The error of an observed value is the deviation of the observed value from the (unobservable) true function value. Do NOT use this tag for SOFTWARE ERROR messages.

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What type of data would have non-normal errors?

I'm trying to understand the assumptions for an OLS model. I get that the error term should be normally distributed if we want easy-to-calculate confidence intervals for our coefficient estimates. ...
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14 views

Regression error - what is theoretical bound [on hold]

I have a question on the theoretical error for Bayesian linear regression problem (or if there is any proof that can be applied to a general regression problem). Is it possible to find it ...
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20 views

Converting between different accuracy/error metrics

I am trying to compare model accuracy between several different measurement metrics. For example, some citations use accuracy while other use error. That one is rather obvious, but there are lots of ...
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18 views

Absolute error or RMSE when you know the exact value?

I'm testing the $k$ neighbour correlation of a uniform random sequence $x_i$ in $[0,1)$. I know its exact expected value to be $1/4$ and I want to show that the error decreases with $\sqrt{N}$ where ...
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1answer
27 views

Definition of residuals versus prediction errors?

I always thought the definition of residuals is the difference between the statistic and the observations. And, the definition ...
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13 views

Generalized Linear Model on SPSS with the 'error': “set to zero because this parameter is redundant”

For my dissertation I have a lot of data and many nominal variables. None of my data is parametric. I tried transforming some of the percentage data with arcsine because it was in proportions and the ...
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2answers
43 views

Best statistic for measuring prediction accuracy that is robust for outliers

I have recently built a model, designed for prediction. Initially, I chose model A over B - better RMSE and better MAPE. However, after carefully evaluating each prediction on my test dataset for ...
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1answer
27 views

How does Stata calculate RMSE in regression with weights?

This problem came up because I was trying to replicate some results I was getting in Stata with R, and I was able to replicate everything except for the root mean squared error. When I run a ...
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1answer
43 views

RMSE is scale-dependent; is RMSE%?

I've got a graph of RMSE% vs. unit size and it declines nicely. Is this scale-dependence or does the "%" compensate for that? $$ \text{RMSE%} = 100\% \cdot \frac{\sqrt{\frac{1}{n}\Sigma_{i=1}^n (y_i ...
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2answers
15 views

Adding Up Margins of Error

I'd like to add data from Census.gov, but I don't know how to add up the Margin of Error. Example, I have the estimate number of renters in Congressional District 1, (203,941 +/- 4,892) and the same ...
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1answer
46 views

Calculating Neural Network Error

I am confused with these two error formulas for artificial neural networks: \begin{align} \text{Error} &= {\rm target} - {\rm output} \\[7pt] \text{Mean Square Error} &= ...
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1answer
785 views

How incorrect is a regression model when assumptions are not met?

When fitting a regression model, what happens if the assumptions of the outputs are not met, specifically: What happens if the residuals are not homoscedastic? If the residuals show an increasing or ...
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10 views

Finding the maximum absolute percentage error (MaxAPE) for a regression model

To find the mean absolute percentage error (MAPE) and maximum absolute percentage error (MaxAPE) for the model, I save the residuals and use the FIT command. However, FIT does not provide the maximum ...
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28 views

Test error of probability “prediction” for little league soccer

Background: I have multiple sets of team's little league soccer scores made up only of whole numbers [0-12 inclusive], eg: ...
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1answer
106 views

Bias vs reducible error

I encountered a question while learning: While doing a homework assignment, you fit a Linear Model to your data set. You are thinking about changing the Linear Model to a Quadratic one. ...
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1answer
46 views

Decompose ridge regression bias error into model bias and estimation bias

How can I show that the in-sample bias error in Ridge regression can be decomposed into model bias plus estimation bias? I.e., if $Avg$ takes the average over all the input variables $x$ in the ...
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1answer
20 views

Averaging results from different experiments where errors may be underestimated

Let's say we have three different published results that measure the same physical quantity $x$ using completely different methods. Experiment 1 says $x=100\pm0.1$, Experiment 2 says $x=102\pm0.2$, ...
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1answer
34 views

Finding optimal beta when there are multiple different errors

I am working on an econometrics model that I'm not sure how to approach. I've made a utility function where the weights have noise as well. In short it's: $$ y_i = (\beta + \epsilon_i)x_i + u_i $$ ...
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4 views

Error term with simple linear model

In simple linear regression model like this.  y =  a + bx + ε If I do not know whether ε(error) is independent and identically distributed how can I deal with the hypothesis test on b?
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1answer
16 views

Error propagation in a linear model

I am currently interested in learning more on error propagation. At the moment I am trying to find out how to calculate the uncertainty of a value that is obtained from a linear model. For the linear ...
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3answers
125 views

Error in a linear regression

I have a set of points and I would like to fit a linear regression model to them, where each point has its own error value, and I want to find the gradient of the regression line. How do I calculate ...
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0answers
26 views

Aggregating error bars on a bar chart

I'm creating a clustered bar chart to show the effect of a software change on the performance of an application. There are two independent variables: the benchmark being run (colors) and the input set ...
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1answer
26 views

Multi level model in R: error comparing models due to different number of observations

I am running a linear multi level model in R. The predictor variable is called "OAI", and the response variable is called "Ens", I am allowing the intercepts and slopes to vary with "ID". Here is a ...
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12 views

Assessing a vector of errors in modeling

The quality of a model is often assessed based on a figure of merit such as RMSE. This reduces the individual errors in the model to a single number without assessing the errors as a population of ...
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23 views

How should the error-term in reporting results be properly written to make sense?

I want to report results obtained from a number of measurements with the average value plus minus the standard deviation. During my studies I was always thaught to use only one signifying digit in the ...
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7 views

What does $R^2$ mean in the context of K-Nearest Neighbors algorithm?

Googling the meaning of $R^2$ gives the following: "R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, ...
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1answer
36 views

SVM Classifier Evaluation in R

I am working on an application to evaluate the performance of SVM on a number of different datasets. SVM is working well, yielding 98% diagonal accuracy. I now need to evaluate the performance of ...
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17 views

How does a curve fit accuracy depend on the number of points?

The accuracy of a curve fit must increase with the number of points (perhaps like sqrt(N)), but I haven't found an equation for it. Trying estimate accuracy of a 2nd order poly fit. Thanks.
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1answer
319 views

Difference between GradienDescentOptimizer and AdamOptimizer (TensorFlow)?

I've written a simple MLP in TensorFlow which is modelling a XOR-Gate. So for: input_data = [[0., 0.], [0., 1.], [1., 0.], [1., 1.]] it should produce the ...
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0answers
10 views

Test error spikes at dimension half of sample size in linear model without regularization

I am training a basic linear model, with input data $x(n)$ and target data $t(n)$. Now, I want to make a model of dimension $d$, such that $$ y(\textbf{x}) = w_0 + \sum_{i=1}^d w_ix_i = w_0 + ...
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1answer
27 views

error rates of knn minimal for k=1

I am trying to find the best parameter $k$ for a nearest neighbour classifier using cross validation for some datasets. After computing and plotting the error rates, I noticed some strange behaviour ...
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9 views

Empirical validation of a regression model estimating the mean and the variance?

I would like to empirically validate over a given dataset a regression model $\mathbb{R}^n \to \mathbb{R}^2$ that outputs both the mean and the variance. In particular, I am seeking a metric that ...
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9 views

How to filter data with artifacts (glitches) and check if we need to reset the device?

I am reading values from a cheap laser (Lidar-Lite v2). The device is not perfect. The laser sometimes returns some bad values Sometimes needs to be reset In this example of dataset on the 202cm ...
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15 views

Systematic Prediction Errors in Inductive ML

This is more a conceptual question than a technical one, though the answer might be technical, I suppose. I do a lot of cross-validated ML, predicting behavioural data given brain data. I've noticed ...
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27 views

Detecting label errors using a classifier in scene labeling

I have a classifier for two classes that was trained in a convolutional neural network using cuda-convnet. Input are hand-labeled greyscale images, it is part of a scene-labeling project. What I'm ...
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46 views

Shouldn't the root mean square error (RMSE) be called root mean square residual?

As far as I understand, estimating the error of a model, say an artificial neural network, requires to know the "true" model. Wikipedia says in its article "Errors and residuals": "The error (or ...
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19 views

Method to quantify differences between prediction and outcome for factual and simulated sample

I have vector with probability values a and binary outcome b: ...
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100 views

How can I find the optimal weighting scheme to aggregate these estimates?

I have data in which about 150 subjects separately estimate 6 different quantities. The quantities are the answers to general knowledge questions like "How many far apart in kilometres are Milan and ...
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1answer
28 views

Fitting data while accounting for error in data

I have data that has error. The error bars in the data represent one standard deviation. I would like to fit a line to these data, while accounting for the fact that the data could vary between my ...
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6 views

Theoretically is model of error as erroneous as the erro itself?

I'm teaching a response model [i_1,i_2,...,i_n] --> <-1,1> i_n is <-1,1> I have chosen recurrent neural network but this might have nothing to do with my question. I will compare model with ...
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8 views

Group level error terms

What is the difference between a regression equation that includes a time fixed effect, a group fixed effect and a composite error term versus a regression equation that include only a group fixed ...
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9 views

Calculating the error on a variable, given the error on a dependant variable

I have a variable which is given by the equation: M = M(a) * (N/20) Now if M(a) has an error of let's say 10%, how do I ...
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57 views

Two-sample Kolmogorov-Smirnov test with errors on data points

Short version I want to test if two samples, which follow a skewed distribution, can be distinguished from each other. A Kolmogorov-Smirnov statistic for two samples would be sufficient if there was ...
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4 views

Measuring / Characterizing error in ordered data

I have two sets of data points. The ground truth set and the measurement set. The magnitude measured is time, and it is important that each data point in the measurement preserves the order in the ...
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20 views

Calculating Error on a Hold-Out Set

I broke some data into a training and a hold out set. Then I clustered the training set with the k-means method. Now I want to calculate error using the holdout set. Do I just take the square the ...
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1answer
48 views

Acceptable limit for MASE

What are good sign of fit from result of forecast::accuracy. How to interpret ...
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28 views

Error propagation with dependent variables

I've posted this in physics but without much help that I can apply to my problem. Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from ...
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42 views

How to calculate prediction intervals based on Chebyshev inequality?

I have recently read the article by Gardner (1988) who proposes Chebyshev inequality-based prediction intervals for forecast: suppose we have a model selected on the usual basis of one-step-ahead ...
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1answer
27 views

Is it possible to use a mean squared error for matrices?

Could I use a mean squared error statistical analysis on a set of 1 x 2 matrices? For example, if I had [123 456] as the actual matrix and [111 222] as the predicted matrix, could I use the mean ...
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18 views

Measuring Prediction vs Actual Difference

To find error we usually measure our predicted y vs actual y. Are there any error terms that measure the error in y AND the error in x, given y? In the image below the line is doing a pretty good ...