COURSE SYLLABUS

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COURSE SYLLABUS

REGRESSION ANALYSIS

STAT 403

SEPTEMBER 2015 1436-1437

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1. Instructor Information

Name Dr. Bothinah Abdullah Altaf (primary) Office hours 11 -12.30 . M . W .

9.30-12.30 . M . W .

Office 3 – 111 , Bld 7

Contact number 6400000 Ext. 26953

Email [email protected]

web page http://baltaf.kau.edu.sa/

Section instructor Dr. Bothinah Abdullah Altaf Lab instructor Tahani Baseer - (office 3 -113)

Email: [email protected] Office hours:

2. Course Information

Course Name Course Code Course Number

Regression Analysis STAT 403

Lectures Time Lectures Venue Lab Time Lab Venue

.M.W. 12.30 -1.50 64 C – Bld 7 ….T 1-1.50 07N L03B

Pre Requisites Statistical Methods (STAT 302) Linear Algebra (MATH 241)

Teaching Method

The form of this course will mainly be lecturing with demonstration and explanation, solving problems, and discussion with conclusion.

Lab

The course lab work involves introduction on R, advance programming using R and the practical application of regression techniques for investigating the relationship between variables in different problems under study.

Learning Resources

Course Text book Kunter, Nachtsheim and Neter (2004) Applied linear regression models

Where to buy? Alshegrey libraray – Central library References Reading list Rawlings, Pantula and Dickey (1998) ‘Applied regression

analysis’ Second edition – online

Software - R

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3. Grading policy

Assessment Grade Date

First exam 17 % 24/12/1436

Second exam 17 % 27/1/1436

Final exam 35 % Week (17-18-19)

Assignments 6 % -

Quizzes 5 % -

Lab exam 20 % Week (16)

Exam 1/Exam 2

 There will be two in-class exams; each weighs 17% for a total of 34 % of your final grade.

 You cannot afford to miss any exam. No Make-up exams will be given to individual students. If necessary, a makeup missed exams- excused and properly documented-will be given in the last week of the semester and may be comprehensive, i.e. includes all of course materials.

Final

 The final exam (34%) will be cumulative and comprehensive. i.e. it will consist of parts covered in Exams 1 and 2 and materials since the last exam

 Exam dates are pre set so plan your schedule accordingly.

 During all exams, you need to bring your University ID card. Use of mobile phone will not be permitted during exams. Any attempt to cheat during exams will not be tolerated.

4. Course Description:

The course general aims are:

 To cover the concepts of simple and multiple linear regression techniques.

 To help student to be able to perform regression analysis and interpret the model.

 To assess the fit of a model to data, and make suggestions as to how to improve it if it is unsatisfactory.

 To develop the skills necessary for the students to apply and interpret regression models using R

Course Summary This course is designed to teach students the theory and practice of regression analysis, for both simple and multiple regression including some problem associated with linear models and remedial measures.

Details are available in the tentative course schedule

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5. Students’ Learning Outcomes

Chapter 1: Linear regression with one predictor variable

After careful study of this chapter, students should be able to:

1. Differentiate between functional and statistical relationship between variables.

2. Demonstrate knowledge of regression models and their uses.

3. Estimate and interpret the parameters of linear regression models, using method of least squares, when one predictor variable is used.

4. Predict the response variable using regression model when one predictor variable is used

Chapter 2: Inference in regression and correlation analysis

1. Draw up inference concerning regression parameters, 𝛽_𝑂and 𝛽₁, including interval estimation and tests.

2. Predict new observation

3. Analysis of variance approach to regression analysis.

4. General linear test approach 5. Calculate correlation coefficient.

Chapter 3: Diagnostics and remedial measures

1. Examine the aptness of regression model for the data using graphical methods and statistical tests.

2. Apply remedial techniques when the data are not in the accordance of the model.

Chapter 5: Matrix approach to simple linear regression analysis

1. Perform simple linear regression discussed in previous chapters using matrix algebra

2. Build the knowledge on how to use matrix algebra to perform multiple regression.

Chapter 6: Multiple regression I

1. Discuss the need for multiple regression.

2. Present the basic statistical result of multiple regression in matrix form.

3. Draw up inference concerning multiple regression parameters, 𝛽₁…,𝛽_𝑘

Chapter 7: Multiple regression II (selected topics)

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1. Discuss the problem when predictor variables are perfectly correlated.

2. Discuss the diagnostic of multicollinearity and its effect

Chapter 8: Regression models for quantitative and qualitative predictors (selected topics)

1. Perform and discuss the polynomial regression models for quantitative predictor variables.

2. Understand the case when qualitative predictor variables need to be considered in regression models.

3. Interpret the regression coefficients when qualitative predictors are considered.

Chapter 9: Building the regression model I: Model selection and validation (selected topics)

1. Select an appropriate regression model based of different criterions 2. Validate the regression model

Chapter 10: Building the regression model II: Diagnostics (selected topics)

1. Diagnose some problems associated with regression models including, outlying observations, influential observations and multicollineraity.

Chapter 11: Building the regression model III: Remedial Measures (selected topics)

1. Discuss a remedial measure used to deal with in appropriate regression models including the cases of multicollinearity and influential observation.

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6. Course Schedule (Tentative)

Week Lecture Reading materials (Chapter – Sections)

Class materials Assignments

Title

1

Lecture 1 9/11 Chapter 1 - Course syllabus & book guided tour Course information

1

Lecture 2 11/11 Chapter 1

1.1 1.2

Linear regression with one predictor variable

 Relation between variables

- Functional and statistical relationship

 Regression models and their uses - Historical origins & basic concepts - Construction of regression models - Uses of regression analysis - Regression and causality

Read Chapter1 (1.1-1.2)

2

1.3

1.4 1.5

 Simple linear regression model with distribution of error terms unspecified

- Formal statement of model - Important features of model - Meaning of regression parameters - Alternative versions of regression model

 Data for regression analysis

- Observational and experimental data

 Overview of steps in regression analysis

2

1.6

1.7

 Estimation of regression function - Method of Least Squares - Normal equations p (17)

- Estimation of regression parameters - Properties of fitted regression line

 Estimation of error terms variance

Read Chapter1 (1.6-1.7) ---

Problems 1.21,1.29,

1.30

3

2.1 2.2

Inference in regression and correlation analysis

 Inference concerning 𝛽₁

 Inference concerning 𝛽₀

3

Lecture 6 25/11 Chapter 2 2.4

2.5 2.7

 Interval estimation of 𝐸(𝑌_ℎ)

 Prediction of new observation

 Analysis of variance approach to regression analysis

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4

2.9

2.10

 General linear test approach

 Descriptive Measures of linear association between X and Y

- Coefficient of determination 𝑅² and its limitations - Coefficient of correlation

 Consideration in applying regression analysis

Read Chapter2 (2.8-2.10) Problems 2.7, 2.16

4 ^Lec

ture 8 3/12 Chapter 3

3.1 3.2

3.3

Diagnostic and remedial measures

 Diagnostics for predictor variables

 Residuals

- Properties of residuals - Semistudentized residuals

- Departure from model to be studied by residual

 Diagnostics for residuals

- Nonlinearity of regression function - Nonconstancy of error variance - Presence of outliers

- Nonindependence of error term

Read Chapter 3

(3.1-3.3)

Hajj break

5

3.3 con 3.4

- Nonnormality or error term

- Omission of important predictor variables - Some final comments

 Overview of tests involving residual - Test for randomness

- Test for constancy of variance - Test for outliers

- Test for normality

Read Chapter 3

(3.3-3.7) Problems 3.6, 3.10

3.14

6

3.7

3.8

 F test for lack of fit - Assumptions - Notation - Full model - Test statistics - ANOVA table

 Overview of remedial measures

6

Lecture 11 24/12

First exam

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7

5.9 5.10

5.11

 Simple linear regression in matrix terms

 Least square estimation of regression parameters - Normal equations

- Estimated regression coefficient.

 Fitted values and residuals - Fitted values

- Residuals

Read and revise linear

algebra 5.1-5.8 Read Chapter 5 (5.9-5.11)

7

5.12

5.13

 Analysis of variance results - Sum of squares

- Sum of squares as quadratic form

 Inference in regression analysis - Regression coefficient

- Mean response

- Prediction of new observation

Read Chapter 5 (5.12-5.13)

Problems 5.6, 5.7 5.25, 5.26

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Multiple linear regression

 Multiple Regression model

- Need for several predictor variables

- First order model with two predictor variables - First order model with more than two predictor variables

Read Chapter 6

(6.1)

8

6.3

 General linear regression model in matrix form

 Estimation of regression coefficient

Read Chapter 6

(6.2-6.3)

9

6.6  Inference about regression parameters - Interval estimation of 𝛽_𝐾

- Tests for 𝛽_𝐾 - Joint inferences

Read Chapter 6

(6.6) Problems 6.15, 6.16

6.17

9

Lecture 19 15/1

section

10

7.6 Multiple regression II

 Multicollinearity and its effect - Uncorrelated predictor variables

- Nature of problem when predictor variables are perfectly correlated.

-

Read Chapter 7

(7.6)

10 Lecture 21 22/1 Chapter 7 - Effect of multicollinearity

- Need for more powerful diagnostic for multicollinearity

Read Chapter 7

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11

Lecture 22 27/1 Second exam

11

8.1

Regression models for quantitative and qualitative predictors

 Polynomial regression models - Uses of polynomial models

- One predictor variable – second order - One predictor variable – third order - One predictor variable – higher order - Two predictor variables - second order - Three predictor variables – second order

Read Chapter 8

(8.1)

12

Lecture 24 4/2 Chapter 8 8.2 - Implementation of polynomial regression models - Some further comments on polynomial regression

 Interaction regression models - Interaction

Read Chapter 8

(8.2)

12

8.3  Qualitative predictors

- Qualitative predictor with two classes - Interpretation of regression coefficients

- Qualitative predictor with more than two predictors

Read Chapter 8

(8.2)

13

9.1

Building the regression model I: Model selection and validation

 Overview of model building process

Read Chapter 9

(9.1)

13

9.3

9.6

 Criteria for model selection - 𝑅_𝑃² or 𝑆𝑆𝐸_𝑝 criterion - 𝑅_𝑎,𝑃² or 𝑀𝑆𝐸_𝑝 criterion - Mallows’ criterion - 𝐴𝐼𝐶_𝑝 or 𝑆𝐵𝐶_𝑝 criteria - 𝑃𝑅𝐸𝑆𝑆_𝑃 criterion Model validation

Read Chapter 9

(9.3, 9.6) Problems

14

10.1 10.2

Building regression model II: Diagnostics (selected topics)

 Model adequacy for a predictor variables

 Identifying Outlying Y observations

Read Chapter 10 (10.1 – 10.2)

14 _Lec

ture 29 20/2 Chapter 10

10.3 10.4

 Identifying Outlying X observations

 Identifying influential cases

Read Chapter 10 (10.3 – 10.4)

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15

10.5  Multicollinearity diagnostics Read

Chapter 10 (10.5)

15

Lecture 31 27/2 Chapter 11 11.2 11.3

Building regression model III: Remedial Measures (selected topics)

 Multicolineraity Remedial measures –Ridge regression

 Remedial measures for influential cases –Robust regression

Read Chapter 11 (11.2 – 11.3)

16

Lecture 32 3/3

section

16

Lecture 33 5/3

Lab exam

Final exam Weeks(17-18-19)

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7. Attendance and Class Policy:

 Regression analysis is not an easy course and much of the material needs to be presented in different ways in order to make sense. It is especially important to master the material thoroughly at the start of the course. It is therefore very important that you attend classes regularly. (There is no grade for attendance).

 You are expected to attend the class from the beginning. It is your responsibility to make up for any missed materials or assignments.

 Please be considerate and put your mobile on silent or turn it off during class. No food is allowed during class. You may come late or leave early without disturbing your classmates. Any disturbance or distraction will not be tolerated.

 You’re expected to follow the University Dress Code, and staying in class with your Abaya on is not part of it. Your appearance in class speaks for your personality.

7. Student Responsibilities

The instructor is not responsible for the student’s learning: the student is. The instructor is responsible for facilitating the student’s learning by providing appropriate resources, managing the learning experience, providing the student with frequent feedback, and encouraging the student to reflect on and assess his or her own learning.

 Take an active role in learning the material. You will understand and remember the material best when you take notes, solve homework problems, quiz yourself, and ask questions.

 You are expected to participate in class.

 Learning requires a sufficient investment of time and effort.

 You are expected to attend all classes. Attendance does not directly affect your grade, although on the basis of past experience, it is the truly exceptional student who can afford to miss more than two or three classes.

 The correct way to study the material is to read the text before coming to class, listen carefully in class, follow the examples, take notes, ask questions, reread carefully the text at home, and finally, do the assigned homework and try to relate the information to your own experience and make up your own examples of the material.

 The resources available to students from the publisher are for you to use Good Luck

Dr. Bothinah Altaf