Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Multiple Linear Regression, Lecture notes of Statistics

Georgia Institute of Technology - Main CampusStatistics

Concepts of Multiple Linear Regression.

Typology: Lecture notes

2024/2025

Uploaded on 06/26/2026

az-fin
az-fin 🇺🇸

7 documents

1 / 9

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Regression Analysis
Multiple Linear Regression
Nicoleta Serban, Ph.D.
Professor
Fundamentals, Objectives and Examples
School of Industrial and Systems Engineering
About This Lesson
Learning Objectives:
•Examine multiple regression
analysis with examples
•Explore the fundamentals and
objectives of multiple regression
analysis
pf3
pf4
pf5
pf8
pf9

Partial preview of the text

Download Multiple Linear Regression and more Lecture notes Statistics in PDF only on Docsity!

Regression Analysis

Multiple Linear Regression

Nicoleta Serban, Ph.D.

Professor

Fundamentals, Objectives and Examples

School of Industrial and Systems Engineering

About This Lesson

Learning Objectives:

  • Examine multiple regression analysis with examples
  • Explore the fundamentals and objectives of multiple regression analysis

The model parameters are: !!, !", … , !#, σ^2

  • Unknown regardless how much data are observed
  • Estimated given the model assumptions
  • Estimated based on data

Multiple Linear Regression: Model

Data : !!,!, … , !!,# , $! , … , !$,!, … , !$,# , $$ Model : $% = && + &!!%,! + &'!%,' + ⋯ + &#!%,# + )%, * = 1 , … , , Assumptions :

  • Linearity / Mean Zero Assumption : E()%) = 0
  • Constant Variance Assumption : Var()%) = σ^2
  • Independence Assumption : {)! ,…, )$} are independent random variables
  • )% ~ Normally distributed for confidence/prediction intervals, hypothesis testing Model in Matrix Form : Y = 9 : + ; Design Matrix 9 =

Response Y=

Error ; =

Coefficients : =

Multiple Linear Regression: Model (cont’d)

Data : !!,!, … , !!,# , $! , … , !$,!, … , !$,# , $$ Model : $% = && + &!!%,! + &'!%,' + ⋯ + &#!%,# + )%, * = 1 , … , ,

1 st^ Order Interaction Model: & = ($ + (%% + (&& + ('%& + + Model with Interactions: Response Surface 2 nd^ Order Interaction Model: & = ($ + (%% + (&& + ('%& + ((%^ &^ + ()&^ &^ + + Simple Linear Regression : Linear regression with one quantitative predicting variable ANOVA : Linear regression with one or more qualitative predicting variables Multiple Linear Regression : Multiple quantitative and qualitative predicting variables

Quantitative and Qualitative Variables

Multiple Linear Regression : Multiple quantitative/qualitative predicting variables x 1 quantitative x 2 qualitative with three levels: D 1 , D 2 , and D 3 dummy variables Model: > = :( + :)?) + :@) + :+@ + ; Intercept varies

If d 1 =0, d 2 =0: :( + :)?)
If d 1 =1, d 2 =0: (:(+:*) + :)?) Parallel regression lines
If d 1 =0, d 2 =1: (:(+:+) + :)?)

If x 1 x 2 interaction: Nonparallel regression lines

Quantitative and Qualitative Variables

Linear Regression: Example 1

Sales^?

Advertisement

The response variable is: Y = State average SAT score (verbal and quantitative combined) The predicting variables are: X 1 = % of total eligible high school seniors in the state who took the exam X 2 = Median income of families of test takers, in hundreds of dollars X 3 = Average number of years that test takers had in social sciences, natural sciences, and humanities X 4 = % of test takers who attended public schools X 5 = State expenditure on secondary schools, in hundreds of dollars per student X 6 = Median percentile of ranking of test takers within their secondary school classes

Linear Regression: Data Example 2

Linear Regression: Example 3

Bike sharing systems are of great interest due to their important role in traffic management. Dataset: Historical data for years 2011 - 2012 for the bike sharing system in Washington D.C.

  • Data source: UCI Machine Learning Repository
  • Data Size: 17380 observations with 17 attributes

The response variable is: Y = Hourly count rentals of bikes Qualitative predicting variables: X 1 = Day of the week X 2 = Month of the year X 3 = Hour of the day (ranging 0-23) X 4 = Year (2011, 2012) X 5 = Holiday Indicator X 6 = Weather condition (with four levels from good weather for level 1 to severe condition for level 4) Quantitative predicting variables: X 7 = Normalized temperature X 8 = Normalized humidity X 9 = Wind speed

Linear Regression: Example 3

Year: A quantitative or a qualitative predicting variable?

  • If observations are made over many years, then consider it to be quantitative
  • If observations are made over only a few years, then consider it to be qualitative

Linear Regression: Example 3

Qualitative predicting variables: X 1 = Day of the week X 2 = Month of the year X 3 = Hour of the day (ranging 0-23) X 4 = Year (2011, 2012) X 5 = Holiday Indicator X 6 = Weather condition (with four levels from good weather for level 1 to severe condition for level 4) Quantitative predicting variables: X 7 = Normalized temperature X 8 = Normalized humidity X 9 = Wind speed