# ::Free Statistics and Forecasting Software::

v1.1.23-r7
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### :: Standard Deviation-Mean Plot ::

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Server date: April 24, 2017, 6:26 am

Note: these SMP calculations are always applied to the untransformed and undifferenced (original) time series.

 SMP of Airline.ds L = 1, d = D = 0 Section Mean(k) SE(k) 1 126.6667 13.7201 2 139.6667 19.0708 3 170.1667 18.4383 4 197 22.9664 5 225 28.4669 6 238.9167 34.9245 7 284 42.1405 8 328.25 47.8618 9 368.4167 57.8909 10 381 64.5305 11 428.3333 69.8301 12 476.1667 77.7371

 Regression: S.E.(k) = alpha + beta * Mean(k) alpha -11.403254142558 beta 0.18861339889948 S.E. 0.0065773318024468 T-Stat 28.676278552546 The above regression result suggests that a relationship exists between the mean level and the standard error of this time series.

 Regression: ln S.E.(k) = -3.7070398932205 + 1.3125925397258 * ln Mean(k) alpha -3.7070398932205 beta 1.3125925397258 S.E. 0.054820180413853 T-Stat 23.943601239847 Lambda -0.31259253972575 AI Conclusion: A Box-Cox transform is likely to induce stationarity of variance.

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From this analysis it can be concluded that the time series under investigation should be transformed according to the Box-Cox transformation with lambda = -0.31. For the sake of convenience we apply lambda = 0.
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 [Select module] Main Menu Equation Plotter   Scientific Forecasting   Descriptive Statistics -Central Tendency -Variability -Skewness/Kurtosis -Quartiles -Percentiles -Stem and Leaf -Histogram -Kernel Density -Harrell-Davis -Univariate EDA -Bootstrap -Blocked Bootstrap -Mean Plot -SD Plot -(P)ACF -Spectrum -SD Mean-Plot -Variance Reduction -Correlation -Kendall Rank Corr. -Simple Regression -Bivariate KDE -Box-Cox Linearity -Regression Validation -Back-Back Histo. -Partial Correlation -Trivariate Scatter -Kendall tau Matrix -Notched Boxplots -Star Plot   Distributions -Normal ML Fit -Beta ML Fit -Cauchy ML Fit -Exponential ML Fit -Gamma ML Fit -Lognormal ML Fit -Logistic ML Fit -Neg. Binom. ML Fit -Poisson ML Fit -Weibull ML Fit -Tukey lambda PPCC -Box-Cox Normality   Hypothesis Tests -Mean -Skewness/Kurtosis   Multiple Regression -Estimate Equation   About this server

 Browser Blue Browser Black/White MS Excel MS Word APE.dsAirline.dsAirline_12.ds[daily1996-2.ds[data series.dsdaily96-13.dssomedata.dstest.dswaterDemand.ds original series Moving Average(3) Moving Average(5) Moving Average(s) Hanning residual series squared residuals interpolation stationary variance stationary range PD Buy and Hold PD Filter-rule PD Filter-rule short PD MACD PD MACD short PD BH - Filter PD BH - Filter short PD BH - MACD PD BH - MACD short [command] Edit data Meta data Show data List datasets Timeplot Simple Decomp. VRM SMP RMP ACF ACF(d,D) FRAC(k) BRAC(k) F/BRAC(k) PACF PACF(d,D) Spectrum Spectrum/(P)ACF Estimate Forecast Central Tendency Concentration Moments Histogram Rootogram Skewness/Kurtosis Quartiles Percentiles Variability Financial Markets US Stocks sel. US Stocks all PDensity PDensity append PD short PD short app. PD MA PD app. MA PD MA short PD app. MA short L = -2-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.100.10.20.30.40.50.60.70.80.911.11.21.31.41.51.61.71.81.92 d = 0123 D = 012 s = 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250 K = 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596 p = 0123456789101112 q = 0123 P = 0123 Q = 012 M = 01 Width: Height: Par 1 Par 2 Par 3 Par 4 Par 5

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