Least-Squares Regression

Ev şêwekar hêj ji bo vî zimanê nehatiye wergerandin. Dîsa jî hun dikarin guhertoya bi Îngilîzî ya li jêr bixebitînin.

Least-Squares Regression Wêneya Dîmenê  Daxîne  Çalkirin
  • Linear Regression
  • Correlation
  • Residuals

Naverok

  • 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.

Mînakên Armancên Fêrbûnê

  • 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

Di rêbera mamosteyan (pdf) de rêwazên aliyê koma PhET ve hatine afirandin hene. ( PDF ).

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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. This contribution was designed by PhET. Diana López MS
HS
UG-Adv
K-5
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Discuss
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Bîrkarî
Fîzîk
Kîmya
How do PhET simulations fit in my middle school program? This contribution was designed by PhET. Sarah Borenstein MS Yên din Fîzîk
Zindîwerzanî
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SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López MS
HS
Yên din Bîrkarî
Fîzîk
Zindîwerzanî
Kîmya
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) This contribution was designed by PhET. Diana López UG-Intro
HS
Yên din Bîrkarî
Kîmya
Fîzîk
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HS
Yên din Kîmya
Zindîwerzanî
Fîzîk
PhET Simulations Aligned for AP Physics C Roberta Tanner HS Yên din Fîzîk
Understanding Line of best fit and Correlation Coefficient Rebecca Battat HS Guided Bîrkarî
Data Detective Kelly Findley, Mary Burr MS Guided Bîrkarî
Correlation vs Causation Andy Braaten UG-Intro
HS
Ez.geh Bîrkarî

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