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# Sum-squared Error

may be challenged and removed. (April 2013) (Learn how and when to remove this template message) In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of sum of squared errors calculator the squares of residuals (deviations predicted from actual empirical values of data). It is a measure

## Sum Of Squared Errors Example

of the discrepancy between the data and an estimation model. A small RSS indicates a tight fit of the model to the data. It sum of squared errors excel is used as an optimality criterion in parameter selection and model selection. In general, total sum of squares = explained sum of squares + residual sum of squares. For a proof of this in the multivariate ordinary least squares total sum of squares (OLS) case, see partitioning in the general OLS model. Contents 1 One explanatory variable 2 Matrix expression for the OLS residual sum of squares 3 See also 4 References One explanatory variable In a model with a single explanatory variable, RSS is given by: R S S = ∑ i = 1 n ( y i − f ( x i ) ) 2 , {\displaystyle RSS=\sum _{i=1}^{n}(y_{i}-f(x_{i}))^{2},} where yi is the i th value of the variable

## Regression Sum Of Squares

to be predicted, xi is the i th value of the explanatory variable, and f ( x i ) {\displaystyle f(x_{i})} is the predicted value of yi (also termed y i ^ {\displaystyle {\hat {y_{i}}}} ). In a standard linear simple regression model, y i = a + b x i + ε i {\displaystyle y_{i}=a+bx_{i}+\varepsilon _{i}\,} , where a and b are coefficients, y and x are the regressand and the regressor, respectively, and ε is the error term. The sum of squares of residuals is the sum of squares of estimates of εi; that is R S S = ∑ i = 1 n ( ε i ) 2 = ∑ i = 1 n ( y i − ( α + β x i ) ) 2 , {\displaystyle RSS=\sum _{i=1}^{n}(\varepsilon _{i})^{2}=\sum _{i=1}^{n}(y_{i}-(\alpha +\beta x_{i}))^{2},} where α {\displaystyle \alpha } is the estimated value of the constant term a {\displaystyle a} and β {\displaystyle \beta } is the estimated value of the slope coefficient b. Matrix expression for the OLS residual sum of squares The general regression model with n observations and k explanators, the first of which is a constant unit vector whose coefficient is the regression intercept, is y = X β + e {\displaystyle y=X\beta +e} where y is an n × 1 vector of dependent variable observations, each column of the n × k matrix X i

be equal to 0. The formula for SSE is: 1. Where n is the number of observations xi is the value residual sum of squares formula of the ith observation and 0 is the mean of all the observations. sum of squared residuals calculator This can also be rearranged to be written as seen in J.H. Ward's paper. 2. At each stage of cluster

## Sum Of Squared Residuals Formula

analysis the total SSE is minimized with SSEtotal = SSE1 + SSE2 + SSE3 + SSE4 .... + SSEn. At the initial stage when each case is its own cluster this of https://en.wikipedia.org/wiki/Residual_sum_of_squares course will be 0. You can stop reading right here if you are not interested in the mathematical treatment of this in Ward's method. It's really not important in getting Ward's method to work in SPSS. Used in Ward's Method of clustering in the first stage of clustering only the first 2 cells clustered together would increase SSEtotal. For cells described by more than 1 variable https://hlab.stanford.edu/brian/error_sum_of_squares.html this gets a little hairy to figure out, it's a good thing we have computer programs to do this for us. If you are interested in trying to make your own program to perform this procedure I've scoured the internet to find a nice procedure to figure this out. The best I could do is this: when a new cluster is formed, say between clusters i & j the new distance between this cluster and another cluster (k) can be calculated using this formula: 3. dk.ij = {(ck + ci)dki + (cj + ck)djk − ckdij}/(ck + ci + cj). Where dk.ij = the new distance between clusters, ci,j,k = the number of cells in cluster i, j or k; dki = the distance between cluster k and i at the previous stage. Back at the first stage (the zeroth stage being individual cells) this means that the two closest cells in terms of (usually) squared Euclidean distance will be combined. The SSE will be determined by first calculating the mean for each variable in the new cluster (consisting of 2 cells). The means of each of the variables is the new cluster cente

is uncorrected sum of squares?What is sum of squares? The sum of squares represents a measure of variation or deviation from the mean. It is calculated as http://support.minitab.com/en-us/minitab/17/topic-library/modeling-statistics/anova/anova-statistics/understanding-sums-of-squares/ a summation of the squares of the differences from the mean. The calculation of the total sum of squares considers both the sum of squares from the factors and from http://www.spiderfinancial.com/support/documentation/numxl/reference-manual/descriptive-stats/sse randomness or error. Sum of squares in ANOVA In analysis of variance (ANOVA), the total sum of squares helps express the total variation that can be attributed to various sum of factors. For example, you do an experiment to test the effectiveness of three laundry detergents. The total sum of squares = treatment sum of squares (SST) + sum of squares of the residual error (SSE) The treatment sum of squares is the variation attributed to, or in this case between, the laundry detergents. The sum of squares of sum of squared the residual error is the variation attributed to the error. Converting the sum of squares into mean squares by dividing by the degrees of freedom lets you compare these ratios and determine whether there is a significant difference due to detergent. The larger this ratio is, the more the treatments affect the outcome. Sum of squares in regression In regression, the total sum of squares helps express the total variation of the y's. For example, you collect data to determine a model explaining overall sales as a function of your advertising budget. The total sum of squares = regression sum of squares (SSR) + sum of squares of the residual error (SSE) The regression sum of squares is the variation attributed to the relationship between the x's and y's, or in this case between the advertising budget and your sales. The sum of squares of the residual error is the variation attributed to the error. By comparing the regression sum of squares to the total sum of squares, you determine the proportion of th

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Phone: +1 (888) 427-9486+1 (312) 257-3777 Contact Us Home >> Support >> Documentation >> NumXL >> Reference Manual >> Descriptive Stats >> SSE SSE Calculates the sum of the squared errors of the prediction function. Syntax SSEi(X, Y) X is the original (eventual outcomes) time series sample data (a one dimensional array of cells (e.g. rows or columns)). Y is the forecasted time series data (a one dimensional array of cells (e.g. rows or columns)). Remarks The time series is homogeneous or equally spaced. The two time series must be identical in size. A missing value (e.g. or ) in either time series will exclude the data point from the SSE. The sum of the squared errors, , is defined as follows:

Where: is the actual observations time series is the estimated or forecasted time series Examples Example 1: A B C 1 Date Series1 Series2 2 1/1/2008 #N/A -2.61 3 1/2/2008 -2.83 -0.28 4 1/3/2008 -0.95 -0.90 5 1/4/2008 -0.88 -1.72 6 1/5/2008 1.21 1.92 7 1/6/2008 -1.67 -0.17 8 1/7/2008 0.83 -0.04 9 1/8/2008 -0.27 1.63 10 1/9/2008 1.36 -0.12 11 1/10/2008 -0.34 0.14 12 1/11/2008 0.48 -1.96 13 1/12/2008 -2.83 1.30 14 1/13/2008 -0.95 -2.51 15 1/14/2008 -0.88 -0.93 16 1/15/2008 1.21 0.39 17 1/16/2008 -1.67 -0.06 18 1/17/2008 -2.99 -1.29 19 1/18/2008 1.24 1.41 20 1/19/2008 0.64 2.37 Formula Description (Result) =SSE($B$1:$B1$9,$C$1:$C$19) SSE (51.375) Files Examples References Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740 Related Links Wikipedia - Residuals sum of squares‹ SAEupHistogram Analysis › Reference SAE MAPE RMSE RMSD Download Sites - NumXL Try our full-featured product free for 14 days

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Residual Squared Error p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of residual sum of squares formula squared residuals SSR or the sum of squared errors of prediction SSE sum of squared residuals calculator is the sum of the squares of residuals deviations predicted from actual empirical values of data It is a p Total Sum Of Squares p measure of the discrepancy between the data and an estimation model A small RSS indicates a tight fit of the

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Residual Sum Of Squares And Standard Error Of Regression p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the sum of squared errors of prediction SSE is the sum of residual standard error definition the squares of residuals deviations predicted from actual empirical values of data It is a measure residual sum of squares formula of the discrepancy between the data and an estimation model A small RSS indicates a tight fit of the model

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Residuals Squared Error p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the sum of squared errors of prediction SSE p Sum Of Squared Errors Formula p is the sum of the squares of residuals deviations predicted from actual empirical values of residual sum of squares data It is a measure of the discrepancy between the data and an estimation model A small RSS indicates a tight fit p Regression Sum Of Squares p of

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Sse Sum Of Squares Due To Error p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the sum of squared errors of prediction SSE is the sum of the squares of residuals deviations predicted from actual sum of squares error formula empirical values of data It is a measure of the discrepancy between the data and an estimation sum of squares error calculator model A small RSS indicates a tight fit of the model to

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Ss Error p be equal to The formula for SSE is Where n is the number of observations xi is the value of the error sum of squares ith observation and is the mean of all the observations This can also p Ss Error Formula p be rearranged to be written as seen in J H Ward's paper At each stage of cluster analysis the total sum of squares error calculator SSE is minimized with SSEtotal SSE SSE SSE SSE SSEn At the initial stage when each case is its own cluster this of course will be You p Sum

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Sse Error Sum Squared p be equal to The formula for SSE is Where n is the number of observations xi is the value of the ith observation and is the mean of all the observations This can also be rearranged to be sum of squared errors formula written as seen in J H Ward's paper At each stage of cluster analysis the total SSE p Sum Of Squares Error Calculator p is minimized with SSEtotal SSE SSE SSE SSE SSEn At the initial stage when each case is its own cluster sum of squared errors example this of course

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Standard Error Residual Sum Of Squares p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of p Calculate Residual Sum Of Squares In R p squared residuals SSR or the sum of squared errors of prediction SSE is residual mean square error the sum of the squares of residuals deviations predicted from actual empirical values of data It is a measure p Residual Sum Of Squares Formula p of the discrepancy between the data and an estimation model A small

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Sum Of Error Squares Classifier p problem of predicting a real-valued function from training examples Then we consider the discrete case of classification Linear regression is the problem of fitting a linear function to a set of input-output pairs given a set of training examples p Least Squares Classification Example p in which the input and output features are numeric Suppose the input features linear classification are X Xn A linear function of these features is a function of the form fw X Xn w w X wn p Svm Classifier p Xn where w lang w w wn rang

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Sum Of Squares Error Definition p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the sum of squared errors of prediction SSE is sum of squared errors formula the sum of the squares of residuals deviations predicted from actual empirical values of data sum of squares error calculator It is a measure of the discrepancy between the data and an estimation model A small RSS indicates a tight fit of the sum of squared errors

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Sum Of Squared Error p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the sum of squared errors of prediction sum of squares error calculator SSE is the sum of the squares of residuals deviations predicted from actual empirical values p Sum Of Squared Errors Example p of data It is a measure of the discrepancy between the data and an estimation model A small RSS indicates a tight sum of squared errors excel fit

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Sum Of Square Error p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the p Sum Of Squares Error Calculator p sum of squared errors of prediction SSE is the sum of the squares of sum of squared errors example residuals deviations predicted from actual empirical values of data It is a measure of the discrepancy between the data and sum of squared errors excel an estimation model A small RSS indicates a tight fit

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Sum Of Squares Error Formula p be equal to The formula for SSE is Where n is the number of observations xi is the value of the ith observation and is the mean of all the observations This can also be rearranged to sum of squared errors example be written as seen in J H Ward's paper At each stage of cluster analysis the total sum of squared errors excel SSE is minimized with SSEtotal SSE SSE SSE SSE SSEn At the initial stage when each case is its sst formula own cluster this of course will be You can

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Sum Of Squared Relative Error p be evaluated and compared Root Mean Squared Error RMSE is a popular sum of squares error formula formula to measure the error rate of a regression model residual sum of squares formula However it can only be compared between models whose errors are measured in the same units regression sum of squares Relative Squared Error Unlike RMSE the relative squared error RSE can be compared between models whose errors are measured in the different units Mean Absolute total sum of squares Error The mean absolute error MAE has the same unit as the original

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Sum Of Squares Of Error p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the sum of squared errors of prediction SSE is the sum of the squares of residuals deviations predicted from p Sum Of Squares Error Calculator p actual empirical values of data It is a measure of the discrepancy between the data and an sum of squared errors example estimation model A small RSS indicates a tight fit of the model to

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Sum Of Error Squares Estimation p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the sum of squared errors of regression sum of squares prediction SSE is the sum of the squares of residuals deviations predicted from actual empirical residual sum of squares formula values of data It is a measure of the discrepancy between the data and an estimation model A small RSS indicates p Error Sum Of Squares p a tight fit of

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Sum Of Squares Due To Error p may be challenged and removed April Learn how and when to remove this template message In statistics the residual sum of squares RSS also known as the sum of squared residuals SSR or the sum of squares error calculator sum of squared errors of prediction SSE is the sum of the squares sum of squared errors example of residuals deviations predicted from actual empirical values of data It is a measure of the discrepancy between the data total sum of squares and an estimation model A small RSS indicates a tight fit of

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