The tag has no wiki summary.

learn more… | top users | synonyms (1)

1
vote
0answers
21 views

Which statistics to use calculating prediction interval of dummy linear regression?

I have performed a linear regression and found a model of the form: $$ \hat{Y} = \alpha + \beta_1 x+ \delta_{high} + \delta_{low} + \epsilon\\ $$ Where: $\beta_1$ is a continuously distributed ...
1
vote
0answers
17 views

Inverse prediction of percentile

Suppose we consider a linear normal regression $y\sim$Normal($\mu,\sigma$) and $\mu=a+bx$. I have seen documentations for methods for obtaining a confidence interval for $x$ for a specific mean value ...
2
votes
0answers
34 views

Multiple regression prediction interval comparison

Here's my situation. I have a multiple linear regression which I've used to come up with a prediction interval to predict a value y for a given (x1,x2,x3,x4,x5,x6). It reads something like lower: ...
1
vote
0answers
37 views

Inventory control - first order quantity of periodic order quantities model

I Have read "Manufacturing Planning and Control for Supply Chain Management 6th Edition" by F.Robert Jacobs. I found the problem on the Periodic Order Quantities (POQ). As I know POQ calculation is ...
8
votes
2answers
177 views

Can we make probabilistic statements with prediction intervals?

I've read through the many excellent discussions on the site regarding interpretation of confidence intervals and prediction intervals, but one concept is still a bit puzzling: Consider the OLS ...
2
votes
0answers
68 views

Forecasting call volumes over short intervals using R

I am trying to do a basic forecast of call volumes using the forecast library for R. I am not having too much trouble forecasting on a daily or monthly interval, however when I try to forecast on an ...
0
votes
0answers
31 views

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 ...
3
votes
2answers
635 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 ...
1
vote
0answers
16 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 ...
1
vote
0answers
61 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 ...
2
votes
1answer
68 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 ...
3
votes
2answers
84 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, ...
9
votes
1answer
409 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 ...
6
votes
2answers
240 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 ...
2
votes
0answers
50 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 ...
0
votes
0answers
57 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 ...
0
votes
0answers
42 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 ...
1
vote
2answers
106 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 ...
2
votes
0answers
40 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 ...
5
votes
1answer
136 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 ...
0
votes
0answers
48 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 ...
0
votes
3answers
496 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 ...
1
vote
0answers
51 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 ...
0
votes
0answers
32 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 ...
6
votes
0answers
111 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 ...
3
votes
1answer
90 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 ...
1
vote
1answer
466 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. ...
0
votes
0answers
48 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 ...
2
votes
1answer
182 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 ...
4
votes
0answers
92 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 ...
5
votes
2answers
123 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), ...
2
votes
0answers
76 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 ...
0
votes
1answer
80 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 ...
2
votes
1answer
236 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 ...
2
votes
0answers
47 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 ...
3
votes
0answers
133 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 ...
1
vote
1answer
125 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 ...
0
votes
0answers
133 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 ...
2
votes
2answers
406 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 ...
2
votes
1answer
731 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 ...
1
vote
1answer
311 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 ...
7
votes
2answers
2k 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 ...
1
vote
1answer
246 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 $$ ...
2
votes
1answer
346 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
votes
1answer
453 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 ...
3
votes
0answers
266 views
3
votes
0answers
97 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
votes
1answer
377 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 ...
2
votes
1answer
230 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. ...
4
votes
1answer
725 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: ...