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11 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 ...
0
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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
8 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
44 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
47 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
11 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
20 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
30 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 ...
0
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1answer
131 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 ...
4
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3answers
219 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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0answers
572 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, ...
0
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1answer
56 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 ...
2
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2answers
477 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
12 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 = ...
0
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1answer
33 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 ...
3
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2answers
164 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 ...
0
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0answers
59 views

Relative Proportion of Variance for each Factor (ANOVA)

I'd like to calculate how much of the variance is related to each of the input factors. For example (in this case some R-code), if one wants to calculate how much of the "Magic Effect" of a magic ...
1
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1answer
268 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 ...
1
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1answer
104 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
56 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: ...
2
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2answers
276 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
691 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
427 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 ...
1
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0answers
180 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
176 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
972 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
53 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
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1answer
894 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
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1answer
35 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
363 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 ...
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1answer
573 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
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1answer
169 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
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0answers
202 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
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1answer
75 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
97 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
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1answer
41 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
222 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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1answer
587 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
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1answer
112 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 ...
2
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1answer
4k 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 ...
0
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1answer
4k views

Calculating sum of squares between groups

I have carried out this ANOVA: ...
3
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0answers
232 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
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0answers
28 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
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1answer
48 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, ...
2
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1answer
2k 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) ...
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2answers
1k 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 ...
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2answers
2k 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 ...