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8 views

How are the between and within sum-of-squares matrices defined?

I was reading Tibishirani's paper, and on page 2 I came across the terms between and within sum-of-squares matrices. How are those matrices defined? Are they related to the Uncorrected Sums of Squares ...
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0answers
13 views

Distribution of Sum Square Total and Error in Textbook?

I'd like to check my understanding that there is an incorrect statement in my textbook. Then, I'd like to check my understanding on what is actually true. Montgomery's Design of Experiments textbook ...
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0answers
74 views

What is the difference between RSS and SSR?

According to this post in Wikipedia the residual sum of squares (RSS), the sum of squared residuals (SSR) and the sum of squared errors of prediction (SSE) are the same. So the RSS = SSR = SSE ...
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0answers
23 views

how to calculate adjusted sum squares for each predictor in a multiple linear regression model?

I don't understand why the sum of adjusted sum squares of each predictor(0.0979+9.08723=9.1851) don't equal the total regression sum of square(11.7778)? And I know how to calculate sum of adjusted ...
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0answers
11 views

SSCP vs correlation matrix [duplicate]

Lets say I have a matrix X, where each row is a subject and each column is a variable. I have a few questions about manipulating this matrix, and what the result is: If I calculate X'X, am I correct ...
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0answers
14 views

Testing the total impact of a predictor in a messy model

Suppose I have a regression model with several predictors ind interactions thereof. For concreteness, suppose we are studying a company's data on salaries and we have predictors ...
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0answers
170 views

adonis in vegan: order of variables or use of strata

I am using the adonis() function in in the vegan package to determine 1) if co-occurring host species vary in their microbial ...
1
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1answer
74 views

Distribution of sum of squares of normals that have mean zero but not variance one?

I am trying to find the distribution of a random variable that is calculated according to $Y:=\sum_{i=1}^n X_i^2$ where $X_i $ is distributed as $ \mathcal{N}(0,\sigma^2_i)$. Does there exist a ...
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0answers
14 views

Why in a multi-factorial ANOVA with a random variable, we use MSinteraction error term for independent variables instea of MSerror?

So can some one please explain this to me in simple language? I know that random variables introduce more uncertainty in our data, but that is perhaps not enough for an answer. Why do we specifically ...
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0answers
22 views

Calculating 'k' for k-Means and Expectation Maximization

This question inspired my question. I've read a lot of articles on the Internet, and it seems like most people use sums of squares to find 'k' for k-Means and they use BIC to find 'k' for Expectation ...
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0answers
24 views

Why sum of the squared distances and not sum of the absolute distances? [duplicate]

Probably an easy question to answer but why do we use the sum of the squared distances to calculate the variance and standard deviation and not the sum of the absolute distances? Here's an example: ...
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0answers
33 views

How to interpret a covariate in ANOVA and why are type II vs type III SS so different?

I am trying to understand the effect of a covariate (COVAR) in a linear mixed effects model with 2 categorical IVs (IV1, IV2). In order to illustrate where I am struggling, I had to paste the rather ...
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1answer
179 views

MSE and MSR in regression question

In a small-scale regression study, five observations on $Y$ were obtained corresponding to $X = 1,4,10, 11$, and $14$. Assume that $\sigma=0.6,B_0=5,B_1=3$ a. What are the expected values ...
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3answers
252 views

Do I have a justified reason to exclude a non-significant covariate from my ANCOVA? How interesting is unequal variance?

I am comparing glutamate concentrations across groups (2 groups). I planned on controlling for age and IQ, simply because this is what is always done in cognitive neuroscience. When doing this, age ...
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1answer
1k views

Multinomial Logistic Loss vs (Cross Entropy vs Square Error)

I observed that Caffe (a deep learning framework) used the Softmax Loss Layer SoftmaxWithLoss as output layer for most of the model samples. As far as I know, ...
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1answer
68 views

Manually calculating SS within for a one way ANOVA

Question Details: group 1 n= 30 M=78 SD=8 group 2 n=30 M=70 SD = 13 group 3 n=30 M=64 SD=13 I have to manually calculate a one way ANOVA summary table. I have been able to work out SS between ...
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2answers
742 views

K-means: Why minimizing WCSS is maximizing Distance between clusters?

From a conceptual and algorithmic standpoint, I understand how K-means works. However, from a mathematical standpoint, I don't understand why minimizing the WCSS (within-cluster sums of squares) will ...
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0answers
18 views

sadists package/ Sum of (non-central) chi-squares to a power

I try use "sadists" package in R to compute quantiles and probabilities on sum of non-central chi-squares distribution, but there are some issues in this package. I give an example: wts = ...
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1answer
50 views

How does ANCOVA increase the variance explained by the categorical predictor?

I'm reading Field (2013), in which there is an ANCOVA example with a categorical predictor Viagra, a continuous covariate, and a continuous outcome variable libido. I understand that in ANCOVA we ...
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2answers
202 views

Difference of two squared normal dependent variables

I need to find the distribution of the random variable $Z$ $Z = \frac{(X - \mu_0)^2}{\sigma_0^2} - \frac{(X - \mu_1)^2}{\sigma_1^2}$, where $X \sim \mathcal{N}(\mu_0, \sigma_0)$. We can find the ...
1
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1answer
395 views

A proof of total sum of squares being equal to within-cluster sum of squares and between cluster sum of squares? [duplicate]

In cluster analysis I have frequently encountered a statement that the total sum of squares $\sum\limits_{i = 1}^n {{{({x_i} - \overline x )}^2}} $ being equal to within-cluster sum of squares ...
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1answer
186 views

Mean squared error versus Least squared error, which one to compare datasets?

I have 3 datasets of the same system. But for the first one, I have 21 measurements. For the second and the third one I have only 9 measurements. Now I made a model using these 3 datasets (so 3 ...
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0answers
59 views

Type III SS, anova - comparison to residuals

Apologies if this topic seems to have been beaten to death, but I couldn't find an exact duplicate. Take this data in R: ...
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2answers
336 views

Mixed Model Type-III Sums of Squares- R vs SPSS

The age old question of comparing sums of squares (SS) between programs has reared its ugly head again. I am trying to replicate output in SPSS, that was computed using Type 3 Sums of Squares, in R. ...
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1answer
1k views

Why report r-squared in Instrumental Variables Estimation?

I mean the the R-squared calculated such as in $R^2=1-\frac{RSS}{TSS}$ when you use the $RSS$ from the original structural model and not recalculation that you should do in order to do an F test. With ...
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1answer
827 views

Why does adding more terms into a linear model always increase the r-squared value?

Many statistics textbooks state that adding more terms into a linear model always reduces the sum of squares and in turn increases the r-squared value. This has led to the use of the adjusted ...
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0answers
260 views

Regression sum of squares (SSR) when $\beta_0 = 0$ in multiple linear regression?

I hope this is not a duplicate but I cannot find the answer to this question. In a linear model $$Y_i = \beta_1 X_{i,1} + \dots + \beta_{p-1} X_{i,p-1} + \varepsilon_i, \qquad i = 1, \ldots, n$$ with ...
2
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1answer
234 views

Sum of Square decomposition

Question about the Total, Explained, and Residual Sum of Squares. I am in the simple linear regression model. Could you help me clarify why the residual sum of squares (SSE where E stands for errors) ...
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4answers
1k views

square things in statistics- generalized rationale [duplicate]

Why do you square things in stats? I have run across this a lot, in both data mining and statistics classes, but no one has ever been able to give me an answer. One specific example is when summing ...
0
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1answer
76 views

Vectorise Within-Groups Sum of Squares in R

I've got a multivariate dataset (p=2) that I'm trying to calculate the W matrix for use in canonical variates analysis If each $x_{kj}$ is the jth observational unit from the kth group, and ...
3
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1answer
581 views

R and JMP produce different regression results due to sum of squares calculation and other factors

I recently started transitioning from JMP to R and to get started, I've been trying to reproduce some of my old JMP results in R. However, when I run a multiple regression with one continuous variable ...
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1answer
2k views

Why does the SSR have 1 degree of freedom in simple linear regression?

I understand degrees of freedom as the number of things that can independently change. And typically, in coming up with the degrees of freedom, if you have n terms, then you just subtract out the ...
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1answer
39 views

ANOVA in R: How MSresiduals are estimated when using Error(interaction)?

I have checked the existing answers, but I found no answer to my question. It is about choosing the right ANOVA model in R and how the MSresiduals are estimated. I have an experiment with two ...
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1answer
403 views

Orthogonal contrasts for four levels - are Helmert contrasts orthogonal?

I am planning to do a 2-way mixed ANOVA with the within-subjects factor having four levels. Since the exact data do not matter, I hope to suffice by only providing a general question. On my ...
4
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1answer
120 views

Beginning anova in R: Phantom significance when testing for interaction terms

Suppose I create a dummy scenario as such: > A <- rnorm(10000) > B <- rnorm(10000) > C <- rnorm(10000) > Y <- A*B + rnorm(10000,sd=0.1) ...
4
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1answer
1k views

What exactly does a Type III test do?

I'm having trouble understanding what exactly Type III test statistic does. Here is what I got from my book: "Type III" tests test for the significance of each explanatory variable, under the ...
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1answer
202 views

Deriving Regression Sum of Squares (SSR)

In a simple linear regression $SSR = \sum(\hat{y} - \bar{y})^2$ $SSXY = \sum(x - \bar{x})(y-\bar{y})$ $SSX = \sum(x - \bar{x})^2$ $SSR$ can be computed by dividing $SSXY^2$ by $SSX$. Namely, $SSR ...
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0answers
349 views

choosing $β_0$ and $β_1$ to minimize the residual sum of squares

I'm reading a book called An Introduction to Statistical Learning: with Applications in R, and I have a question in regards to the material inside. I understand that we can find the residual sum of ...
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1answer
87 views

Partition of sums of squares (ANOVA)

Can anyone explain the theory (or the formula) about computing Sum Sq (bold highligh below) related to regression items? The Wikipedia link gives an introduction on how to calculate the total, model, ...
2
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0answers
104 views

How can I make 2-way ANOVA (Type I, II and III) with R?

I have the following data with factor 1 (A, B and C) and factor 2 (D and E): $$ \begin{array}{ccc} \hline & D & E\\ \hline A & 68 & 59\\ & 65 & 57\\ & 63 & 54\\ ...
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1answer
47 views

On the connection between SSE and absolute deviation from the centroids

Is there any connection between sum of squared error SSE and the absolute deviation from the centroids after clustering. More formally, I have clustered $T=\{x_i\}, i\in\{1,\ldots,n\}$ and the ...
1
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1answer
55 views

Squared sum of errors

Why does $\mbox{SST} = \mbox{SSR} + \mbox{SSE}$ hold? It is understandable that $\sqrt{\mbox{SST}} = \sqrt{\mbox{SSR}} + \sqrt{\mbox{SSE}}$ but how can $\mbox{SST} = \mbox{SSR} + \mbox{SSE}$ hold? ...
0
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1answer
267 views

First order condition of sum of squares with respect to variance of residuals

Consider the criterion function for ordinary least squares $$ S(b)=(Y-X'b)'(Y-X'b) $$ with Y, a matrix of dependent variables, and X, a matrix of explanatory variables. It is of course known that: ...
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0answers
150 views

What's an intuitive way to explain SS decomposition for a Mixed ANOVA with 1 B/S and 1 W/S variable?

For teaching I need to explain the following diagram to undergraduate students. The diagram is taken from the 7th Edition of Howell's "Statistical Methods for Psychology". The students are familiar ...
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1answer
704 views

Decomposing total sum of squares

Consider the general linear regression model: $$y_i = \beta_0 + \beta_1x_{i1} + \beta_2x_{i2} + \cdots + \beta_px_{ip} + \epsilon_i = \mathbf{x}_i^t \beta + \epsilon_i$$ where $\textbf{x}_i = ...
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1answer
114 views

Least Squares Fits to Experimental Data

My attempt at making sense of the problem: The problem provides us with the sum of squares (SS; I believe that's the $18.1$). We can use the SS along with the number of samples $(21)$ to get the ...
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1answer
5k views
1
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1answer
37 views

Regarding sum of squares two ways how are they connected

$$ \sum(X^2) - \frac{(\sum X)^2}{n} = \sum(X^2) - m\sum X $$ This was nicely derived in Sum of squares two ways, how are they connected? But why is the second term called the "correction term for the ...
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1answer
5k views

Calculating sum of squares between groups

I have carried out this ANOVA: ...
3
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0answers
265 views

Degrees of freedom in regression analysis

I'm studying regression analysis but I'm struggling with really understanding how degrees of freedom are calculated. For example, if we have the simple scenario where $Y_i=\beta_0+\beta_1 X_i + ...