Least-Squares Regression

Aceste simulări nu au fost încă traduse în limba română . Puteți accesa simularea, din meniul de mai jos, în limba engleză.

Least-Squares Regression Imagine  Descarcă  Include
  • Regresie liniară
  • Corelații
  • Reziduuri


  • Regresie liniară
  • Corelații
  • Reziduuri
  • Outlier
  • Data


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.

Studii de caz

  • 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

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.
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.
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.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
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.
Informally assess the fit of a function by plotting and analyzing residuals.
Fit a linear function for a scatter plot that suggests a linear association.
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Versiune 1.1.20

Sfaturi pentru profesori

Descarcă ghidul profesorului Ghidul profesorului conține un sumar al elementelor de control ale simulării, modelul ideal, perspective asupra gândirii elevilor ( PDF ).

Video Primer

Autentificare pentru a urmări video primer

Activități ale profesorilor

How do PhET simulations fit in my middle school program? This contribution was designed by PhET. Sarah Borenstein MS Other Chemistry
Earth Science
Middle School Math Sim Alignment This contribution was designed by PhET. Amanda McGarry MS Other Mathematics
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López MS
Other Mathematics
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) This contribution was designed by PhET. Diana López UG-Intro
Other Mathematics
Preguntas de razonamiento para todas las simulaciones HTML5 This contribution was designed by PhET. Diana López MS
MS and HS TEK to Sim Alignment Elyse Zimmer HS
Other Biology
Mapping of PhET and IBDP Physics Jaya Ramchandani HS Other Physics
PhET Simulations Aligned for AP Physics C Roberta Tanner HS Other Physics
Understanding Line of best fit and Correlation Coefficient Rebecca Battat HS Guided Mathematics
Data Detective Kelly Findley, Mary Burr MS Guided Mathematics
Correlation vs Causation Andy Braaten HS
Lab Mathematics
Correlación vs Causalidad Andy Braaten (traducción Mayra Tavares) UG-Intro
Lab Mathematics

Limba Download or Run Tips
Albanian All shqip Download Run now Regresioni i katrorëve më të vegjël
Arabic All العربية Download Run now انحدار المربعات الصغرى
Basque All Euskara Download Run now Karratu minimoen erregresioa
Bosnian All Bosanski Download Run now Regresija najmanjih kvadrata
Brazilian Portuguese All português (Brasil) Download Run now Regressão por Quadrados Mínimos
Chinese - Simplified All 中文 (中国) Download Run now 一次线性函数的拟合
Chinese - Traditional All 中文 (台灣) Download Run now Least-Squares Regression_最小平方法迴歸
Czech All čeština Download Run now Regrese metodou nejmenších čtverců
Danish All Dansk Download Run now Mindste kvadraters regression
Dutch All Nederlands Download Run now Kleinste kwadraten regressie
French All français Download Run now Régression des moindres carrés
German All Deutsch Download Run now Lineare Regression
Greek All Ελληνικά Download Run now Παλινδρόμηση ελάχιστων τετραγώνων
Hebrew All עברית Download Run now שיטת הריבועים הפחותים
Hungarian All magyar Download Run now Legkisebb négyzetek módszere
Irish All Gaeilge Download Run now Cúlchéimniú na nÍoschearnóg
Italian All italiano Download Run now Metodo dei minimi quadrati
Japanese All 日本語 Download Run now 最小二乗法
Kannada All Kannada Download Run now ಕನಿಷ್ಠ-ವರ್ಗಗಳ ಹಿಂಜರಿತ
Kazakh All Kazakh Download Run now Регрессия және ең кіші квадраттар әдісі
Korean All 한국어 Download Run now 최소자승회귀
Latvian All Latviešu Download Run now Mazāko kvadrātu metode
Mongolian All Монгол (Монгол) Download Run now Хамгийн бага Квадратын Регресс
Polish All polski Download Run now Regresja (najmniejsze kwadraty)
Russian All русский Download Run now Регрессия и метод наименьших квадратов
Serbian All Српски Download Run now Регресија најмањих квадрата
Spanish All español Download Run now Regresión de mínimos cuadrados  Descarcă ghidul profesorului
Spanish (Mexico) All español (México) Download Run now Regresión de mínimos cuadrados  Descarcă ghidul profesorului
Spanish (Peru) All español (Perú) Download Run now Regresión de Mínimos Cuadrados
Tamil All Tamil Download Run now குறைந்த-வர்க்க சார்புக் கணிப்பு
Uzbek All Uzbek Download Run now Eng kichik kvadratik regressiyasi
Vietnamese All Tiếng Việt Download Run now Hồi quy bình phương cực tiểu

HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems on modern web browsers. If you are experiencing issues using an HTML5 sim on a supported platform, please disable any browser extensions.

iOS 12+ Safari
iPad compatible sims

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

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

Windows Systems:
Microsoft Edge, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.13+, Safari 13+, latest version of Chrome.

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

Echipa de proiectare Alţi colaboratori Mulţumiri
  • 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