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

Scatterplot Smoothing: A Statistical Method for Exploring Data with R, Study notes of Statistics

University of South Carolina (USC) - ColumbiaStatistics

An overview of scatterplot smoothing, a statistical method used for exploratory data analysis. Various versions of scatterplot smoothing, including robust and non-robust methods, and their applications. The document also discusses weighted least squares regression and local regression, which are related techniques. Based on the stat 517 course at the university of south carolina.

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

koofers-user-m96
koofers-user-m96 🇺🇸

10 documents

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
STAT 517: Scatterplot Smoothing Grego
Scatterplot Smoothing
•Scatterplot smoothing is an Exploratory Data Analysis method
•Multiple versions are available
–Robust methods (lowess–locally weighted scatterplot smoothing)
–Non-robust methods (loess–local regression–and scatter.smooth)
–loess is the most flexible; scatter.smooth is used primarily as a graph-
ing function
University of South Carolina Page 1
pf3
pf4
pf5

Partial preview of the text

Download Scatterplot Smoothing: A Statistical Method for Exploring Data with R and more Study notes Statistics in PDF only on Docsity!

Scatterplot Smoothing

  • Scatterplot smoothing is an Exploratory Data Analysis method
  • Multiple versions are available - Robust methods (lowess–locally weighted scatterplot smoothing) - Non-robust methods (loess–local regression–and scatter.smooth) - loess is the most flexible; scatter.smooth is used primarily as a graph- ing function

Scatterplot Smoothing Weighted Least Squares Regression

  • Simple linear regression estimates the slope and intercept of the line y = β 0 + β 1 x by minimizing the least squares function: Q = ∑n i= [yi − (β 0 + β 1 xi)] 2
  • Weighted least squares regression minimizes the weighted least squares function: Qw = ∑n i= wi [yi − (β 0 + β 1 xi)] 2
  • WLS is traditionally used to downweight observations with more variability

Scatterplot Smoothing Weight functions for Local Regression

  • We use a different prediction equation at each xi
  • These prediction equations give more weight to observations near xi
  • loess uses the tricubic function to weight each observation in the subset Si: w(x) = (1 − ‖x − xi‖/maxSi ‖x − xi‖) 3 ) 3 , ‖x − xi‖ < maxSi ‖x − xi‖

Scatterplot Smoothing loess in R

  • Important arguments include formula, span, degree
  • Model objects such as these have alot of attributes
  • Inference is possible, though simple concepts in linear regression, such as model df, are now more subtle
  • Use predict to overlay a smoothed line