Design of experiments | Least squares | Analysis of variance | Statistical hypothesis testing

Lack-of-fit sum of squares

In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well. The other component is the pure-error sum of squares. The pure-error sum of squares is the sum of squared deviations of each value of the dependent variable from the average value over all observations sharing its independent variable value(s). These are errors that could never be avoided by any predictive equation that assigned a predicted value for the dependent variable as a function of the value(s) of the independent variable(s). The remainder of the residual sum of squares is attributed to lack of fit of the model since it would be mathematically possible to eliminate these errors entirely. (Wikipedia).

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Lesson: Factoring a Sum or Difference of Cubes

This video verifies for factoring formulas and provides examples on how to factor a sum or difference of cubes. http://mathispower4u.com

From playlist Factoring a Sum or Difference of Cubes

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Factoring a Difference of Squares

This video explains how to factor a difference of squares. http://mathispower4u.yolasite.com/

From playlist Factoring Polynomials

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Determine a Line of Best Fit Using the Least-Squares Solution

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From playlist Least Squares Solutions

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Lecture 15: Response surface modeling and process optimization Instructor: Duane Boning, David Hardt View the complete course at: http://ocw.mit.edu/2-830JS08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 2.830J, Control of Manufacturing Processes S08

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Ex: Factor a Difference of Squares in the Form a^2 - x^2

This video provides an example of how to factor a binomial that is a difference of squares with the constant term first and the variable term second. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com

From playlist Factoring a Difference of Squares

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Method of Finite Differences - Formula for First n Squares

I created this video with the YouTube Video Editor (http://www.youtube.com/editor)

From playlist Proofs

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(New Version Available) Factoring a Sum or Difference of Cubes

New Version: https://youtu.be/pRgiZ9pLnOc The video explains how to fact polynomials in the form a^3 + b^3 and a^3 + b^3. http://mathispower4u.wordpress.com/

From playlist Factoring a Sum or Difference of Cubes

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From playlist Math Problems with Number 2023

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From playlist Probability, statistics, and stochastic processes

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Lec 13 | MIT 2.830J Control of Manufacturing Processes, S08

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From playlist MIT 2.830J, Control of Manufacturing Processes S08

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Nadav Cohen: "Implicit Regularization in Deep Learning: Lessons Learned from Matrix & Tensor Fac..."

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From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021

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Sum of cubes

In this video, I give an explicit formula for the sum of cubes, and I show in particular why it’s the square of the sum of integers. It is really clever and neat, enjoy! Sum of squares: https://youtu.be/gVMEtOXdhs8 Subscribe to my channel: https://youtu.be/c/drpeyam

From playlist Cool proofs

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From playlist Stanford CS229: Machine Learning Full Course taught by Andrew Ng | Autumn 2018

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Calculus 2: Polar Coordinates (19 of 38) Area Bounded by a Polar Curve

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From playlist CALCULUS 2 CH 10 POLAR COORDINATES

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Related pages

F-distribution | Analysis of variance | Statistics | Chi-squared distribution | Cumulative distribution function | Residual sum of squares | Null hypothesis | Noncentral chi-squared distribution | Independence (probability theory) | F-test | Least squares | Variance | Likelihood-ratio test | Goodness of fit | Replication (statistics) | Linear regression | Normal distribution | Degrees of freedom (statistics) | Expected value | Fraction of variance unexplained