# Least-Squares Regression

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Use this HTML code to display a screenshot with the words "Click to Run". Linear Regression هاوگری Residuals PhET پشتیوانی ئه بێ له لایه ن و فێرکارانێ وه ک ئێوه.

### ناوه‌ڕۆک

• Linear Regression
• هاوگری
• 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.

### Sample Learning Goals

• 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 1.1.20

### Teacher Tips

 Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

### Teacher-Submitted Activities

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

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Design Team Third-party Libraries سوپاس بۆ
• Martin Veillette (developer)
• Patricia Loeblein
• Ariel Paul
• Kathy Perkins
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• FileSaver-b8054a2.js
• fontawesome-webfont-3.0.2.svg
• jama-1.0.2
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