Least-Squares Regression
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محتوا
- Linear Regression
- همبستگی
- 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.
نمونه ای از هدف های آموزشی
- 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 1.1.12
Teacher Tips
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راهنمای معلم مجموعه توصیه های تولید شده توسط گروه PHET به صورت pdf. ( PDF ). |
Video Primer
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Teacher-Submitted Activities
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نویسنده | سطح | نوع | Subject |
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| Preguntas de razonamiento para todas las simulaciones HTML5 |
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Diana López | پیش دانشگاهی 1 دبیرستان پیش دانشگاهی 2 سال تحصیلی دبستان راهنمایی |
کار در خانه Discuss |
شیمی نجوم فیزیک ریاضیات |
| Alignment of PhET sims with NGSS |
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Trish Loeblein | دبیرستان | سایر | فیزیک شیمی زیست شناسی علوم زمین |
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| How do PhET simulations fit in my middle school program? |
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Sarah Borenstein | راهنمایی | سایر | علوم زمین زیست شناسی شیمی فیزیک |
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| CCSS Math Alignment with Sims |
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Amanda McGarry | دبستان دبیرستان راهنمایی |
سایر | ریاضیات | |
| MS and HS TEK to Sim Alignment | Elyse Zimmer | راهنمایی دبیرستان |
سایر | زیست شناسی شیمی فیزیک |
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| PhET Simulations Aligned for AP Physics C | Roberta Tanner | دبیرستان | سایر | فیزیک | ||
| Understanding Line of best fit and Correlation Coefficient | Rebecca Battat | دبیرستان | Guided | ریاضیات | ||
| Data Detective | Kelly Findley, Mary Burr | راهنمایی | Guided | ریاضیات | ||
| Correlation vs Causation | Andy Braaten | دبیرستان پیش دانشگاهی 1 |
آزمایشگاه | ریاضیات |
| Windows 7+ | Mac OS 10.10+ | iPad and iPad Mini with iOS | Chromebook with Chrome OS |
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Microsoft Edge and Internet Explorer 11, latest version of Firefox, latest version of Chrome.
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Safari 9+, latest version of Firefox, latest version of Chrome.
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Latest version of Safari
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Latest version of Chrome
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| گروه طراحی | Third-party Libraries | با تشکر از |
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