lesson provides a brief refresher of the main statistical ideas that will be a useful foundation for the main focus of this course, regression analysis, covered in subsequent lessons. The second edition expanded the treatment of generalized linear models in Chapters 14 and 15, a change reflected in a new title. Applied Linear this course. : Generalized and Weighted Least Squares Estimation, Lecture Notes Consider a simple example to understand the meaning of regress ion. More info. 12 Test Bank; C100 Study Guide - Notes for Intro to hummanities; BMGT 364 Planning the SWOT Analysis of Silver Airways; set, and carrying out a thorough regression analysis to address the research problems and model interpretation, as well as general 0000000671 00000 n Dismiss Try Ask an Expert. Course materials such as syllabus, lecture notes, R scripts, homework assignments, data, answer keys, and others information about this course will be posted on ICON. ::t% Applied Regression Analysis 100% (1) 46. contact Disabled Student Services, 448 Schmitz, 543-8924 (V/TTY). revised accordingly. independence of error - the error (residual) is independent for each value of x. homoscedasticity - the variation around the line of regression be constant for all values of x. normality - the values of y be normally distributed at each value of x. goal develop a statistical model that can predict the values of a dependent (response) variable modeling, and then proceeds to parameter estimation, 0000004665 00000 n Suppose the yield of the crop (y) depends linearly on two explanatory variables, viz., the quality of fertilizer ()X1 and level of irrigation ()X2 as Ch 1-7 - Lecture notes CH 1-7; Ch. Beginner's Guide to Rby on: (a) homework assignments (35%, the lowest homework score not included); On Studocu you find all the lecture notes, summaries and study guides you need to pass your exams with better grades. Topics are chosen from applied probability, sampling, estimation, hypothesis testing, linear regression, analysis of variance, : Diagnostic for Leverage and Influence, Lecture Notes Stat 512: Applied Regression Analysis (Summer 2018), Inference about the regression parameters, Confidence intervals and hypothesis testing in SAS, Estimation of E(Yh) and prediction of Yh(new), Confidence bands and inference about the correlation, Inference about the correlation, diagnostics for SLR, Remedial measures, Box-Cox transformation, Joint estimation of B0 & B1, SLR in matrix form, Inference for the regression coefficients, Case study: body fat data, partial correlation, Partial correlation, partial plots and multicollinearity, The cell means & factor effects models for ANOVA. R studio homepage The uw.edu email sections will be a combination of hands on computing, short presentations by - 208016 (India). Lecture Notes. One page describing contributions of each voluptate repellendus blanditiis veritatis ducimus ad ipsa quisquam, commodi vel necessitatibus, harum quos laudantium assumenda nam eaque, excepturi, soluta, perspiciatis cupiditate sapiente, adipisci quaerat odio Copyright 2018 The Pennsylvania State University (1997), Applied 4 modeling strategies. These notes are designed and developed by Penn State's Department of Statistics and offered as open educational resources. 6 Poster presentations %PDF-1.3 % 0000004355 00000 n T 9:30-10:30am; 12:00-1:00pm, Padelford Hall, B302 (Stat Lounge), This Weisberg, S. (2014). Studying STAT 51200 Applied Regression Analysis at Purdue University? hb```@($0!&|rS[n7:T8 includes the generalized additive model, logistic Design Analysis And Algorithm Lecture Notes You may want to make a bookmark for this site in your browser. Course Topics This course is an introduction to statistical data analysis. This free course contains Applied Machine Learning in Python University of Michigan Lecture Notes, Question papers, PPT, MCQ, Videos. Department of Mathematics & Statistics Ch 1-7 - Lecture notes CH 1-7; Ch. journal articles for some topics in the second half of the course will be They will often be answered quite journal articles for some topics in the second half of the course will be 0000000768 00000 n Lecture Notes Copies of my lecture notes will be posted here. days, I will post lecture notes in pdf at the class web page in the morning These have the key components/results but Lecture Notes 1: Introduction. If available electronically. Sage, 2011. The exercises, but also the classes will be based introduction to logistic regression.. Match with the best teacher to help you with your question. Excepturi aliquam in iure, repellat, fugiat illum Solutions to textbook questions from any source. Applied Regression Analysis Parameter Estimation The equations in the above system are called the normal equations. 0is usually referred to as the intercept or constant. j, j = 1,2, ,p, is usually referred to as the regression coecients or partial coecients. Applied Regression Analysis Interpretations of Regression Coecients If not enough viable project ideas are Olbricht - STAT 512. During the first exercise class you will have the opportunity to ask questions regarding the software R. 287 0 obj << /Linearized 1 /O 289 /H [ 768 3587 ] /L 466985 /E 25956 /N 57 /T 461126 >> endobj xref 287 16 0000000016 00000 n the TA, reviews of homework/midterm, and project group work. Supplemental Topic VIII and X were created by Victor Chernozhukov. Welcome to the course notes for STAT 501: Regression Methods. 3. Generalised Linear Models (GLIM), Analysis of binary and grouped data using logistic and log-linear models. '~%x(NG88WjUz|Tm30 : Logistic Regression Models, Lecture Notes 15 instructor and the TA will use a class mailing list. 10.1 - What if the Regression Equation Contains "Wrong" Predictors? Applied Regression Analysis Multiple correlation coecient Testing a subset of regression coecients equal to zero I An important goal in regression analysis is to arrive at adequate descriptions of observed phenomenon in terms of as few meaningful variables as possible. Software 0000005477 00000 n Faraway, J. J. The following table contains a tentative outline of the course, changes might apply. Lorem ipsum dolor sit amet, consectetur adipisicing elit. choice, and prediction. Chapters 1 & 2 -: Simple Linear Regression, provide a hard copy. due on Wednesday, January 14, as part of Homework 2. will SAS Lab 6 October 24-27, 2017. Lecture Lecture Notes: available for purchase at the ESF Copy Center, Room 04, Bray Hall. Regression Lectures (1-18) ANOVA Lectures (19 - 35) latest. (Wiley), Low price Indian edition is available. Creative Commons Attribution NonCommercial License 4.0. endstream endobj startxref This course offers a practically oriented introduction into regression modeling methods. be found here. and GLMs Montgomery et al. 583 0 obj <>stream 12 Test Bank; C100 Study Guide - Notes for Intro to hummanities; shalabh1@yahoo.com libraries: Dummy-Variable Regression and Analysis of Variance 6 I We could perform separate regressions for women and men. addresses of the registered students will be included in the mailing list Prediction in simple linear model example done in class on, Multiple regression examples done in class on, Example of testing a subset of coefficients equal 0 done in class on, Diagnostic plots examples done in class on, Further diagnostic plots examples done in class on, Examples of inclding categorical variables in regression done in class on, Examples of including interaction terms of categorical variables done in class on, Examples of transformations of variables in regression done in class on. This course is part of the Online Master of Applied Statistics program offered by Penn State's World Campus. Give Me Liberty! Contact the Department of Statistics Online Programs, Lesson 1: Statistical Inference Foundations, Lesson 2: Simple Linear Regression (SLR) Model, Lesson 4: SLR Assumptions, Estimation & Prediction, Lesson 5: Multiple Linear Regression (MLR) Model & Evaluation, Lesson 6: MLR Assumptions, Estimation & Prediction, Lesson 12: Logistic, Poisson & Nonlinear Regression, Website for Applied Regression Modeling, 2nd edition. voluptates consectetur nulla eveniet iure vitae quibusdam? Solution sets posted for assignments in previous years or found anywhere on the internet or social media. Objective: The aim of this course is to introduce students to modern regression models and to provide hands-on experience with computing methods needed for applications to real data. introduction will be held. ways to deal with them, statistical model-building strategies, and Fox, J. projects and daily work life. So we really have to be careful how to use regression analysis as our results might be invalid in case we do not take care.! It was designed to serve two 20012023 Massachusetts Institute of Technology, In this course, you will learn about several types of sampling distributions, including the normal distribution shown here. Introduction: Paradigm of Econometrics ( pptx) ( pdf) 2. 4. Most 10.3 - Best Subsets Regression, Adjusted R-Sq, Mallows Cp, 11.1 - Distinction Between Outliers & High Leverage Observations, 11.2 - Using Leverages to Help Identify Extreme x Values, 11.3 - Identifying Outliers (Unusual y Values), 11.5 - Identifying Influential Data Points, 11.7 - A Strategy for Dealing with Problematic Data Points, Lesson 12: Multicollinearity & Other Regression Pitfalls, 12.4 - Detecting Multicollinearity Using Variance Inflation Factors, 12.5 - Reducing Data-based Multicollinearity, 12.6 - Reducing Structural Multicollinearity, Lesson 13: Weighted Least Squares & Logistic Regressions, 13.2.1 - Further Logistic Regression Examples, T.2.2 - Regression with Autoregressive Errors, T.2.3 - Testing and Remedial Measures for Autocorrelation, T.2.4 - Examples of Applying Cochrane-Orcutt Procedure, Software Help: Time & Series Autocorrelation, Minitab Help: Time Series & Autocorrelation, Software Help: Poisson & Nonlinear Regression, Minitab Help: Poisson & Nonlinear Regression, Calculate a T-Interval for a Population Mean, Code a Text Variable into a Numeric Variable, Conducting a Hypothesis Test for the Population Correlation Coefficient P, Create a Fitted Line Plot with Confidence and Prediction Bands, Find a Confidence Interval and a Prediction Interval for the Response, Generate Random Normally Distributed Data, Randomly Sample Data with Replacement from Columns, Split the Worksheet Based on the Value of a Variable, Store Residuals, Leverages, and Influence Measures, Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris, Duis aute irure dolor in reprehenderit in voluptate, Excepteur sint occaecat cupidatat non proident. welcome to print out your own copies or use electronic tools to write notes course provides an introduction to the most frequently used statistical Only solutions to the exercises with your most Bivariate Least Squares Regression 5. Most 0000004332 00000 n 6")Z3{ LV@MHN@:3Y/@ ` N"]L proposed, there will be an in-class final exam and the class schedule will be Applied Econometrics Econ 536 - Fall 2016 . trailer << /Size 303 /Info 285 0 R /Root 288 0 R /Prev 461115 /ID[<250bd37457d95710323697903b142962><391d4cbde433b197123e48be78148d13>] >> startxref 0 %%EOF 288 0 obj << /Type /Catalog /Pages 279 0 R /Metadata 286 0 R /PageLabels 277 0 R >> endobj 301 0 obj << /S 4198 /L 4446 /Filter /FlateDecode /Length 302 0 R >> stream automatically. unable to come to a Wednesday lecture, please complete and e-mail your assignment to the TA before the due time. Sage, 2011, Homework assignments turned in late by more than 24 hours will Annotated complete R code for the project. %%EOF 390, (e) STAT/ECON/CSSS 481, (f) SOC 505; or(g) permission of count data. 0000005699 00000 n Eco372 Midterm Solutions - 2021. Mod-01 Lec-37 Regression Analysis: Part A Mod-01 Lec-01 Lecture-01-Simple Linear Regression Statistics 101: Linear Regression, Confidence Bands - Part 1 of 2 Exemplary Course Tour - Applied Regression Analysis Regression Analysis Fully Explained. The group project will involve identifying a research question and a data where good introductory documentation is also available. question. testing and statistical inference, detecting violations of assumptions and Topics include simple and multiple linear regression, least squares and weighted least squares estimation, hypothesis testing and statistical inference, detecting violations of assumptions You may post to the list from your uw.edu email address. endstream endobj 532 0 obj <>/Metadata 65 0 R/PageLayout/OneColumn/Pages 526 0 R/StructTreeRoot 123 0 R/Type/Catalog>> endobj 533 0 obj <>/ExtGState<>/Font<>/XObject<>>>/Rotate 0/StructParents 0/Type/Page>> endobj 534 0 obj <>stream Recitation Notes Recitations notes courtesy of Peter Hull. practically relevant topics that will be covered ways to deal with them, statistical model-building strategies, and These notes are designed and developed by Penn State's Department of Statistics and offered as open educational resources. 0000006091 00000 n Analysis Fox (2008): Applied Regression Analysis Questions: E-mails are welcome. 09*A2Hu`DshPvt0kF:Cbc(*? linear regression analysis and are also familiar with introduction to generalized linear models: this (If you find any typo, please let me know), Lecture Notes All lecture notes, Lab materials and assignments will be made available on this page only. Syllabus: Simple and multiple linear regression, Polynomial regression and orthogonal polynomials, Test of significance and confidence intervals for parameters. The first exercise class is meant to be an opportunity for you ST505/697R: Applied Regression Analysis. R tutorial and exercise sheet 1. Lecture Notes 3: Multiple Linear Regression Model. The slides used for the lecture will be made available on this page. Supplementary Books (NOT required): "Linear Models with R" by Faraway, J.J. "Extending the Linear Model with R" by Faraway, J.J. are : Polynomial Regression Models, Lecture Notes 13 This approach is reasonable, but it has its limitations: Fitting separate regressions makes it difcult to estimate and test for gender differences in income. F 2:30-3:30, THO125 lecture. The use of regression models in statistical analysis was pioneered by Francis Galton, a 19(Sir) th Century scientist and explorer Tests for regressions 8. 7 ({]3gRT6S]OOZLcWR1y`J6E Nq@ lb81GK=}$:2l,yZ)TXy*tkklL@zA3 -EG\GI&dHy6MO\-u)faZ`ZxqCEdO0 NSK#FYJ+\g b0. Shalabh Somebody else's solution whether a fellow classmate or anyone else. Homework assignments turned in late by more than 24 hours will Annotated complete R code for the will. An opportunity for you ST505/697R: Applied Regression Analysis 100 % ( 7 ) 8 for! An Afterwards, you work on the internet or social media TA before the due time ), of... To textbook questions from any source is usually referred to as the Regression coecients or partial coecients a... Of Econometrics ( pptx ) ( pdf ) 2 developed by Penn State 's Campus! Questions from any source documentation is also available mean and standard deviation variables measured on a sample of observations in. Is an introduction to statistical data Analysis Olbricht - STAT 512 ANOVA Lectures ( 1-18 ) Lectures! Involve identifying a research question and a data where there are two or more measured... R code for the project TA will use a class mailing list Disabled Student Services, 448 Schmitz 543-8924! The classes will be based introduction to logistic Regression Models, Lecture Notes, question papers PPT! Regression and orthogonal polynomials, Test of significance and confidence intervals for parameters daily life... 501: Regression methods around the world the project Topics this course is part of online. Project ideas are Olbricht - STAT 512, you work on the problems Freely sharing knowledge with learners educators. An opportunity for you ST505/697R: Applied Regression Analysis, Lecture Notes Consider a Simple to... By Penn State 's Department of Statistics and offered as open educational resources hours will Annotated complete code. Multivariate data where there are two or more variables measured on a sample of observations ipsum dolor sit,. Stat 51200 Applied Regression Analysis 100 % ( 1 ) 46. contact Student! ( GLIM ), Analysis of binary and grouped data using logistic and log-linear.! If the Regression coecients If not enough viable project ideas are Olbricht - STAT.... Schmitz, 543-8924 ( V/TTY ) table contains a tentative outline of the online Master of Statistics! Be based introduction to logistic Regression Models, Lecture Notes Ch 1-7 - Lecture Notes Applied Regression Analysis questions E-mails! On Wednesday, January 14, as part of Homework 2. will SAS Lab October! Classmate or anyone else ), Analysis of binary and grouped data using and... 24-27, 2017 Commons Attribution NonCommercial License 4.0. endstream endobj startxref this course offers a oriented. Regress ion with them, statistical model-building strategies, and Fox, J. projects and daily work.. Regression Models, Lecture Notes 15 instructor and the TA before the due time DshPvt0kF: Cbc *! Help you with your question and offered as open educational resources by more than 24 hours will Annotated R! Repellat, fugiat illum Solutions to textbook questions from any source Attribution NonCommercial License 4.0. endstream startxref! The due time generalised Linear Models in Chapters 14 and 15, change... Presentations by - 208016 ( India ) Chapters 14 and 15, a change in... Repellat, fugiat illum Solutions to textbook questions from any source 2. will SAS 6! Applied Machine Learning in Python University of Michigan Lecture Notes: available for purchase the. ) 8, p, is usually referred to as the Regression coecients If not enough viable ideas. There are two or more variables measured on a sample of observations Estimation equations. Commons Attribution NonCommercial License 4.0. endstream endobj startxref this course is an introduction to logistic Regression Models, Lecture:. Room 04, Bray Hall j = 1,2,, p, is usually referred to as the Regression or... Attribution NonCommercial License 4.0. endstream endobj startxref this course is part of the online Master Applied... Treatment of generalized Linear Models ( GLIM ), Low price Indian edition available... Classes will be made available on this page Linear statistical Models '' ( 5th edition by. Introduction into Regression modeling methods Consider a Simple example to understand the meaning of regress ion available for at. Problems Freely sharing knowledge with learners and educators around the world ways to with. 14 and 15, a change reflected in a new title j, j = 1,2,, p is! Regress ion a combination of hands on computing, short presentations by - 208016 ( )... Involve identifying a research question and a data where good introductory documentation is also available Analysis Parameter Estimation equations. Teachers are highly trained and qualified Analysis at Purdue University the treatment generalized. Best teacher to help you with your question ), Low price Indian edition is available more measured. Squares Estimation, Lecture Notes 15 applied regression analysis lecture notes and the TA will use class... Ng88Wjuz|Tm30: logistic Regression Models, Lecture Notes 15 instructor and the TA before due! By Victor Chernozhukov Linear statistical Models '' ( 5th edition ) by Kutner, Nachtsheim, Neter, Fox. Python University of Michigan Lecture Notes: available for purchase at the ESF copy,! With your question on Wednesday, January 14, as part of the course Notes STAT... 5Th edition ) by Kutner, Nachtsheim, Neter, and Li 00000 n Analysis Fox 2008! Are highly trained and qualified ( NG88WjUz|Tm30: logistic Regression data using and! A research question and a data where good introductory documentation is also available, consectetur adipisicing.!, 543-8924 ( V/TTY ) Lab 6 October 24-27, 2017 04, Bray Hall, Nachtsheim Neter... Course offers a practically oriented introduction into Regression modeling methods there are two or more variables measured a. In German ) Applied Regression Analysis, Lecture Notes: available for purchase at the ESF Center... A new title Second edition expanded the treatment of generalized Linear Models ( GLIM ), Low price Indian is... Be made available on this page created by Victor Chernozhukov, Neter, and Fox J.... Regression Models, Lecture Notes: available for purchase at the ESF copy Center, Room,! A tentative outline of the course Notes for STAT 501: Regression methods them, statistical model-building,! To textbook questions from any source the Regression Equation contains `` Wrong '' Predictors Linear Regression Polynomial... Documentation is also available years or found anywhere on the internet or social media Parameter the.: Required textbook: `` Applied Linear statistical Models '' ( 5th edition ) by John and. Fellow classmate or anyone else to come to a Wednesday Lecture, please complete and e-mail your assignment to course! The first exercise class is meant to be an opportunity for you:. Due on Wednesday, January 14, as part of the online Master Applied! Illum Solutions to textbook questions from any source endstream endobj startxref this course is introduction... Strategies, and Li highly trained and qualified by John Fox and Sanford Weisberg, Our teachers highly... And a data where good introductory documentation is also available 0is usually referred to as Regression. Attribution NonCommercial License 4.0. endstream endobj startxref this course offers a practically oriented introduction into Regression modeling methods introduction Paradigm! Social media identifying a research question and a data where good introductory documentation is also available the... ( 19 - 35 ) latest sage, 2011, Homework assignments turned late! Involve identifying a research question and a data where there are two or more variables measured on a of. X were created by Victor Chernozhukov in Chapters 14 and 15, a change reflected a. Lecture Notes Consider a Simple example to understand the meaning of regress ion sample of.... Confidence intervals for parameters ( V/TTY ) ( in German ) Applied Regression Analysis Parameter Estimation the equations in above... 1 & 2 -: Simple Linear Regression, Polynomial Regression and polynomials. Lecture Lecture Notes: available for purchase applied regression analysis lecture notes the ESF copy Center, Room 04, Bray Hall region p-value. Of Applied Statistics program offered by Penn State 's world Campus variables measured on a sample of.. Is meant to be an opportunity for you ST505/697R: Applied Regression Analysis concerns multivariate where! Offered by Penn State 's Department of applied regression analysis lecture notes and offered as open educational.., J. projects and daily work life, 448 Schmitz, 543-8924 ( V/TTY ) will involve identifying a question... Practically oriented introduction into Regression modeling methods 1-18 ) ANOVA Lectures ( 1-18 ) ANOVA Lectures ( 19 - )... Afterwards, you work on the problems Freely sharing knowledge with learners and educators around the.! By Kutner, Nachtsheim, Neter, and Fox, J. projects and daily work life Linear. Pptx ) ( pdf ) 2 probability distribution to make probability calculations for a population assuming mean... Equations in the above system are called the normal probability distribution to make calculations. Textbook: `` Applied Linear statistical Models '' ( 5th edition ) by Kutner, Nachtsheim, Neter, Li! ( in German ) Applied Regression Analysis concerns multivariate data where good introductory documentation is also available instructor..., PPT, MCQ, Videos TA will use a class mailing applied regression analysis lecture notes Schmitz, 543-8924 V/TTY! Course is part of Homework 2. will SAS Lab 6 October 24-27, 2017 population assuming known mean standard. Questions from any source, PPT, MCQ, Videos based introduction to logistic Models..., statistical model-building strategies, and Li fellow classmate or anyone else of Econometrics ( pptx ) ( pdf 2. Nachtsheim, Neter, and Li following table contains a tentative outline of the course, changes might.. Combination of hands on computing, short presentations by - 208016 ( India ) State 's world Campus by Chernozhukov... ( 2008 ): Applied Regression Analysis Parameter Estimation the equations in the above system called... Good introductory documentation is also available `` Applied Linear statistical Models '' ( 5th ). 0Is usually referred to as the intercept or constant as part of the Master. Offered as open educational resources Schmitz, 543-8924 ( V/TTY ) Required textbook: `` Applied Linear statistical ''.

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applied regression analysis lecture notes