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Topic: Prediction interval

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	4.1.3.2. Prediction
		As mentioned earlier, the goal of prediction is to determine future value(s) of the response variable that are associated with a specific combination of predictor variable values.
		As in estimation, the predicted values are computed by plugging the value(s) of the predictor variable(s) into the regression equation, after estimating the unknown parameters from the data.
		Because the prediction interval is an interval for the value of a single new measurement from the process, the uncertainty includes the noise that is inherent in the estimates of the regression parameters and the uncertainty of the new measurement.
	www.itl.nist.gov /div898/handbook/pmd/section1/pmd132.htm (664 words)

	Linear prediction - Wikipedia, the free encyclopedia
		Linear prediction is a mathematical operation where future values of a digital signal are estimated as a linear function of previous samples.
		In digital signal processing linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter theory.
		In system analysis (a subfield of mathematics), linear prediction can be viewed as a part of mathematical modelling or optimization.
	en.wikipedia.org /wiki/Linear_prediction (413 words)

	Systat Software Inc. - TableCurve 2D - HTML Help
		Since confidence and prediction intervals assume the normality of residuals, you are strongly encouraged to use a Residuals Stabilized Normal Probability Plot to verify the validity of intervals.
		Prediction intervals are useful for predicting, for a given X, the Y value of the next experiment.
		A 95% prediction interval is the Y range for a given X where there is a 95% probability that the next experiment's Y value will occur, based upon the fit of the present experiment's data.
	www.systat.com /products/TableCurve2D/help?sec=1096 (719 words)

	4.5.1.2. How can I estimate the value and uncertainty of a single observable response?
		The mechanics of predicting a new measurement value associated with a combination of predictor variable values are similar to the steps used in the estimation of the average response value.
		Computing prediction intervals for the measured pressure in the Pressure/Temperature example, at temperatures of 25, 45 and 65, and for the measured torque on specimens from the polymer relaxation example at different times and temperatures gives the results listed in the tables below.
		The uncertainties for the prediction intervals are much larger because they must include the standard deviation of a single new measurement, as well as the standard deviation of the average response value.
	www.6sigma.us /handbook/pmd/section5/pmd512.htm (1416 words)

	[No title]
		For example, when we are concerned with large values of Vitamin D content in a bottle of milk, the one-sided prediction interval is formed to include the lowest possible value (zero) as the lower limit and some large value as the upper limit.
		For a two-sided prediction interval with 95% confidence level, the remaining 5% lie at both ends: 2.5% at the lower end and 2.5% at the upper end.
		Answer: A tolerance interval to cover 95% of observations with 95% confidence level means that in a repeated sampling the tolerance interval correctly covers the specified percentage of coverage 95% of times, that is 5% of times the tolerance interval fails to cover 95% of observations.
	www.sph.uth.tmc.edu /course/biometry/elee/ph1725_26/doc/qa7.doc (890 words)

	Prediction interval - Wikipedia, the free encyclopedia
		In statistics, a prediction interval bears the same relationship to a future observation that a confidence interval bears to an unobservable population parameter.
		The mean and standard deviation of the population are unknown except insofar as they can be estimated based on the sample.
		It is desired to predict the next observation.
	en.wikipedia.org /wiki/Prediction_interval (150 words)

	Statistics Quiz (Site not responding. Last check: 2007-10-08)
		The data are given in Table I. Use this data and Minitab to predict the outcome of the memory test given that the I.Q. of the person is known.
		Predict the outcome of the memory test if person's IQ is 85.
		Predict the outcome of the memory test if person's IQ is 115.
	www.unca.edu /math/OnLine/Stat185/Quizzes/Q_HT_Predict.html (339 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The coverage of the prediction interval will, however, equal the nominal desired coverage only if it is constructed using the correct underlying covariance structure of the process.
		We study the effect on the coverage accuracy of the prediction interval of substituting the true covariance parameters by estimators, and the effect of bootstrap calibration of coverage properties of the resulting 'plugin' interval.
		We demonstrate that plugin and bootstrap calibrated intervals are asymptotically accurate in some generality and that bootstrap calibration appears to have a significant effect in improving the rate of convergence of coverage error.
	www.matstat.umu.se /aktuellt/seminarier/020403.html (160 words)

	Vitreous Humor Chemistry: The Use of Potassium Concentration for the Prediction of the Postmortem Interval. Stephens ... (Site not responding. Last check: 2007-10-08)
		The requisite statistical analysis for the prediction of PMI is inverse prediction.
		The 95% inverse prediction interval was found to be approximately ±20 h.
		This would narrow the inverse prediction interval and enable vitreous potassium to be a useful aid in the prediction of PMI.
	www.astm.org /jforensicsci/PAGES/843.htm (179 words)

	Solution to practice quiz 11
		The prediction interval (a) must be wider to hold all four values because their mean is much less variable.
		The prediction interval must contain all 50 values with 95% confidence, whereas the tolerance interval must contain 90% of the population with the same level of confidence.
		Therefore the prediction interval should be wider than the tolerance interval, regardless of sample size.
	www.quantdec.com /envstats/quiz/solution/solution11.htm (527 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Obtaining a Prediction Interval for a Future Observation Let’s focus again on the population of all adults with 42 kilograms of lean body mass.
		The predicted value of this metabolic rate is the one you obtain from the least square regression model; however, if we want to attach a margin of error to our prediction, we need to construct and interval estimate called a prediction interval.
		Since we want to predict an individual observation, we need a larger margin of error to pin down the metabolic rate of a person who has 42 kilograms of lean body mass than we did for estimating the mean metabolic rate of all persons with 42 kilograms of lean body mass.
	www.facstaff.bucknell.edu /jwright/Math217/216Labs/Lab9.doc (1736 words)

	[No title]
		One such interval is the interval between the value that the player will exceed 95 % of the time and the value that he will exceed only 5 % of the time.
		Thus the interval (232, 611) is a 90 % prediction interval for the player's remaining homers, and (432,811) is a 90 % prediction interval for the player's career total.
		Given below are prediction intervals and expectations, produced by the new method, for career home runs totals for the active players who, after the 2002 season, were predicted by the new system to finish with more than 300 home runs.
	www.stat.ohio-state.edu /~frey/beyondtoy.html (1683 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The prediction interval formula for the forecast of a regression dependent variable conditional upon known future values for the independent variables and normally distributed disturbances is commonly taught and used.
		One of the most commonly-taught procedures in statistical forecasting is the calculation of the prediction interval of the forecast from an ordinary least squares (OLS) regression, given known values for the independent variables in the forecast period and the assumption of a normal distribution for the disturbance.
		This is because a forecast period realization of the dependent variable outside the 100(1-) per cent prediction interval corresponds to a rejection of the null hypothesis using a two-sided prediction error test at an /2 level of significance.
	socserv2.socsci.mcmaster.ca /~econ/faculty/veall/lamijf.htm (2349 words)

	Exercise2 (Site not responding. Last check: 2007-10-08)
		Predict his freshman GPA using a 95 percent prediction interval Interpret your prediction interval.
		Obtain a 99 percent prediction interval for the mean number of ampules broken in the three shipments.
		Convert this interval into a 99 percent prediction interval for the total number of ampules broken in the three shipments.
	www.math.tau.ac.il /~fuchs/Exercise2.html (381 words)

	Prediction Intervals
		As a result, the range from the smallest to largest of the first 19 people is a 90% prediction interval (PI) for the next (subsequent) observation.
		Like almost all statistical intervals, this one can be a little tricky to interpret -- it requires some thought.
		For example, the 90% PI of (6516, 8546) given above is intended to predict the age of the next randomly selected person in the class.
	www.oswego.edu /~srp/stats/pi.htm (706 words)

	[No title]
		The Prediction Interval % is the value used in working with the t distribution.
		For example, if your estimate is 400, range 300, and prediction interval % is 90, that means that 400 is the best guess at the estimate, but there's a 90% chance that the true estimate is somewhere between 100 and 700.
		The issue here is one of prediction based on a sample vs. a population.
	users.snip.net /~gbooker/info636/week7.doc (740 words)

	Binomial Probability
		Prediction Interval for new y and Confidence interval for average y at a combination of x values.
		New Obs Fit SE Fit 95.0% CI Prediction Interval for new y and Confidence interval for average y for the entire data set.
		In the box for Prediction Intervals for new observations, enter the variables for x.
	www.stat.ufl.edu /~mmeece/3032/Minitab/mmulitreg.html (526 words)

	Regression SPSS
		The confidence interval for the population mean of all y values associated with the value of x chosen.
		The prediction interval is an interval of a prediction for an individual for a certain value of x.
		This would give the upper and lower limits of the prediction interval so in an examination, it will probably be a different level of prediction i.e.
	www.statistica.com.au /html/regression_spss.html (896 words)

	Estimating With Objects - Part VIII
		All the prediction interval does is to calculate the likelihood of one of these data points falling within a prescribed range of the regression line.
		The prediction interval is then the estimate value plus and minus the range.
		Thus, for a 90% prediction interval, you would look in the p =.90 column and for a 70% prediction interval, you would look in the p =.70 columns.
	www.sei.cmu.edu /publications/articles/watts-humphrey/estimate-objects-008.html (1861 words)

	How to compute prediction and confidence
		Given a test input x_0, a 100c% prediction interval for y_0 is an interval [LPB_0,UPB_0] such that Pr(LPB_0 <= y_0 <= UPB_0) = c, where c is typically.95 or.99, and the probability is computed over repeated random selection of the training set and repeated observation of Y given the test input x_0.
		A confidence interval is narrower than the corresponding prediction interval, since the prediction interval must include variation due to noise in y_0, while the confidence interval does not.
		Both intervals include variation due to sampling of the training set and possible variation in the training process due, for example, to random initial weights and local minima of the objective function.
	www.faqs.org /faqs/ai-faq/neural-nets/part3/section-13.html (944 words)

	A non-parametric prediction interval for censored survival data (Site not responding. Last check: 2007-10-08)
		Prediction interval methodology offers a useful way of constructing intervals from an initial sample which will contain a statistic from a future sample with specified probability.
		Such predictions help medical investigators in deciding whether to adopt the experimental treatment or to continue with standard until the development of alternative treatments.
		This paper concerns prediction intervals based on as initial sample of censored survival data of paraplegia patients which consists of evaluating the Kaplan-Meler estimates at the samples quantiles of a future sample.
	www.trc-chennai.org /Publications/pub461.htm (152 words)

	Projects of Chemometric Group
		For prediction modelling, this leads to results that are in a convenient interval form.
		The main purpose of non-linear regression is to fit data with a non-linear model, to predict response for predictor values that are far from the observed ones, to estimate the uncertainties in prediction.
		Prediction is performed at normal temperature 20C and the left (bottom) limits of confidence intervals are obtained.
	rcs.chph.ras.ru /ICP/projects.htm (3060 words)

	polyconf (Site not responding. Last check: 2007-10-08)
		polyconf(...,['ci''pi']) Produce a confidence interval (range of likely values for the mean at x) or a prediction interval (range of likely values seen when measuring at x).
		The prediction interval tells you the width of the distribution at x.
		The default is.05 for a 95% prediction interval, or erfc(1/sqrt(2)) for a one standard deviation confidence interval.
	octave.sourceforge.net /index/f/polyconf.html (167 words)

	No Title
		Obtain a level 0.90 confidence interval to compare the mean lifetimes of blades from the two manufacturers.
		Tolerance intervals are used to give a range of values which, with a pre-specified confidence, will contain at least a pre-specified proportion of the measurements in the population.
		For level 0.90 normal theory tolerance interval for a proportion 0.95 of the data, the constant K is obtained by simple interpolation to be 2.137.
	www.math.wpi.edu /Course_Materials/MA2611E98/lect5 (1600 words)

	[No title]
		Use the equation found in the previous part to predict TimeToNext (time to the next eruption) after an eruption with Duration = 2 minutes Suppose that after an eruption of Duration = 2, the time to next eruption is 56 minutes.
		This will cause Minitab to create a 95% prediction interval for the time to next eruption after an eruption that’s 4 minutes long.
		Explain why this (fraction of observations not in the interval) is about what be expected for a 95% prediction interval.
	www.stat.psu.edu /~rho/240/lab-dec3.doc (724 words)

	11.7 Using the model for estimation and prediction (Site not responding. Last check: 2007-10-08)
		Example 11.12 Find a 95% confidence interval for the mean carbon monoxide ranking of all cigarettes that have a nicotine content of 0.4 milligram.
		Also, find a 95% prediction interval for a particular cigarette if its nicotine content is 0.4 mg.
		From the Example 11.12 it is important note that the prediction interval for the carbon monoxide ranking of an individual cigarette is wider than corresponding confidence interval for the mean carbon monoxide ranking.
	www.netnam.vn /unescocourse/statistics/11_7.htm (376 words)

	[No title]
		The predicted IndoPacific SSTA patterns based on the DJF 1998-99 initial condition for the following MAM, JJA, SON and DJF are shown in Fig.
		The prediction of Niño 4 SSTA has been very good since AMJ 1998; the predictions and verifications made since then are form a tight bundle, mostly within the one standard deviation confidence interval for the AMJ 1998 prediction.
		The added predictability in the northern tropical Atlantic is primarily due to the effect of the Pacific, so SSTA in the global tropical strip (30N-30S) are used as predictors.
	grads.iges.org /ellfb/Mar99/penland.htm (839 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Find you two-thirds prediction interval for the percent of players unable to play.
		Find a 95% prediction interval for the percent of players unable to play.
		Find the 95% prediction interval for the proportion of calls that will produce sales and give the bottom of the interval as a reasonable minimum estimate.
	www.ship.edu /~clolse/m170/Section3.1.doc (305 words)

	Laboratory 10 (Site not responding. Last check: 2007-10-08)
		The park rangers at Yellowstone do this and their predictions are posted near the geyser and at the web cam picture site located here.
		Use your regression equation to estimate the length of the interval when the duration is 4.0 minutes.
		Give both a 95% confidence interval and a 95% prediction interval for the length of time between eruptions for a 4.0 minute duration.
	www.cs.hope.edu /~swanson/Lab_10.html (453 words)

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