
PREDICTION BOUNDSName:
A conservative approximation for r_{(1\( \alpha \),m,n)} is
with t denoting the t percent point function. Dataplot uses the tabulated values given in Table A.13 of Hahn and Meeker when n and m are both less than or equal to 10. Otherwise, the approximation above is used. The corresponding onesided interval is
\( \mbox{upper limit} = \bar{x} + r'_{(1  \alpha;m,n)} s \) A conservative approximation for r'_{(1\( \alpha \),m,n)} is
with t denoting the t percent point function. Dataplot uses the tabulated values given in Table A.14 of Hahn and Meeker when n and m are both less than or equal to 10. Otherwise, the approximation above is used. In the formula above, the only value from the new observations is the sample size. That is, it can be applied before the new data is actually collected. The number of observations for the new sample is entered with the command
If NNEW is not defined, then a value of 1 is used. The difference between the PREDICTION BOUNDS command and the PREDICTION LIMITS command is that the PREDICTION LIMITS command generates a prediction interval for the mean of m new observations while the PREDICTION BOUNDS command generates a prediction interval to contain all of the new observations. This prediction interval is based on the assumption that the underlying data is approximately normally distributed. Due to the central limit thereom, prediction limits for the mean are fairly robust against nonnormality. However, the central limit thereom does not apply to prediction intervals to cover all of the new observations. So the PREDICTION BOUNDS command is much more sensitive to nonnormality than is the PREDICTION LIMITS command.
<SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If LOWER is specified, a onesided lower prediction limit is returned. If UPPER is specified, a onesided upper prediction limit is returned. If neither is specified, a twosided limit is returned. If the keyword LOGNORMAL is present, the log of the data will be taken, then the normal prediction bounds will be computed, and then the computed normal lower and upper limits will be exponentiated to obtain the lognormal prediction bounds. Similarly, if the keyword BOXCOX is present, a BoxCox transformation to normality will be applied to the data before computing the normal prediction bounds. The computed lower and upper limits will then be transformed back to the original scale. This syntax supports matrix arguments for the response variable.
PREDICTION BOUNDS <y1> ... <yk> <SUBSET/EXCEPT/FOR qualification> where <y1> .... <yk> is a list of 1 to 30 response variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax will generate a prediction interval for each of the response variables. If LOWER is specified, a onesided lower prediction limit is returned. If UPPER is specified, a onesided upper prediction limit is returned. If neither is specified, a twosided limit is returned. If the keyword LOGNORMAL is present, the log of the data will be taken, then the normal prediction bounds will be computed, and then the computed normal lower and upper limits will be exponentiated to obtain the lognormal prediction bounds. Similarly, if the keyword BOXCOX is present, a BoxCox transformation to normality will be applied to the data before computing the normal prediction bounds. The computed lower and upper limits will then be transformed back to the original scale. This syntax supports matrix arguments for the response variables.
PREDICTION BOUNDS <y> <x1> ... <xk> <SUBSET/EXCEPT/FOR qualification> where <y> is the response variable; <x1> .... <xk> is a list of 1 to 6 groupid variables; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax performs a crosstabulation of the <x1> ... <xk> and generates a prediction interval for each unique combination of the crosstabulated values. For example, if X1 has 3 levels and X2 has 2 levels, six prediction intervals will be generated. If LOWER is specified, a onesided lower prediction limit is returned. If UPPER is specified, a onesided upper prediction limit is returned. If neither is specified, a twosided limit is returned. If the keyword LOGNORMAL is present, the log of the data will be taken, then the normal prediction bounds will be computed, and then the computed normal lower and upper limits will be exponentiated to obtain the lognormal prediction bounds. Similarly, if the keyword BOXCOX is present, a BoxCox transformation to normality will be applied to the data before computing the normal prediction bounds. The computed lower and upper limits will then be transformed back to the original scale. This syntax does not support matrix arguments.
PREDICTION BOUNDS Y1 SUBSET TAG > 2 MULTIPLE PREDICTION BOUNDS Y1 TO Y5 REPLICATED PREDICTION BOUNDS Y X
LET NNEW = <value>
LET A = LOWER PREDICTION BOUNDS Y
LET A = SUMMARY LOWER PREDICTION BOUNDS YMEAN YSD N The first two commands specify the significance level and the number of new observations. The next four commands are used when you have raw data. The last four commands are used when only summary data (mean, standard deviation, sample size) is available. In addition to the above LET command, builtin statistics are supported for about 20 different commands (enter HELP STATISTICS for details).
SKIP 25 READ ZARR13.DAT Y SET WRITE DECIMALS 5 LET NNEW = 5 . PREDICTION BOUNDS Y LOWER PREDICTION BOUNDS Y UPPER PREDICTION BOUNDS YThe following output is generated TwoSided Prediction Bounds for All Observations Response Variable: Y Summary Statistics: Number of Observations: 195 Sample Mean: 9.26146 Sample Standard Deviation: 0.02278 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  50.0 9.22370 9.29922 80.0 9.21422 9.30870 90.0 9.20786 9.31505 95.0 9.20202 9.32089 99.0 9.18988 9.33303 99.9 9.17483 9.34808 OneSided Lower Prediction Bounds for All Observations Response Variable: Y Summary Statistics: Number of Observations: 195 Sample Mean: 9.26146 Sample Standard Deviation: 0.02278 Number of New Observations: 5 OneSided Lower Prediction Bounds for All Observations  Confidence Lower Value (%) Limit  50.0 9.23208 80.0 9.22125 90.0 9.21422 95.0 9.20786 99.0 9.19490 99.9 9.17914 OneSided Upper Prediction Bounds for All Observations Response Variable: Y Summary Statistics: Number of Observations: 195 Sample Mean: 9.26146 Sample Standard Deviation: 0.02278 Number of New Observations: 5 OneSided Upper Prediction Bounds for All Observations  Confidence Upper Value (%) Limit  50.0 9.29084 80.0 9.30166 90.0 9.30870 95.0 9.31505 99.0 9.32801 99.9 9.34377Program 2: SKIP 25 READ GEAR.DAT Y X SET WRITE DECIMALS 5 LET NNEW = 5 . REPLICATED PREDICTION BOUNDS Y XThe following output is generated TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 1.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99800 Sample Standard Deviation: 0.00434 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.98560 1.01039 95.0 0.98356 1.01243 99.0 0.97869 1.01730 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 2.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99910 Sample Standard Deviation: 0.00521 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.98422 1.01397 95.0 0.98177 1.01642 99.0 0.97592 1.02227 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 3.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99540 Sample Standard Deviation: 0.00397 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.98405 1.00674 95.0 0.98219 1.00860 99.0 0.97773 1.01306 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 4.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99820 Sample Standard Deviation: 0.00385 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.98721 1.00918 95.0 0.98540 1.01099 99.0 0.98108 1.01531 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 5.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99190 Sample Standard Deviation: 0.00757 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.97029 1.01350 95.0 0.96673 1.01706 99.0 0.95823 1.02556 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 6.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99879 Sample Standard Deviation: 0.00988 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.97061 1.02698 95.0 0.96596 1.03163 99.0 0.95488 1.04271 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 7.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 1.00150 Sample Standard Deviation: 0.00787 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.97904 1.02395 95.0 0.97533 1.02766 99.0 0.96650 1.03649 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 8.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 1.00039 Sample Standard Deviation: 0.00362 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.99005 1.01074 95.0 0.98835 1.01244 99.0 0.98428 1.01651 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 9.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99829 Sample Standard Deviation: 0.00413 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.98650 1.01009 95.0 0.98455 1.01204 99.0 0.97991 1.01668 TwoSided Prediction Bounds for All Observations Response Variable: Y Factor Variable 1: X 10.00000 Summary Statistics: Number of Observations: 10 Sample Mean: 0.99479 Sample Standard Deviation: 0.00532 Number of New Observations: 5 TwoSided Prediction Bounds for All Observations  Confidence Lower Upper Value (%) Limit Limit  90.0 0.97960 1.00999 95.0 0.97710 1.01249 99.0 0.97112 1.01847Program 3: . Following example from Hahn and Meeker's book. . let ymean = 50.10 let ysd = 1.31 let n1 = 5 let nnew = 3 let alpha = 0.05 . set write decimals 5 let slow1 = summary lower prediction bounds ymean ysd n1 let supp1 = summary upper prediction bounds ymean ysd n1 let slow2 = summary one sided lower prediction bounds ymean ysd n1 let supp2 = summary one sided upper prediction bounds ymean ysd n1 print slow1 supp1 slow2 supp2The following output is generated PARAMETERS AND CONSTANTS SLOW1  44.74603 SUPP1  55.45397 SLOW2  45.75080 SUPP2  54.44920  
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Date created: 04/15/2013 