# Questions tagged [sums-of-squares]

sum of squares plays an important role in statistical models based on the normal distribution, like ANOVA.

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### Cannot understand why total SS＝explained SS+unexplained SS

I cannot understand why total SS＝explained SS+unexplained SS because geometrically the sum of two small squares is not equal to a big square. I wish someone could explain that to me. Thank you.
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### Different results for type I and type II ANOVA

I am performing an ANOVA for a research question. I want to to test whether "Grade", "Nim" and "Tim" has a significant influence on "value". My question is ...
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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 $\|\mathbf{X}\|^2 = \sum_{i=1}^d ... • 111 1 vote 1 answer 409 views ### In a PCA setting, is there any relationship with the sum of squares of the scores (t1) with the eigenvalue of that principal component? When one computes the vector of scores (t1) using the principal component (p1) the data is being projected over the direction of biggest variation. One could measure the distance between the point ... • 65 3 votes 1 answer 397 views ### What is the lowest sum of squared errors (sse) of a dataset? Given$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$is the ... • 153 1 vote 0 answers 52 views ### How are terms in SS (corrected sum of squares) independent? What does the highlighted test mean? How are the terms not independent? Can someone elaborate in detail? 0 votes 1 answer 314 views ### Source for BIC with residual sum of squares? Wikipedia states that under certain circumstances,$\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. ... • 273 1 vote 1 answer 331 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 ... 0 votes 0 answers 77 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 ... • 67 3 votes 3 answers 2k 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 $$I \colon y_i=\... • 1,367 3 votes 2 answers 2k views ### Simplifying the Matrix Form of the Solution to Ridge Regression I'm trying to understand how to obtain the solution to an objective function by solving for the parameter vector \theta in ridge regression. I found an example here from Naomi which takes an example ... • 133 1 vote 0 answers 1k views ### What is the correct implementation of BIC with residual sum of squares? BIC is most often calculated by maximizing the log likelihood function. However, it is also possible to calculate BIC with residual sums of squares. This is pretty easy to find online and not an issue ... • 401 2 votes 0 answers 225 views ### Formula for type III sum of squares of the intercept term in linear multiple regression assume we have the regression model:$$Y = b_0 + b_1 x_1 + \dots + b_k x_k + \varepsilon $$I know the formulas for all type III sum of squares for the regression terms except the formula for SS of ... • 101 6 votes 2 answers 182 views ### Coefficient of determination relationship? R^2 = \frac{SSREG}{SSTOT} or R^2 = 1-\frac{SSRES}{SSTOT} If X is the predictor random variable for science SAT and Y is the predictor random variable science GPA given by equation$$\hat Y =... • 183 2 votes 1 answer 2k 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 ... • 85 0 votes 0 answers 794 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? • 1 2 votes 1 answer 249 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. ... 0 votes 1 answer 21k 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/... 0 votes 0 answers 84 views ### 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 ... • 109 2 votes 1 answer 743 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 ... • 171 4 votes 1 answer 5k 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 ... 1 vote 1 answer 473 views ### 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 (... • 698 3 votes 0 answers 194 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 ... • 723 2 votes 2 answers 2k 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 ...
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