Least squares

Explained sum of squares

In statistics, the explained sum of squares (ESS), alternatively known as the model sum of squares or sum of squares due to regression (SSR – not to be confused with the residual sum of squares (RSS) or sum of squares of errors), is a quantity used in describing how well a model, often a regression model, represents the data being modelled. In particular, the explained sum of squares measures how much variation there is in the modelled values and this is compared to the total sum of squares (TSS), which measures how much variation there is in the observed data, and to the residual sum of squares, which measures the variation in the error between the observed data and modelled values. (Wikipedia).

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Sum of integers squared explained

Explanation on deriving the equation. In arithmetic, we often come across the sum of n natural numbers. Sum of squares refers to the sum of the squares of numbers. It is basically the addition of squared numbers. Support my channel with this special custom merch! https://www.etsy.com/list

From playlist Math formulas, proofs, ideas explained

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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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Number Theory | Sums of Squares Part 1.

This is the first in a series of videos where we establish which natural numbers are expressible as the sum of two squares. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Sums of Squares

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Number Theory | Sums of Squares Part 7.

Our final video in this series where we have examined which natural numbers are expressible as a sum of various numbers of square integers. Here we show that all natural numbers are expressible as a sum of four squares. http://www.michael-penn.net http://www.randolphcollege.edu/mathematic

From playlist Sums of Squares

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Number Theory | Sums of Squares Part 4

We provide a few examples of writing natural numbers as sums of two squares. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Sums of Squares

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Number Theory | Sums of Squares Part 5

We establish which natural numbers can be written as the sum of three squares. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Sums of Squares

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Sum of Squares (Total, Between, Within)

What is "sum of squares" in ANOVA? How to calculate SSW, SST, SSB. 0:00 Intro 0: 11 What is Total Sum of Squares? 0:51 TSS Example 1:25 What are SSW SSB? 1:49 How to Calculate SSW 3:11 How to Calculate SSB 3:54 How to Calculate TSS

From playlist ANOVA

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Number Theory | Sums of Squares Part 3

We classify which natural numbers are expressible as the sum of two squares. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Sums of Squares

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Linear Regression, Clearly Explained!!!

The concepts behind linear regression, fitting a line to data with least squares and R-squared, are pretty darn simple, so let's get down to it! NOTE: This StatQuest comes with a companion video for how to do linear regression in R: https://youtu.be/u1cc1r_Y7M0 You can also find example co

From playlist StatQuest

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Find a Partial Sum Using Summation Formula: Sum(5i^3-2i)

This video explains how to determine a partial sum given in sigma notation using summation formulas. http://mathispower4u.com

From playlist Series (Algebra)

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Linear Regression - r and r-squared

I recently uploaded 200 videos that are much more concise with excellent graphics. Click the link in the upper right-hand corner of this video. It will take you to my youtube channel where videos are arranged in playlists. In this older video: Must see video that explains r and r-squared

From playlist Unit 3: Linear and Non-Linear Regression

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The F ratio is a test of overall significance in a multivariate regression (FRM T2-20)

[here is my xls https://trtl.bz/2HC3OWN] The F ratio is given by (ESS/df)/(RSS/df) and can be used to test the significance of the overall regression; or the significance of the multiple R-squared. Discuss this video here in our forum: https://trtl.bz/2wcGpmS Subscribe here https://www.yo

From playlist Quantitative Analysis (FRM Topic 2)

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FRM: Coefficient of determination (r-squared)

In a linear regression, you often see the R-squared quoted. To explain the R-squared (coefficient of determination), I compare it to the standard error of estimate (a measure of the line's accuracy) and the correlation (the square root of the coefficient of determination). All three are me

From playlist Statistics: Linear regression

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Basic Excel Business Analytics #47: SST = SSR + SSE & R Squared & Standard Error of Estimate

Download files: https://people.highline.edu/mgirvin/AllClasses/348/348/AllFilesBI348Analytics.htm Learn: 1) (00:14) What we will do in this video: SST, SSR, SSE, R^2 and Standard Error 2) (00:44) What we did last video 3) (01:11) How do we think about “How good our Estimated Regression Li

From playlist Excel Business Analytics (Forecasting, Linear Programming, Simulation & more) Free Course at YouTube (75 Videos)

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Regression: Crash Course Statistics #32

Today we're going to introduce one of the most flexible statistical tools - the General Linear Model (or GLM). GLMs allow us to create many different models to help describe the world - you see them a lot in science, economics, and politics. Today we're going to build a hypothetical model

From playlist Statistics

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Excel 2010 Statistics 91: Linear Regression #5: Coefficient of Determination: Goodness of Fit

Download Excel File: https://people.highline.edu/mgirvin/AllClasses/210Excel2010/Content/Ch14/Busn210ch14.xlsx 1. Calculate Total Sum Of Squares (Total Y Deviations Squared) = SST = How well observations cluster around Y Bar (Y Mean Plotted Line) = Total squared deviations of y observed a

From playlist Excel 2010 Statistics Formulas Functions Charts PivotTables

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Regression: Excel's linest array function and its goodness-of-fit measures (FRM T2-19b)

[Here is my xls https://trtl.bz/2vmGHd2] Excel's linest array function returns the R^2, SER and F-ratio which are interrelated as goodness-of-fit measures. Discuss this video here in our forum: https://trtl.bz/30GUcQA Subscribe here https://www.youtube.com/c/bionicturtle?sub-confirmation=

From playlist Quantitative Analysis (FRM Topic 2)

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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

Related pages

Total sum of squares | Simple linear regression | Fraction of variance unexplained | Regression analysis | Ordinary least squares | Coefficient | Residual sum of squares | Statistics | Lack-of-fit sum of squares