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  • #36612

    indresh
    Participant

    dear all,
    this is the regression equation, can some expert explain me in detail the interpretation of this and the best equation between the mou and the significantly related factors
    thanks in advance
    rgds
    The regression equation is
    MOUs =36599928 – 789 Completion Call Rate
    + 36360 Trunk Route Utilization Rate (N
    + 38967 Trunk Route Congestion Rate (NB + 559 TCH Congestion (secs)
    – 159041 TCH Blocking (%) – 308935 TCH Assignment Success Rate
    + 1685 TCH Setup Success Rate – 46118 TCH HO Success Rate
    – 287708 TCH Drop Call Rate – 7808 Erlang Minutes Per Drop
    Predictor Coef StDev T P VIF
    Constant 36599928 12679454 2.89 0.034
    Completi -789 4730 -0.17 0.874 4.5
    Trunk Ro 36360 3300 11.02 0.000 3.6
    Trunk Ro 38967 12856 3.03 0.029 4.5
    TCH Cong 559.2 133.2 4.20 0.009 4.7
    TCH Bloc -159041 108851 -1.46 0.204 4.4
    TCH Assi -308935 133528 -2.31 0.069 2.3
    TCH Setu 1685 2697 0.62 0.560 3.1
    TCH HO S -46118 37986 -1.21 0.279 4.1
    TCH Drop -287708 160825 -1.79 0.134 2.0
    Erlang M -7808 6755 -1.16 0.300 1.9
    S = 21072 R-Sq = 99.4% R-Sq(adj) = 98.1%
    Analysis of Variance
    Source DF SS MS F P
    Regression 10 3.42892E+11 34289246051 77.22 0.000
    Residual Error 5 2220118872 444023774
    Total 15 3.45113E+11
    Source DF Seq SS
    Completi 1 2.39871E+11
    Trunk Ro 1 74613158797
    Trunk Ro 1 8446748250
    TCH Cong 1 11878456059
    TCH Bloc 1 1120127731
    TCH Assi 1 5153312380
    TCH Setu 1 1195061
    TCH HO S 1 196517334
    TCH Drop 1 1018707527
    Erlang M 1 593112860
    Obs Completi MOUs Fit StDev Fit Residual St Resid
    1 36.3 3512121 3512386 19719 -265 -0.04
    2 36.7 3665404 3670482 14181 -5078 -0.33
    3 36.7 3648550 3640871 13699 7680 0.48
    4 35.7 3804114 3803195 17763 919 0.08
    5 37.9 3846882 3831783 13389 15099 0.93
    6 42.5 3895527 3922642 16464 -27115 -2.06R
    7 39.9 3884823 3880760 20016 4063 0.62
    8 33.3 3481989 3491303 20330 -9314 -1.68
    9 40.9 3878068 3875680 19044 2389 0.26
    10 40.3 3908256 3902561 16354 5695 0.43
    11 39.5 3878523 3874420 12268 4103 0.24
    12 39.1 3968607 3984011 17553 -15404 -1.32
    13 41.4 3948145 3932004 18130 16141 1.50
    14 40.4 3871377 3863087 18657 8290 0.85
    15 39.6 3893843 3911944 19113 -18102 -2.04R
    16 39.9 3926892 3915992 19902 10900 1.57
    R denotes an observation with a large standardized residual

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    #106061

    MBBoli
    Participant

    Hi Indresh,
     
    haven’t got to much time to go into in in great detail, but I would try the following:
    1. Look at R² and R²adj -> look both pretty good!
    2. Reduce model to have only significant factors in it -> erase all factors with p-value > 0,05 one by one starting with highes p (e.g. this one: Completi -789 4730 -0.17 0.874 4.5)
    3. Check VIFs. Should be below 5 -> seems ok!
    For further details refer to appropriate literature, e.g (Intro to regression analysis by Motgomery & Peck)
    Hope that helped!
     

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    #106073

    Robert Butler
    Participant

    Your regression equation is telling you that you still have a lot of work to do.  What you have posted is a gross overfit of the existing data.  As posted it appears all you have done is take 9 regressors and run them against 16 measurements and dumped the results to a file.
      If we ignore everything but the printout you have provided then what your printout is saying is the following:
      The p values would indicate the only variables with any significant degree of correlation to MOU’s are:
      Trunk Route Utilization Rate
      Trunk Route Congestion Rate
     and TCH congestion.
      It is suggesting the only model your 16 data points can support would be one with these three terms.
      What your printout is telling me is the following:
      1.The magnitude of the MOU measure is such that your first move should be to build a model against the log of the values. A quick check of their distribution indicates they look to be log normal.
     2. You have not checked to see if the various regressors are independent of one another.  The printout gives me the impression that some of the regressors are related to the others to the point where they may not be independent of one another (for example Trunk Route Congestion and TCH Congestion). While the VIF’s are within limits they are large and they may point to underlying problems. You should also plot MOU against all of the regressors of interest and you should plot all of the regressors against each other. These plots will help you identify problems with your choice of regressors and, if your pet variable is not one of the three listed above, it may help you understand why not.
    3. You didn’t run your analysis using any kind of stepwise procedure.  If you don’t have this capability you will have to do it manually. You can use the existing model as the first step in this kind of procedure.  Completion call rate has the worst p value so the first step in your backward procedure would be to eliminate it and re-run the analysis.  Continue doing this until the remaining terms all have p< .05 (Yes, this is arbitrary, but I’m assuming you have happenstance data and not data from a design).
    4. Points 6, 12, and 15 are tails wagging a dog. The residual plot indicates you need to investigate the circumstances surrounding these three because they appear to be significantly different from the other data you gathered.
    5. The range of your Y is pretty narrow. If you are going to attempt to use the final equation for predictive purposes you will have to keep this in mind because the model has only been fit over the range of your initial data and things may change drastically outside of the current limits.

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