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Confidence and prediction intervals

The difference between confidence and prediction intervals has been explained in plain English on Cross Validated: Difference between confidence intervals and prediction intervals However, when ...
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2answers
597 views

Can a mathematically sound prediction interval have a negative lower bound?

I have used R to form a 95% prediction interval for the number of endemic species on an island. My lower bound is negative – is that mathematically sound? In the linear model used in the prediction ...
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7 views

Joint vs. marginal prediction intervals for path forecasts (with k-family wise error rate)

I am trying to become comfortable with the bootstrapping of joint prediction regions described in this paper: http://www.nccr-finrisk.uzh.ch/media/pdf/wp/WP748_A3.pdf This calculates the prediction ...
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35 views

Prediction Intervals for General Linear Model

How do I derive prediction intervals for a general linear model? My general linear model written in matrix form is, $$ \mathbf{Y} = \mathbf{X} \mathbf{B} + \mathbf{R}$$ with each of the rows of ...
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1answer
46 views

Prediction interval on untransformed scale

I am attempting to use simple linear regression to construct a 95% prediction interval for a continuous response variable (Y) using a continuous input variable (X). When examining my data, I realized ...
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2answers
67 views

What does error refer to in linear regression notation?

I regularly see linear regression models written in this notation: $y = a + \beta X + error$ I've never really pinned down what $error$ actually refers to. In the linear regression plotted below, ...
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1answer
166 views

Shape of confidence interval for predicted values in linear regression

I have noticed that the confidence interval for predicted values in an linear regression tends to be narrow around the mean of the predictor and fat around the minimum and maximum values of the ...
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2answers
150 views

Shape of confidence and prediction intervals for nonlinear regression

Are the confidence and prediction bands around a non-linear regression supposed to be symmetrical around the regression line? Meaning they do not take on the hour-glass shape as in the case of the ...
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0answers
43 views

Which confidence interval should I use to bound actual values around a predicted value?

I have a 'black box' model that outputs model predictions, but I don't know what actually goes on inside the model. I also have a bunch of data that I can pass through the model so that I can compare ...
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41 views

Prediction intervals predict.Arima r

I would like to ask how the long-term (multiple step ahead) prediction intervals are calculated by function predict.Arima in R. I am particularly interested in ...
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0answers
41 views

Why do matching algorithms use point estimates rather than intervals?

I'm developing a matching algorithm, and I am wondering why websites choose using point estimates, e.g. "You match 60% with person X". Given that there will be most likely be missing data, rather ...
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2answers
89 views

Estimate the sum of predicted variables by a linear model in R

I have a dataset with 3000 sub-regions with data about their population by income range and their value spending in a commodity. I made a OLS model with log-log transformation using ...
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0answers
31 views

Prediction interval in principal component regression

I would like to obtain a prediction interval from a model returned by the R package 'pls'. The predict method does not seem to be able to return this value. I wonder if anyone has a suggested ...
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1answer
117 views

Does more variables mean tighter confidence intervals?

Assume that the true (but unknown) relationship in a population between $Y$ and $X1, X2, X3, X4$ is $$Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \beta_4 X_4.$$ Further assume that I have a ...
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0answers
43 views

Prediction interval with measurement error

My data is $(Y,X)_i,i=1...N$ and i want to fit a regression model to relate $Y$ and $X$. It is known that $X$ and $Y$ are erroneous measurement of true variable $(U,V)$, but the standard errors ...
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3answers
337 views

Why do we estimate the mean response in Confidence interval but predict individual outcome in prediction?

I have tried to understand the differences. Just to be clear, I think I understand the two sources of variation in prediction comes from the variation in the distribution of the location of Y and ...
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0answers
46 views

Question about prediction bands for non-linear regression computation?

I am interested in computing prediction bands for a non-linear regression (log-logistic function with 3 parameters). I have read the Prism help page: The calculation of the confidence and ...
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27 views

Leave-out data approach to get intervals for predictive performance of a regression model

When measuring predictive performance of a regression model, I am thinking about using repeated data splitting (or leave-out data at random) instead of using bootstrapping. By "repeated data ...
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87 views

Detecting outliers using 95% PI around a natural spline fit

Please see the picture below: I wanted to mark the points that are not consistent with their adjacent points as outlier. What I did was to fit a natural spline fit to 1000 observations (the purple ...
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1answer
67 views

Prediction interval = credible interval?

I am wondering if prediction interval and credible interval evaluate the same thing. For instance with a linear regression, when you estimate the prediction interval of a fitted values, you estimate ...
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1answer
355 views

Calculating Prediction Interval

I have the following data located here. I am attempting to calculate the 95% confidence interval on the mean purity when the hydrocarbon percentage is 1.0. In R, I enter the following. ...
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0answers
45 views

Determine over/under of regression prediction

I've created a regression analysis in Excel and using the model I have created a prediction point for Y for a given input of X. I'd like to add an "over/under" to the Y value to show the range that Y ...
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1answer
134 views

How do I obtain prediction intervals for fixed effects of Generalized Linear Mixed Model?

Suppose I use R to fit a Generalized Linear Mixed Model from the binomial family and with a logit link. How do I obtain the prediction intervals (as opposed to the confidence intervals) for the fixed ...
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86 views

How do I compute a prediction interval from generalized estimating equation output?

Suppose I have repeated observations on individuals, which I've analyzed using a generalized estimating equation (GEE). What is the procedure for computing the prediction interval for future ...
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74 views

How to understand prediction interval?

Suppose we have observation a sample $X$, and would like to find a prediction interval $R(X)$ for a random variable $Y$ based on $X$ with probability $\alpha$. From Wikipedia, it seems to me that ...
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2answers
107 views

What can I do if the confidence intervals of the predicted mean are small but the predicted intervals are large

I am conducting a linear regression: $Y=\alpha+\beta\times X+\epsilon$, $\epsilon\sim N(0,\sigma^2)$. It turned out that the confidence interval for the predicted mean $Y$ was really small (figure 1), ...
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0answers
64 views

left-censored dependent variables and prediction

I'm coding up a monte-carlo analysis; I've got a deterministic model that depends on parameters that are uncertain. One of those uncertain parameters is a partially-observed vector of prices by ...
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1answer
77 views

Confidence or prediction limits for significant difference between forecast and observation?

My task is to to forecast business data without advertising and compare the real observations (with advertising effect) to the forecasted values in order to measure the effect of advertising. I am ...
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1answer
203 views

Backtesting/cross-validation for time-series and prediction intervals

Suppose I carry out the following exercise with my trusty statistics software: Fit some time-series model to the data $y_1,\dots,y_t$ and calculate $\hat{y}_{t+1}$, the fore­cast of the next ...
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56 views

K-Nearest-Neighbors Probability Distributions

I have a question about K-nearest-neighbors and whether it is possible to output more estimates than just the weighted estimate that the R package KKNN package gives you. I am predicting sports ...
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40 views

Prediction errors for Adaboost

I understand how the adaboost algorithm works to produce a prediction of a class, however one thing I haven't seen is how to get a measure of accuracy for that prediction. For example, if I fit a ...
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0answers
120 views

Predicting the year computers will be able to do 1 exaFLOPS using historical data (time series forcasting using prediction interval)

Put simply, I need to make a prediction interval (or confidence interval?) for the x value when y reaches a certain number given historical data for x versus y. Long Version: I have data on the ...
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1answer
116 views

Why are my prediction intervals a little too narrow?

I'm trying to make a little function to make population-level predictions from a model that includes random effects, which in turn was fit using a package that doesn't support ...
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0answers
124 views

How to calculate the prediction interval for my 24-hour forecast?

I'm doing time series analysis and I would like to calculate the prediction interval. I have predicted the next 24 values for my time series, but now I would also like to calculate the prediction ...
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2answers
361 views

How to calculate multi-step prediction intervals for time series data?

I need to manually calculate multi-step prediction intervals for time series data. I know packages like 'forecast' in R provide these, but I cannot use these packages as the production infrastructure ...
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1answer
640 views

How do I calculate prediction intervals for random forest predictions?

In regression problems random forests yield a prediction for each case by averaging the results of each single tree in the forest. I would like to draw a 95% prediction interval around each ...
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1answer
289 views

Uncertainty from linear fit on additional data

Let's say I have 5 known data points with coordinates $X$ : Area under curve $Y$ : Activity The 5 points have individual error ($\Delta X_{i}$,$\Delta Y_{i}$) on both $X$ and $Y$ and I know that ...
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2answers
1k views

How to: Prediction intervals for linear regression via bootstrapping

I am having trouble to understand how to use bootstrapping to calculate prediction intervals for a linear regression model. Can somebody outline a step-by-step procedure? I searched via google but ...
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1answer
223 views

Prediction interval for simple linear regression

I have been given two formulas: $$ \hat{\sigma}^2 = \frac{1}{n-p} (Y - X \beta)^T(Y - X\beta) $$ $$ = \frac{1}{n-p} \sum ( y_i - \hat{\beta_0} - \hat{\beta_1}x_i)^2 $$ I also have $$ ...
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1answer
320 views

How is a prediction interval generated for many input observations?

I am aware that the "prediction interval", as defined in most textbooks on linear models, is focused on the uncertainty in the model being fit and is used to estimate an output prediction range for ...
2
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1answer
414 views

Prediction interval for the one-way random effect ANOVA

I don't find a textbook presenting prediction intervals for mixed models. Moreover I'm only looking for a prediction interval for the balanced one-way random effect ANOVA model. Do you know a formula ...
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244 views
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94 views

Validating a logistic regression for a specific $x$

I have a logistic regression model for 0/1 binary response data that is built from samples $(x_1,Y_1),\ldots,(x_m,Y_m)$, where $x_1,\ldots,x_m$ are, fixed, nonrandom, real values and $Y_1,\ldots,Y_m$ ...
3
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1answer
310 views

Prediction interval for robust regression with MM-estimator

In their book "Robust Statistics", Maronna et al. consider the following model for robust regression: $y_i = \beta x_i + u_i$, where $u_i$ are independent of the $x_i$, and are i.i.d, with finite ...
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1answer
198 views

How to get prediction intervals at mean & at max of covariate values in R

I'm still working on R problems from a book, and using my spending data. Part 1: I need to predict the amount that a male with average data for status, income and verbal would spend along a 95% CI. ...
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1answer
665 views

How to calculate the prediction interval from two independent forecasts of time series?

Lets say I have two time series a and b and I predict the next value and a prediction interval (say lower and upper 80%) of each of these two. I end up with something like that: a: [10, 20, 30] and b: ...
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0answers
289 views

Calculating prediction intervals when using cross validation

Are standard deviation estimates calculated via: $ s_N = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}. $ (http://en.wikipedia.org/wiki/Standard_deviation#Sample_standard_deviation) for ...
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1answer
243 views

Independent and serial correlation

I have a set of 76 annual occurrences of $x$ and $y$. When I run a linear regression, $y$ is significantly correlated to $x$. The Durbin-Watson test shows $y$ is also serially correlated. My goal ...
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166 views

Derivation of prediction intervals for a normally distributed population with unknown population standard deviation

I have via the ISO standard 16269 found the solution to a problem that I've been working on. Based on a couple of independent samples from a normally distributed population, I would like to determine ...
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3answers
938 views

Should I use the mean-squared-prediction-error from LOOCV for prediction intervals?

I have a question about which prediction variance to use to calculate prediction intervals from a fitted lm object in R. For a certain multiple linear regression ...