Newest 'sums-of-squares' Questions

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Fitting data to sums of squares of sinusoids

I am given some time series data $(t, y(t))$ sampled at regular intervals $t=0,s,2s,3s,\ldots,1$ for some step size $s$, obtained from a function $$ y(t) = y(t, \vec A, \vec \delta) = \sum_{i=1}^N ...

asked May 19 at 15:54

J Bausch

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Proof that more predictor variables will lead to less SSR [duplicate]

Say I have a multilinear model $y = X\beta - \varepsilon_1$, let's call this A. I also have another multilinear model $y = X_i\gamma - \varepsilon_2$, let's call this B. Where $X_i$ is a subset of $X$,...

regression multiple-regression sums-of-squares nested-models

asked Apr 28 at 7:41

Gerry

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Which type of sums of squares does lm-function in R use?

I ran a two-way ANCOVA in R: ancova = lm(DV ~ IV1*IV2 + CV1 + CV2 + CV3, data = Data) summary.aov(ancova) Anybody know if this uses type III sums of squares? I ...

r ancova function sums-of-squares

asked Apr 10 at 7:24

ge36fiy

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1answer

15 views

How unbalanced is unbalanced for factorial ANOVA?

Colleagues and I conducted an experiment with participants randomly allocated to each condition using survey software. Unfortunately, the cell sizes ended up being more unbalanced than we anticipated: ...

anova unbalanced-classes sums-of-squares

asked Feb 26 at 20:28

Gabriel

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234 views

Is least squares means (lsmeans) statistical nonsense?

I recently came accross this quote from Brian Ripley, who seems to be well-regarded as a statistician. "Some of us feel that type III sum of squares and so-called ls-means are statistical ...

regression anova sums-of-squares history lsmeans

asked Feb 23 at 17:09

Joe King

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1answer

81 views

Proof that Regression Sum of Squares and Residual Sum of Squares are independent random variables

Having consulted a number of sources, I still can't find a complete proof that Regression Sum of Squares ($SS_{regression}$) and ($SS_{residual}$) are independent random variables. I'll be doubly ...

regression anova sums-of-squares

asked Feb 19 at 4:46

ColorStatistics

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Shortcut for computing RSS at different split point when building regression trees?

I'm coding regression trees from scratch in R. For a given ordered predictor variable, $X$, obviously I have to compute the RSS at each unique ordered value of $X_i$. When moving over to the next ...

cart computational-statistics sums-of-squares

asked Jan 30 at 22:16

Matt B

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Oneway ANOVA Sums of square calculation questions

From reading this explanation (https://www.r-bloggers.com/2011/03/anova-%E2%80%93-type-iiiiii-ss-explained/) of typeI-III anova sums of squares(SS) i'm under the impression that for a oneway/one ...

anova sums-of-squares

asked Jan 19 at 17:05

Edy

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Why contrast in ANOVA has one degree of freedom?

I thought I understood the degree of freedom after reading Wikipedia explanation, but came across the sum of squares for contrasts $\{c_i\}$ $$SS_C = \frac{(\sum_i {c_i \bar{y_i}})^2}{\sum_i c_i^2 /...

anova degrees-of-freedom contrasts sums-of-squares

asked Jan 8 at 10:55

Tom

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Contrasts in ANOVA - need intuitions to understand its sum of squares and its degree of freedom

I have two questions about contrasts in ANOVA for testing the hypothesis that $\sum_i c_i y_i = 0$. How is the sum of squares for contrasts $\{c_i\}$, $SS_C = \frac{(\sum_i {c_i \bar{y_i}})^2}{\sum_i ...

anova degrees-of-freedom contrasts sums-of-squares

asked Nov 12 '20 at 14:33

Tom

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19 views

Distribution of the squared length of a multivariate normal vector [duplicate]

Let $\mathbf{X} \sim \mathcal{N}(\mathbf{\mu}, \mathbf{\Sigma})$ be a multivariate Normal variable with $d$ dimensions. I'm interested in the marginal distribution of $\|\mathbf{X}\|^2 = \sum_{i=1}^d ...

normal-distribution multivariate-analysis sums-of-squares norm

asked Oct 26 '20 at 13:18

macjan

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50 views

What exactly is explained sum of squares, and why do we focus on minimizing error rather than maximizing explained variability?

In the third of my questions about decomposing the total sum of squares, I want to focus on the sum of squares of the regression. I can make sense of what the sum of squares of the residuals means: ...

regression machine-learning least-squares error sums-of-squares

asked Sep 12 '20 at 20:41

Dave

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In a PCA setting, is there any relationship with the sum of squares of the scores (t1) with the eigenvalue of that principal component?

When one computes the vector of scores (t1) using the principal component (p1) the data is being projected over the direction of biggest variation. One could measure the distance between the point ...

pca sums-of-squares

asked Sep 10 '20 at 10:41

Ralphns

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1answer

61 views

What is the lowest sum of squared errors (sse) of a dataset?

Given $X \subset R^d$ a set of data points, $z \in R^d$ a vector, $SSE(X)=\sum_{i=1}^{|X|}||X_i-z||^2$, I wonder what is the best value of $z$ so that $SSE$ is the lowest? I suspect that $z$ is the ...

mathematical-statistics optimization least-squares k-means sums-of-squares

asked Sep 1 '20 at 15:31

curiosus

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How are terms in SS (corrected sum of squares) independent?

What does the highlighted test mean? How are the terms not independent? Can someone elaborate in detail?

experiment-design independence degrees-of-freedom sums-of-squares

asked May 8 '20 at 13:55

stockulum

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71 views

Source for BIC with residual sum of squares?

Wikipedia states that under certain circumstances, $\mathrm{BIC} $ can be calculated as: $$\mathrm{BIC} = n \ln(\mathrm{RSS}/n) + k \ln(n),$$ where $\mathrm{RSS}$ is the residual sum of squares. ...

residuals aic bic sums-of-squares

asked Mar 4 '20 at 19:02

Nos

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91 views

Kruskal–Wallis one-way analysis of variance is related to what kind of regression?

One-way anova is similar to regular linear regression because both use the F-test which involves sums of squares among other reasons. Is Kruskal–Wallis one-way analysis of variance similar to some ...

regression anova nonparametric kruskal-wallis-test sums-of-squares

asked Jan 20 '20 at 23:26

user271077

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63 views

Difficulty with averaging corrected sample variances of different degrees of freedom:

I have a number of measurement samples of which some have 2 measurements and some have 3. I wish to make the most accurate estimation of population variance I can, and understand that ignoring data ...

anova variance mse sums-of-squares bessels-correction

asked Nov 12 '19 at 3:16

MCC

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3answers

810 views

Residual sum of squares in a regression

I understand that in a linear regression model, the residual sum of squares will either remain same or fall with the addition of a new variable. What if the two models were $$ I \colon y_i=\...

regression residuals sums-of-squares

asked Oct 3 '19 at 9:42

Harry

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2answers

288 views

Simplifying the Matrix Form of the Solution to Ridge Regression

I'm trying to understand how to obtain the solution to an objective function by solving for the parameter vector $\theta$ in ridge regression. I found an example here from Naomi which takes an example ...

multiple-regression matrix ridge-regression sums-of-squares gradient

asked Sep 13 '19 at 20:11

theupandup

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What is the correct implementation of BIC with residual sum of squares?

BIC is most often calculated by maximizing the log likelihood function. However, it is also possible to calculate BIC with residual sums of squares. This is pretty easy to find online and not an issue ...

maximum-likelihood residuals aic bic sums-of-squares

asked Aug 23 '19 at 4:21

JElder

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156 views

Formula for type III sum of squares of the intercept term in linear multiple regression

assume we have the regression model: $$Y = b_0 + b_1 x_1 + \dots + b_k x_k + \varepsilon $$ I know the formulas for all type III sum of squares for the regression terms except the formula for SS of ...

regression anova multiple-regression intercept sums-of-squares

asked Aug 17 '19 at 18:12

Kourabi

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4

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2answers

128 views

Coefficient of determination relationship?

$R^2 = \frac{SSREG}{SSTOT}$ or $R^2 = 1-\frac{SSRES}{SSTOT}$ If $X$ is the predictor random variable for science SAT and $Y$ is the predictor random variable science GPA given by equation $$\hat Y =...

regression interpretation sums-of-squares

asked May 22 '19 at 23:26

Tree Garen

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1answer

746 views

Sum of Squared Error Chi-Square distribution degree of freedom in Multilinear Regression

In this link it says that $Y$ variables has zero covariance (because covariance matrix has only diagonal terms) which implies they are independent. Actually in linear regression $Y$ takes its ...

regression machine-learning multiple-regression chi-squared-distribution sums-of-squares

asked Mar 30 '19 at 11:41

mertcan

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494 views

What is the difference between the residual, lack of fit and pure error In F test for Regression Analysis?

What is the difference between the residual, lack of fit and pure error and how to calculate each of them in ANOVA F test for nonlinear regression?

regression anova f-test sums-of-squares

asked Feb 23 '19 at 23:17

Mohamed Abubakr

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1answer

109 views

Two way ANOVA, no difference between tests based on type I vs type II sums of squares

I'm learning about two way ANOVA possibly with interaction. I'm following this tutorial http://www.sthda.com/english/wiki/two-way-anova-test-in-r This is their code. ...

r hypothesis-testing anova sums-of-squares two-way

asked Dec 21 '18 at 3:48

user231906

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1answer

16k views

Calculating SSE in R

I'm following the "Intro to Statistics" course in Data Camp and I'm having some trouble as it seems that the course is contradicting itself: https://s3.amazonaws.com/assets.datacamp.com/production/...

r sums-of-squares

asked Dec 20 '18 at 6:18

René Martínez

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Why is regression line represented as $y = b0 + b1 * x$?

I am new to Data Science and ran into Regression Line formula which is $ y = b0 + b1 *x $ (where x is dependent variable, y is predicted variable) I understood the meaning of this formula as a ...

regression linear sums-of-squares

asked Dec 2 '18 at 17:40

Poream3387

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1answer

394 views

Better to Minimize Absolute Error or Sum of Squared Error?

I have an Excel model which predicts the number of customers for a given month. The prediction depends on a churn rate. I have the absolute error (actual vs predicted), along with squared error and ...

error sums-of-squares minimum-variance

asked Nov 28 '18 at 18:51

alexsmith2

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2k views

Why error sum of squares has n-2 df (possibly not duplicate, please read on)? (Regression Question Series - Part 4)

In simple linear regression, the error sum of squares is given by $$ \text{SSE} = \sum_{i=1}^n(y_i - \hat{y_i})^2 \\ \hat{\sigma}^2 = s^2 = \dfrac{\text{SSE}}{n-2} $$ where $n-2$ is the degrees of ...

regression error degrees-of-freedom chi-squared-distribution sums-of-squares

asked Nov 23 '18 at 12:29

Parthiban Rajendran

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Minimize Logged Sum of Squares?

When numerically maximizing the likelihood function it is standard practice to do this indirectly by minimizing the negative log-likelihood. When numerically minimizing the residual sum of squares (...

least-squares sums-of-squares

asked Nov 20 '18 at 12:28

Estacionario

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105 views

R: anova(lm): What is the Sum Sq when we have two inputs

What is the formula to calculate the Sum sq column for the inputs? Answers to some other questions state, that it should be $RSS = \sum (\hat Y_i -\bar Y)^2$, yet this is false, it only gives the ...

r regression anova linear-model sums-of-squares

asked Nov 15 '18 at 16:37

PascalIv

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2answers

1k views

Showing that $\sum_{i=1}^n (y_i-\hat{y_i})(\hat{y_i} - \bar{y}) = 0$ for the generalized linear model [closed]

Exercise : Prove that for the generalized linear model, it is : $$\sum_{i=1}^n (y_i-\hat{y_i})(\hat{y_i} - \bar{y}) = 0$$ Question : How would one proceed with proving that for the generalized ...

regression self-study generalized-linear-model linear sums-of-squares

asked Oct 30 '18 at 18:54

Rebellos

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1answer

53 views

Squaring floats between -1 and 1 reduces sum of squares, so why do it? [duplicate]

I have been learning basic statistical testing as it relates to agriculture and have become familiar with the common practice of summing squared raw deviation values, whether in something simple like ...

sums-of-squares arithmetic

asked Oct 19 '18 at 15:06

Dodge

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2answers

216 views

Calculating F-statistic, why is SS used instead of just $r^2$?

The calculations and question are for a simple regression (one independent and one dependent variable). SSres = SSy * (1 - $r^2$) SSreg = SSy * $r^2$ F = (SSreg / DFreg)/(SSres / DFres) So, I've ...

regression correlation sums-of-squares f-statistic

asked Oct 19 '18 at 1:57

PsyPhi

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1answer

420 views

Understanding ANOVA as regression / type III SS in R

I'm confused about how type III SS are calculated for a "main effect". According to what I have read, Type III SS is calculated by evaluating the change in the SSE by removing only the variable in ...

r anova sums-of-squares

asked Oct 12 '18 at 18:17

TeeVee

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1answer

1k views

2-way ANOVA in Python statsmodels yields different Sum of Squares than SPSS

I am learning to use Python for my statistical analyses, and while figuring out how to perform a 2-way ANOVA with statsmodels I found that my Python code yielded slightly aberrant values. Comparing ...

anova python spss sums-of-squares statsmodels

asked Sep 19 '18 at 22:55

user219200

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137 views

In regression, when partitioning SS among predictors, what determines which predictors get the SS that can be attributed to more than one predictor?

In regression analysis, predictors sometimes correlate (and in my field, psychology, they always do; often because they are simply measurements of the same aspects of human psychology). If predictors ...

regression linear-model regression-coefficients sums-of-squares

asked Jul 13 '18 at 10:06

Matherion

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2answers

1k views

How should Type II SS be calculated in a mixed model?

I have a data set (and corresponding mixed model) which gets very different p-values for one of the two-way interactions when tested using Type I (sequential, taking care that it's last), and Type II (...

r anova mixed-model sums-of-squares

asked Jun 12 '18 at 14:45

Aaron left Stack Overflow

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Deriving the F-test from ${{SSE_R-SSE_F}\over{(n-q)-(n-p)}}/{{SSE_F}\over{n-p}}$

Given a Full and Reduced model, the F-test to see if the reduced model is significant is given by $$ {{SSE_R-SSE_F}\over{(n-q)-(n-p)}}/{{SSE_F}\over{n-p}} $$ I'm trying to understand how this is ...

f-test sums-of-squares

asked May 19 '18 at 11:33

Frank Vel

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92 views

Find the Sum of Squares and using them complete an F-test for goodness of fit

I have this question ( would be grateful if someone could put it on for me) https://gyazo.com/5afe5d7c9d12acdff8f9c55db74f97c9 And I am concerned with part b). I know what $RSS = SSE$ is due to the ...

self-study statistical-significance anova sums-of-squares f-statistic

asked May 15 '18 at 11:36

user162934

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1answer

3k views

Which one to choose Type-I, Type-II, or Type-III ANOVA? [duplicate]

I don't understand what the difference is between TypeI and TypeIII? Since my background is not very mathematics, it's very difficult for me to understand this mathematical notation; Type I SS: SS(A) ...

r anova sums-of-squares tukey-hsd-test

asked May 11 '18 at 14:10

Kynda

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206 views

Does forward model selection by $R^2$ or SSR differ?

I'm trying to implement forward selection and need to add a feature only if it will make the sum of squared residuals (SSR) lower. I am using Python's statsmodels ...

multiple-regression python feature-selection r-squared sums-of-squares

asked May 3 '18 at 4:03

user2584325

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68 views

The Sums of squares in 3 way Anova in R output has changed as the order of the variables in the modes changes [duplicate]

I am trying to fit a 3 way ANOVA using R. Then i realized the sums of squares of the output has changed when the order of the variables in the model are changed.Can anyone figure out the reason for ...

r anova sums-of-squares

asked Mar 28 '18 at 1:34

Sam88

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votes

2answers

331 views

Mixed-effect model single term deletion — should I change my random effects?

In short I recently had a little conversation on the lme4 project's GitHub on how to properly test the significance of effects in a mixed-effect model, which made ...

anova mixed-model model-comparison sums-of-squares

asked Mar 27 '18 at 12:03

Arthur Spoon

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0answers

242 views

Test significance using Type II ANOVA following Type III ANOVA?

I hope you can help me with a theoretical question about how to proceed in my analysis. I have come across many posts discussing differences between Type II and III SS Anovas, however, because I don't ...

anova interaction glmm sums-of-squares

asked Mar 22 '18 at 16:19

Is_S

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115 views

Trying to understand hierarchical testing of nested regression models

I've learned multiple regression, but never did I learn hierarchical regression (i.e., the hierarchical testing of nested regression models) before. Based on the image attached, I assume because the ...

hypothesis-testing multiple-regression sums-of-squares

asked Feb 24 '18 at 0:11

user196525

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1answer

1k views

In regression analysis, How can R^2 represent the total explained variance, if it can be computed from an equation with only unique contributions?

Background In regression analysis, $R^2$, the squared multiple correlation, represents the proportion of explained variance by the regression model. Most software's default setting uses Type-III sums ...

multiple-regression linear-model sums-of-squares

asked Jan 17 '18 at 16:29

Matherion

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votes

1answer

3k views

Is Square Root of the Variance of a Regression Coefficient the Standard Error?

Quick question, in the textbook "Introductory Econometrics", the variance of a Regression Coefficient is given as: $var(\hat\beta_j) = \frac{\sigma^2}{SST_j(1-R_j^2)}$ where, $SST_j$= $\sum_{i=1}^n (...

regression multiple-regression regression-coefficients r-squared sums-of-squares

asked Jan 8 '18 at 4:23

ricksanchez

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2answers

242 views

Why do type III sums of squares require orthogonal contrasts?

I have read many times that one has to set orthogonal contrast to get correct type III sums of square. E.g. John Fox says To compute Type-III tests using incremental F-tests, one needs contrasts ...

anova multiple-regression intuition contrasts sums-of-squares

asked Dec 9 '17 at 12:47

statmerkur

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