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2
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4answers
64 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
votes
1answer
20 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 ...
4
votes
1answer
70 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 ...
0
votes
1answer
26 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 ...
1
vote
1answer
80 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 ...
3
votes
1answer
60 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 ...
1
vote
1answer
68 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 ...
1
vote
0answers
64 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 ...
1
vote
0answers
43 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
votes
0answers
58 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\\ ...
1
vote
1answer
27 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
vote
1answer
44 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
votes
1answer
97 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: ...
1
vote
1answer
119 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
vote
1answer
101 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 ...
1
vote
1answer
1k views
1
vote
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 ...
0
votes
1answer
959 views

Calculating sum of squares between groups

I have carried out this ANOVA: ...
3
votes
0answers
87 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 + ...
1
vote
0answers
25 views

Reading and interpreting the scatter matrix [duplicate]

The scatter matrix is defined as $$S = \sum_{j=1}^n (\mathbf{x}_j-\overline{\mathbf{x}})(\mathbf{x}_j-\overline{\mathbf{x}})^T$$ The trace (sum of the diagonal elements) of this matrix is ...
0
votes
1answer
40 views

Sum of squares proof where $N=n_{UC}+n_{TX}$

$TX$ is variable that indicates treatment status ($TX=1$ if the patient gets the new treatment, and $0$ otherwise, and $UC = 1 - TX$ indicates they got the standard treatment). Of $N$ patients, ...
0
votes
1answer
502 views

SSB - Sum of squares between clusters

I got a little confused with the squares and the sums. As far as I know, the variance or total sum of squares (TSS) is smth like $\sum_{i}^{n} (x_i - \bar x)^2$ and the sum of squares within (SSW) ...
1
vote
2answers
464 views

Sum of squared difference and Gaussian noise model

I have been reading that when the underlying error is distributed normally, then minimising the sum of squared difference between the observed data and the model is the appropriate cost function to do ...
8
votes
2answers
1k views

Distribution of sum of squares of T-distributed random variables

I am looking at the distribution of the sum of squares of T-distributed random variables, with tail exponent $\alpha$. Where X is the r.v., the Fourier transform for $X^2$, $\mathscr{F}(t)$ gives me a ...
1
vote
0answers
120 views

Explain the difference between type 1,2,3,4 sums of squares

Can someone explain the difference between type 1:4 sums of squares using examples with relatable variables?
1
vote
0answers
509 views

Total Sum of Squares (TSS) - Exponential Regression

The total sum of squares is expressed as below [1][2], \begin{align} \rm{TSS} &= MSS + ESS \end{align} \begin{align} \sum_{i=1}^n (y_{i}-\overline{y})^2 &= \sum_{i=1}^n ...
3
votes
1answer
202 views

Does the standard error in OLS not need to be corrected by n?

The standard error of an estimator is defined as the square root of the the estimator variance (or mean squared error, MSE, for unbiased estimators). More specifically, if we wanted to get the ...
0
votes
0answers
128 views

Sum of residuals squared

How can I write the sum of squared residuals as a function of the sample mean and variance of $y$, given that the regression equation is: $y = \beta_0 + \beta_1(x-\bar{x}) + \epsilon$ where ...
5
votes
2answers
5k views

Why do we use a one-tailed test [F-test] in analysis of variance (ANOVA)?

Can you give the reason for using a one tailed test in the analysis of variance test? Why do we use a one-tail test - the F-test - in ANOVA?
0
votes
1answer
106 views

Partitioned sum of squares

I'm trying to calculate partitioned sum of squares in a linear regression. In the first model, there are two predictors. In the second model, one of these predictors in removed. In the model with two ...
0
votes
1answer
242 views

ANOVA sum of squares between groups

I'm trying to get an intuitive understanding of why the sum of squares between groups needs to be multiplied by the number of observations within each group. Using the ...
2
votes
1answer
71 views

Looking for simple examples of how to calculate type III and type IV SS

I have data collected on five species of fish at half a dozen locations in a lake over four years. The categories are not (at all) fully crossed, and I have a lot of empty cells due to logistical ...
9
votes
3answers
4k views

Choice between Type-I, Type-II, or Type-III ANOVA

We have a dataset with three variables (dV: self-reported measure on scale 1-5, assumed to be metric; iV1: factor with 4 levels; iV2: factor with 8 levels). We are interested whether the dV differs in ...
1
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0answers
76 views

Are the sequential sum of squares appropriate when treatments must be applied in sequence?

I'm working with some modeled future stream flow data that was created in two steps. First, future precipitation predictions (at certain points in a watershed) were created by running historical ...
1
vote
2answers
1k views

Why is the k-means algorithm minimizing the within cluster variance?

I have read that the k-means algorithm tries to minimize the within cluster sum of squares (or variance). With some brainstorming, a question popped up. Why is it that k-means or any other clustering ...
1
vote
0answers
100 views

How to Partition An Interaction SS in ANOVA

I'm a new user of R and I'm trying to replicate Table 6.18 on page 262 in Statistical Procedures in Agricultural Research, By K. A. Gomez and A. A. Gomez. New York, Chichester, etc.: Wiley (1984). ...
8
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1answer
411 views

Type III sums of squares

I have a linear regression model with one categorical variable $A$ (male & female) and one continuous variable $B$. I set up contrasts codes in R with ...
6
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1answer
2k views

R, Differences between lm and aov

What does explain the differences in p.values in the following aov and lm ? Is the difference only due to different types of Sum of square calculations ? ...
3
votes
1answer
178 views

Assessing quality of clusters

I am running into problem of assessing the quality of clusters. In my case, I have plotted the data after determining data classes. For each class (1, 2, 3) there are two clouds that appear separately ...
3
votes
1answer
116 views

Monette & Fox's conditional hypotheses

G. Monette and J. Fox provide in these slides a framework for the Type II Analysis of Variance/Deviance tests in terms of conditional hypothesis. My questions are: In this frequentist approach, the ...
3
votes
2answers
405 views

Which are the correct sum of squares for repeated measures ? (balanced example)

Below are three ways to fit a MANOVA model in R and to extract ANOVA tables from the fitted model. The design is balanced. All methods give different results. The data are 5 groups of 4 individuals ...
1
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0answers
79 views

Type I ANOVA tests not depending on the order of the factors

I have a dataset with two factors A and B and the following design (contigency table showing the number of individuals for each ...
2
votes
0answers
230 views

Expectation of Sums of Squares

$\mu$=mean, $\sigma$=standard dev show that if $H_0:\mu_1=...=\mu_k$ in the normal one way classification then the Total Sum of Squares has expectation $E(T)=(N-1)\sigma^2$ the Within Groups Mean ...
1
vote
1answer
491 views

Comparison of k-means clustering output

I am trying to compare the outputs of k-means algorithm coded by me and the outputs of R's kmeans. Since the objective of the algorithm is to minimize the total ...
1
vote
1answer
328 views

Significance of the component in a multivariate linear model (“within-design”)

I'm trying to test the significance of the "component" effect in a multivariate regression model. I'm not sure what is the right way. Using R, I have tried a way with ...
1
vote
0answers
103 views

Different Mean Square partitions in an unbalanced bifactorial ANOVA (with random factor) between R and Statistica

I am trying to extract variance components for selection and chance in a bifactorial design with Generation as a fixed factor and Replicate as a random term, for early fecundity. Since I am using ...
2
votes
0answers
217 views

Sum of Squares reduction test: Convergence criteria met, but not all parameters of the model estimated

Background: I am using weighted non-linear regression to model the growth of plant organs, with dummy variables for different species. I am using a sum of squares reduction test (SSRT) to compare the ...
1
vote
1answer
5k views

How to calculate sum of squared errors (SSE or SSR) with Stata 12 software?

I have a techincal issue with Stata: I need to calculate the SSE of a regression model, but the automatic output just gives me RMSE; I need SSE of this constrained model because I have to test if this ...
1
vote
1answer
769 views

Unique variance with regression analysis

I have some questions about unique variance and hope some of you can help. For instance, let say I have 3 predictors and 1 dependent variable (DV). I ran a regression analysis with a sequence of 3 ...
0
votes
0answers
19 views

How do I get the SSE for predictions using SAS? [duplicate]

Possible Duplicate: How to get SSE for predictions using SAS? I'm trying to get the sum of squared errors for my predictions in SAS, but I'm not sure I'm doing it correctly. I'm not sure ...