Unexpected result for Multivariate regression/Multiple Linear Regression solution

I am doing analysis on the observations that are taken from a system.

Could you please help me to find an answer for my following question ?

I have applied Multiple Linear Regression Analysis on matlab in the attached files. And also I used the mvregress function on Matlab for the multivariate regression. But the solution includes negatif values which is not acceptable where I have 8 independent variable.

Since the solution vector will represent some factors that will give us information about the sytem utilization which can’t be negatif value.

I have taken some observations below which includes information on service level (Service A, Service B, Service C, Service D). I have 4 independent variable and 1 dependent output here. Variables are: CPU impact of Service A service, CPU impact of Service B service ...

In the attached file you can find the the solution on service level.

If I continue one step further, we have some type of subscribers so called prepaid and postpaid. And I want to find a solution on the type of subscriber level as well. So the independent variable number should be twice wrt the service level analysis. CPU impact of Service A service for Prepaid subscriber, CPU impact of Service A service for Postpaid subscribers, CPU impact of Service B service for Prepaid subscribers, CPU impact of Service B service for Postpaid subscribers, ...

Unfortunately the solution where I have 8 independet variable and 1 dependet variable has some negatif values which is not acceptable.

Should I apply an other technique rather than Multiple Linear Analysis? MANOVA?

To switch to the type of subscriber level:

Assumption:

----------------

%30 of the total Service D are coming from Prepaid Subscribers,

%52 of the total Service A sessions are coming from Prepaid Subscribers,

%53 of the total Service B session/direct debit is coming from Prepaid Subscribers,

%1 of the total Service C traffic is coming from Prepaid Subscribers.

CPU Impact:

-------------

>> A=[150.86 14.01 0.91 50.03 139.26 12.46 89.72 116.73;

152.34 13.74 0.89 49.52 140.62 12.18 88.21 115.54;

152.89 13.20 0.87 48.68 141.13 11.71 86.06 113.58;

156.48 13.38 0.86 48.52 144.45 11.87 85.22 113.20;

156.17 14.17 0.91 52.38 144.15 12.56 90.32 122.21;

197.58 13.58 0.54 45.59 182.39 12.05 52.99 106.39;

159.46 13.11 0.32 39.18 147.20 11.63 31.64 91.41 ;

161.17 13.72 0.89 51.10 148.78 12.16 87.62 119.24;

153.40 13.71 0.98 49.36 141.60 12.15 97.19 115.17;

163.60 13.71 0.97 48.24 151.02 12.15 95.68 112.56;

150.73 15.16 0.80 48.39 139.13 13.44 79.32 112.90;

149.37 14.71 0.81 48.80 137.88 13.05 80.08 113.86;

152.71 14.65 0.80 48.38 140.97 12.99 78.99 112.88;

156.71 14.53 0.78 48.27 144.65 12.88 76.83 112.64;

154.62 14.69 0.23 51.53 142.73 13.03 23.11 120.23 ;

189.39 14.43 0.51 47.10 174.83 12.79 50.09 109.90;

163.25 14.14 0.32 40.53 150.70 12.53 31.70 94.56 ;

161.25 14.66 0.78 49.88 148.85 13.00 77.49 116.40;

154.51 14.77 0.88 48.94 142.63 13.09 87.50 114.18;

157.83 14.23 0.87 47.40 145.69 12.61 86.23 110.61];

>>

>>

>>

>> size(A)

ans =

    20     8

>>

>>

>>

>>

>>

>>

>>

C=[39.78;

39.54 ;

39.20 ;

39.37 ;

40.88 ;

41.77 ;

34.06 ;

40.87 ;

39.96 ;

41.04 ;

38.99 ;

38.74 ;

38.90 ;

39.00 ;

40.18 ;

41.00 ;

34.93 ;

40.12 ;

39.52 ;

39.48];

>>

>>

>> size(C)

ans =

    20     1

>> predictors=A;

target=C;

>> pred_cell = cell(20,1);

>> for i = 1:20,

    % For each of the n points, set up a design matrix specifying

    % a different intercept but common slope terms

    pred_cell{i,1} = [eye(1), repmat(predictors(i,:),1,1)];

end

b = mvregress(pred_cell, target);

>>

>>

>>

>>

>> b

b =

   -0.9161

   -6.6618

   -2.0475

-11.1524

-13.1241

    7.3208

    2.2994

    0.1311

    5.8361

>> C

C =

   39.7800

   39.5400

   39.2000

   39.3700

   40.8800

   41.7700

   34.0600

   40.8700

   39.9600

   41.0400

   38.9900

   38.7400

   38.9000

   39.0000

   40.1800

   41.0000

   34.9300

   40.1200

   39.5200

   39.4800

>> Y

Y =

   39.5506

   39.5784

   39.0582

   39.5684

   41.1379

   41.6759

   34.1781

   41.2660

   40.0695

   40.1857

   38.7558

   38.9063

   39.1285

   39.1432

   39.8764

   41.2011