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43 views

### Calculate interaction sum of squares by hand

I'm trying to manually calculate the sums of squares (SSs) in a two-way ANOVA in Python. However, I cannot seem to get the correct result for the interaction SS. I'm using the ...
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### regression sum of squares in multiple linear regression

I'm looking for some help with the following practice question for an upcoming midterm:
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### Will Tukey multiple comparison be the same for different types of Sum Of Squares of ANOVA for an unbalanced design

I am working on Two-Way ANOVA for an unbalanced design. Will Tukey multiple comparison be the same for different types (I, II & III) of Sum Of Squares of ANOVA for an unbalanced design. I am ...
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### ANOVA analysis in regression

I have an issue regarding ANOVA analysis. Let me explain what I am looking for…You have 3 factors (A,B,C). Now in CCD or BBD you get ANOVA for ...
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### 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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### Distribution of Sum Square Total — Is there an error in my 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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### 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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### 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 sum ...
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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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 off ...
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### 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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### 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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### 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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### 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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### 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 = c(0.5000,...
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### 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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### 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 ...
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### 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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### 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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### 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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### 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 ...
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### 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) ...
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### 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 ...
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, $SSR =... 0answers 385 views ### choosing$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 ... 1answer 95 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, ... 0answers 108 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): $$\begin{array}{ccc} \hline & D & E\\ \hline A & 68 & 59\\ & 65 & 57\\ & 63 & 54\\ &... 1answer 47 views ### On the connection between SSE and absolute deviation from the centroids Is there any connection between sum of squared error SSE and the absolute deviation from the centroids after clustering. More formally, I have clustered T=\{x_i\}, i\in\{1,\ldots,n\} and the ... 1answer 55 views ### Squared sum of errors Why does \mbox{SST} = \mbox{SSR} + \mbox{SSE} hold? It is understandable that \sqrt{\mbox{SST}} = \sqrt{\mbox{SSR}} + \sqrt{\mbox{SSE}} but how can \mbox{SST} = \mbox{SSR} + \mbox{SSE} hold? ... 1answer 274 views ### First order condition of sum of squares with respect to variance of residuals Consider the criterion function for ordinary least squares$$ S(b)=(Y-X'b)'(Y-X'b) $$with Y, a matrix of dependent variables, and X, a matrix of explanatory variables. It is of course known that:$$... 0answers 151 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 ... 1answer 736 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 = (1,x_{...
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 ...