# Least-Squares Regression_最小平方法迴歸

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### 標題

• Linear Regression
• 關聯
• Residuals
• Outlier
• Data

### 描述

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.

HTML5 版本之翻譯：

### 學習目標

• 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.

### 標準對齊

#### 共用核心 - 數學

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.

### 教學提示

 模擬教學的控制概觀、模型簡化與引導學生思考 ( PDF ).

### 老師提供的活動

Preguntas de razonamiento para todas las simulaciones HTML5 Diana López 國中
K-5

SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López 國中

PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López 大學-簡介

How do PhET simulations fit in my middle school program? Sarah Borenstein 國中 其它 地球科學

Middle School Math Sim Alignment Amanda McGarry 國中 其它 數學
Mapping of PhET and IBDP Physics Jaya Ramchandani 高中 其它 物理
MS and HS TEK to Sim Alignment Elyse Zimmer 國中

PhET Simulations Aligned for AP Physics C Roberta Tanner 高中 其它 物理
Understanding Line of best fit and Correlation Coefficient Rebecca Battat 高中 指引 數學
Data Detective Kelly Findley, Mary Burr 國中 指引 數學
Correlation vs Causation Andy Braaten 高中

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

iOS 12+ Safari

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

Chromebook:
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:

Macintosh Systems:

Linux Systems:

• 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