Least-Squares Regression

See simulatsioon pole veel sellesse keelde tõlgitud. Ingliskeelne versioon on saadaval allpool.

Least-Squares Regression Ekraanipilt  Lae alla  Manusta
  • Linear Regression
  • Correlation
  • Residuals

Sisu

  • Linear Regression
  • Correlation
  • Residuals
  • Outlier
  • Data

Description

Create your own scatter plot or use real-world data and try to fit a line to it! Explore how individual data points affect the correlation coefficient and best-fit line.

Näidis-õpieesmärgid

  • Interpret r (the correlation coefficient) as data points are added, moved, or removed.
  • Interpret the sum of the squared residuals while manually fitting a line.
  • Interpret the sum of the squared residuals of a best-fit line as a data point is added, moved, or removed.
  • Compare the sum of the squared residuals between a manually fitted line and the best-fit line.
  • Determine if a linear fit is appropriate.

Standards Alignment

Common Core - Math

8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
8.SP.A.2
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
HSS-ID.B.6
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
HSS-ID.B.6a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
HSS-ID.B.6b
Informally assess the fit of a function by plotting and analyzing residuals.
HSS-ID.B.6c
Fit a linear function for a scatter plot that suggests a linear association.
HSS-ID.C.8
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Version 1.1.17

Teacher Tips

Õpetajate juhend (pdf) sisaldab PhETi poolt loodud nõuandeid. ( PDF ).

Video Primer

Please sign in to watch the video primer

Teacher-Submitted Activities

Preguntas de razonamiento para todas las simulaciones HTML5 A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Selle kaastöö koostas PhET. Diana López K-5
ÜÕ-Sissejuhatus
L
ÜÕ-Kõrgem tase
PK
KK
Discuss
KT
Keemia
Füüsika
Matemaatika
Astronoomia
Alignment of PhET sims with NGSS Selle kaastöö koostas PhET. Trish Loeblein KK Muu Füüsika
Maateadus
Keemia
Bioloogia
How do PhET simulations fit in my middle school program? Selle kaastöö koostas PhET. Sarah Borenstein PK Muu Bioloogia
Keemia
Füüsika
Maateadus
CCSS Math Alignment with Sims Selle kaastöö koostas PhET. Amanda McGarry K-5
PK
KK
Muu Matemaatika
Mapping of PhET and IBDP Physics Jaya Ramchandani KK Muu Füüsika
MS and HS TEK to Sim Alignment Elyse Zimmer PK
KK
Muu Füüsika
Keemia
Bioloogia
PhET Simulations Aligned for AP Physics C Roberta Tanner KK Muu Füüsika
Understanding Line of best fit and Correlation Coefficient Rebecca Battat KK Guided Matemaatika
Data Detective Kelly Findley, Mary Burr PK Guided Matemaatika
Correlation vs Causation Andy Braaten KK
ÜÕ-Sissejuhatus
Pr Matemaatika

Keel Download or Run Tips
araabia All العربية Download Run now انحدار المربعات الصغرى
baski All Basque Download Run now Karratu minimoen erregresioa
bosnia All Bosanski Download Run now Regresija najmanjih kvadrata
heebrea All עברית Download Run now שיטת הריבועים הפחותים
hiina (lihtsustatud) All 中文 (中国) Download Run now 一次线性函数的拟合
hiina (trad.) All 中文 (台灣) Download Run now Least-Squares Regression_最小平方法迴歸
hispaania All español Download Run now Regresión de mínimos cuadrados 
hispaania (Peruu) All español (Perú) Download Run now Regresión de Mínimos Cuadrados
hollandi All Nederlands Download Run now Kleinste kwadraten regressie
iiri All Gaeilge Download Run now Cúlchéimniú na nÍoschearnóg
itaalia All italiano Download Run now Metodo dei minimi quadrati
kannada All Kannada Download Run now ಕನಿಷ್ಠ-ವರ್ಗಗಳ ಹಿಂಜರಿತ
kasahhi All Kazakh Download Run now Регрессия және ең кіші квадраттар әдісі
korea All 한국어 Download Run now 최소자승회귀
kreeka All Ελληνικά Download Run now Παλινδρόμηση ελάχιστων τετραγώνων
läti All Latviešu Download Run now Vismazāko kvadrātu metode
mongoli All Монгол (Монгол) Download Run now Хамгийн бага Квадратын Регресс
poola All polski Download Run now Regresja (najmniejsze kwadraty)
portugali (Brasiilia) All português (Brasil) Download Run now Regressão por Quadrados Mínimos
prantsuse All français Download Run now Régression des moindres carrés
saksa All Deutsch Download Run now Lineare Regression
serbia All Српски Download Run now Регресија најмањих квадрата
Spanish (Mexico) All español (México) Download Run now Regresión de mínimos cuadrados 
taani All Dansk Download Run now Mindste kvadraters regression
tamili All Tamil Download Run now குறைந்த-வர்க்க சார்புக் கணிப்பு
tšehhi All čeština Download Run now Regrese metodou nejmenších čtverců
ungari All magyar Download Run now Legkisebb négyzetek módszere
vene All русский Download Run now Регрессия и метод наименьших квадратов
vietnami All Tiếng Việt Download Run now Hồi quy bình phương cực tiểu

The new HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iPad:
iOS 11+ Safari
iPad compatible sims

Android:
Not officially supported. If you are using the HTML5 sims on Android, we recommend using the latest version of Google Chrome.

Chromebook:
Latest version of Google Chrome
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:
Microsoft Edge and Internet Explorer 11, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.9.5+, Safari 9+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.

Kujundajad Kolmandate osapoolte materjalid Täname
  • Amanda McGarry (lead)
  • Martin Veillette (developer)
  • Patricia Loeblein
  • Ariel Paul
  • Kathy Perkins
  • almond-0.2.9.js
  • easing-equations-r12
  • FileSaver-b8054a2.js
  • fontawesome-webfont-3.0.2.svg
  • jama-1.0.2
  • jquery-2.1.0.js
  • lodash-2.4.1.js
  • pegjs-0.7.0.js
  • seedrandom-2.4.2.js
  • text-2.0.12.js
  • Tween-r12.js