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ASSIGNMENT




                       Centre for Management Studies
                   University of Petroleum & Energy Studies




Submitted to:                                                 Submitted by:

Prof. I. Krishnamurthy                                         Richa Pandey

                                                              MBA (Avm)

                                                               R120108036
Dataset
Consumption    Income   Liquid Asset
    220         238.1      182.7
   222.7        240.9       183
   223.8        245.8      184.4
   230.2        248.8       187
    234        253.3       189.4
   236.2       256.1       192.2
    236        255.9       193.8
   234.1       255.9       194.8
   233.4       254.4       197.3
   236.4       254.8        197
    239         257        200.3
   243.2       260.9       204.2
   248.7        263        207.6
   253.7       271.5       209.4
   259.9       276.5       211.1
   261.8       281.4       213.2
   263.2        282        214.1
   263.7       286.2       216.5
   263.4       287.7       217.3
   266.9        291        217.3
   268.9       291.1       218.2
   270.4       294.6       218.5
   273.4       296.1       219.8
   272.1       293.3       219.5
   268.9       291.3       220.5
   270.9       292.6       222.7
   274.4       299.9        225
   278.7       302.1       229.4
   283.8       305.9       232.2
   289.7       312.5       235.2
   290.8       311.3       237.2
   292.8       313.2       237.7
   295.4       315.4        238
   299.5       320.3       238.4
   298.6        321        240.1
   299.6       320.1       243.3
    297        318.4       246.1
   301.6       324.8        250
Solution
Solving the given data set by using regression analysis we get-


Regression Analysis: C1 versus C2, C3

The regression equation is


C1 = - 10.6 + 0.682 C2 + 0.373 C3


Predictor           Coef      SE Coef           T          P
Constant         -10.627        3.273       -3.25      0.003
C2               0.68166      0.07098        9.60      0.000
C3               0.37252      0.09656        3.86      0.000


S = 1.76348          R-Sq = 99.5%           R-Sq(adj) = 99.5%


Analysis of Variance



Source                  DF       SS         MS            F           P
Regression               2    23165      11583      3724.45       0.000
Residual Error          35      109          3
Total                   37    23274


Source      DF    Seq SS
C2           1     23119
C3           1        46




   (i)     The regression model will be
           Consumption = -10.6 + 0.682 Income + 0.373 liquid asset.

   (ii)    Here the value of R square = 99.5 %. Since R square is very high then it can
           be said that there may be existing the problem of multi co -linearity

   (iii)   Standard Error is 3.273, which is not high. So it will be difficult to say
           anything out of this observation.
(iv)    “t-value” for Income(C1) and liquid asset(C2) are 9.60 and 3.86 respectively,
            and both are greater than 2, it implies that these values are significant. So
            again the problem of multi co-linearity may exist.




Correlations: C2, C3


Pearson correlation of C2 and C3 = 0.988
P-Value = 0.000

Correlation between the Income and liquid asset is very high , that is 0.988. It is an indication for
the existence of correlation

After dropping the last observation the new result will be as follows


Regression Analysis: C1 versus C2, C3

The regression equation is
C1 = - 12.2 + 0.657 C2 + 0.413 C3


Predictor            Coef        SE Coef            T           P
Constant          -12.185          3.396        -3.59       0.001
C2                0.65690        0.07193         9.13       0.000
C3                0.41272        0.09902         4.17       0.000


S = 1.73621            R-Sq = 99.5%             R-Sq(adj) = 99.5%


Analysis of Variance

Source                     DF       SS          MS             F            P
Regression                  2    21647       10824       3590.60        0.000
Residual Error             34      102           3
Total                      36    21750
Source      DF     Seq SS
C2           1      21595
C3           1         52

After dropping the last observation the new regression model is

Consumption = -12.185 + 0.657 Income + 0.413 liquid asset.

Here there is not much change is the coefficient after dropping an observation. So we
cannot conclude anything from this observation.

Variance Inflation Factor (VIF) :
VIF(Income) = 1/(1-Rsquare i )

Regression Analysis: C2 versus C3

The regression equation is
C2 = - 5.64 + 1.34 C3


Predictor           Coef         SE Coef       T          P
Constant          -5.638           7.628   -0.74      0.465
C3               1.34394         0.03528   38.09      0.000


S = 4.14102           R-Sq = 97.6%          R-Sq(adj) = 97.5%


Analysis of Variance

Source                   DF         SS      MS           F           P
Regression                1      24884   24884     1451.15       0.000
Residual Error           36        617      17
Total                    37      25502


Unusual Observations
Obs   C3       C2    Fit                   SE Fit     Residual       St Resid
 13 208 263.000 273.364                     0.726      -10.364          -2.54R

R denotes an observation with a large standardized
residual.

VIF = 41.322

When the value of the predictor is more than 10 then the predictors are highly correlated.
Theils measure
Excluding Income
Regression Analysis: C1 versus C3

The regression equation is
C1 = - 14.5 + 1.29 C3


Predictor      Coef     SE Coef        T       P
Constant    -14.470       6.107    -2.37   0.023
C3          1.28863     0.02825    45.62   0.000


S = 3.31535     R-Sq = 98.3%      R-Sq(adj) = 98.3%


Analysis of Variance

Source            DF       SS       MS         F       P
Regression         1    22878    22878   2081.45   0.000
Residual Error    36      396       11
Total             37    23274


Unusual Observations

Obs    C3        C1        Fit    SE Fit   Residual   St Resid
 34   238   299.500    292.739     0.844      6.761       2.11R

R denotes an observation with a large standardized residual.


Excluding liquid asset
Regression Analysis: C1 versus C2
The regression equation is
C1 = - 7.16 + 0.952 C2


Predictor       Coef    SE Coef        T       P
Constant      -7.160      3.705    -1.93   0.061
C2           0.95213    0.01300    73.25   0.000


S = 2.07583     R-Sq = 99.3%      R-Sq(adj) = 99.3%


Analysis of Variance

Source            DF       SS       MS         F       P
Regression         1    23119    23119   5365.14   0.000
Residual Error    36      155        4
Total             37    23274




Unusual Observations

Obs    C2        C1        Fit    SE Fit   Residual   St Resid
 13   263   248.700    243.252     0.432      5.448       2.68R

R denotes an observation with a large standardized residual.




m = 0.9953-((0.9953-0.9829)+(0.9953-0.9933))

       = 0.9809

Since m is not equal to zero ,hence we can say that multicollinearity exists.

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Regression analysis

  • 1. ASSIGNMENT Centre for Management Studies University of Petroleum & Energy Studies Submitted to: Submitted by: Prof. I. Krishnamurthy Richa Pandey MBA (Avm) R120108036
  • 2. Dataset Consumption Income Liquid Asset 220 238.1 182.7 222.7 240.9 183 223.8 245.8 184.4 230.2 248.8 187 234 253.3 189.4 236.2 256.1 192.2 236 255.9 193.8 234.1 255.9 194.8 233.4 254.4 197.3 236.4 254.8 197 239 257 200.3 243.2 260.9 204.2 248.7 263 207.6 253.7 271.5 209.4 259.9 276.5 211.1 261.8 281.4 213.2 263.2 282 214.1 263.7 286.2 216.5 263.4 287.7 217.3 266.9 291 217.3 268.9 291.1 218.2 270.4 294.6 218.5 273.4 296.1 219.8 272.1 293.3 219.5 268.9 291.3 220.5 270.9 292.6 222.7 274.4 299.9 225 278.7 302.1 229.4 283.8 305.9 232.2 289.7 312.5 235.2 290.8 311.3 237.2 292.8 313.2 237.7 295.4 315.4 238 299.5 320.3 238.4 298.6 321 240.1 299.6 320.1 243.3 297 318.4 246.1 301.6 324.8 250
  • 3. Solution Solving the given data set by using regression analysis we get- Regression Analysis: C1 versus C2, C3 The regression equation is C1 = - 10.6 + 0.682 C2 + 0.373 C3 Predictor Coef SE Coef T P Constant -10.627 3.273 -3.25 0.003 C2 0.68166 0.07098 9.60 0.000 C3 0.37252 0.09656 3.86 0.000 S = 1.76348 R-Sq = 99.5% R-Sq(adj) = 99.5% Analysis of Variance Source DF SS MS F P Regression 2 23165 11583 3724.45 0.000 Residual Error 35 109 3 Total 37 23274 Source DF Seq SS C2 1 23119 C3 1 46 (i) The regression model will be Consumption = -10.6 + 0.682 Income + 0.373 liquid asset. (ii) Here the value of R square = 99.5 %. Since R square is very high then it can be said that there may be existing the problem of multi co -linearity (iii) Standard Error is 3.273, which is not high. So it will be difficult to say anything out of this observation.
  • 4. (iv) “t-value” for Income(C1) and liquid asset(C2) are 9.60 and 3.86 respectively, and both are greater than 2, it implies that these values are significant. So again the problem of multi co-linearity may exist. Correlations: C2, C3 Pearson correlation of C2 and C3 = 0.988 P-Value = 0.000 Correlation between the Income and liquid asset is very high , that is 0.988. It is an indication for the existence of correlation After dropping the last observation the new result will be as follows Regression Analysis: C1 versus C2, C3 The regression equation is C1 = - 12.2 + 0.657 C2 + 0.413 C3 Predictor Coef SE Coef T P Constant -12.185 3.396 -3.59 0.001 C2 0.65690 0.07193 9.13 0.000 C3 0.41272 0.09902 4.17 0.000 S = 1.73621 R-Sq = 99.5% R-Sq(adj) = 99.5% Analysis of Variance Source DF SS MS F P Regression 2 21647 10824 3590.60 0.000 Residual Error 34 102 3 Total 36 21750
  • 5. Source DF Seq SS C2 1 21595 C3 1 52 After dropping the last observation the new regression model is Consumption = -12.185 + 0.657 Income + 0.413 liquid asset. Here there is not much change is the coefficient after dropping an observation. So we cannot conclude anything from this observation. Variance Inflation Factor (VIF) : VIF(Income) = 1/(1-Rsquare i ) Regression Analysis: C2 versus C3 The regression equation is C2 = - 5.64 + 1.34 C3 Predictor Coef SE Coef T P Constant -5.638 7.628 -0.74 0.465 C3 1.34394 0.03528 38.09 0.000 S = 4.14102 R-Sq = 97.6% R-Sq(adj) = 97.5% Analysis of Variance Source DF SS MS F P Regression 1 24884 24884 1451.15 0.000 Residual Error 36 617 17 Total 37 25502 Unusual Observations Obs C3 C2 Fit SE Fit Residual St Resid 13 208 263.000 273.364 0.726 -10.364 -2.54R R denotes an observation with a large standardized residual. VIF = 41.322 When the value of the predictor is more than 10 then the predictors are highly correlated.
  • 6. Theils measure Excluding Income Regression Analysis: C1 versus C3 The regression equation is C1 = - 14.5 + 1.29 C3 Predictor Coef SE Coef T P Constant -14.470 6.107 -2.37 0.023 C3 1.28863 0.02825 45.62 0.000 S = 3.31535 R-Sq = 98.3% R-Sq(adj) = 98.3% Analysis of Variance Source DF SS MS F P Regression 1 22878 22878 2081.45 0.000 Residual Error 36 396 11 Total 37 23274 Unusual Observations Obs C3 C1 Fit SE Fit Residual St Resid 34 238 299.500 292.739 0.844 6.761 2.11R R denotes an observation with a large standardized residual. Excluding liquid asset Regression Analysis: C1 versus C2
  • 7. The regression equation is C1 = - 7.16 + 0.952 C2 Predictor Coef SE Coef T P Constant -7.160 3.705 -1.93 0.061 C2 0.95213 0.01300 73.25 0.000 S = 2.07583 R-Sq = 99.3% R-Sq(adj) = 99.3% Analysis of Variance Source DF SS MS F P Regression 1 23119 23119 5365.14 0.000 Residual Error 36 155 4 Total 37 23274 Unusual Observations Obs C2 C1 Fit SE Fit Residual St Resid 13 263 248.700 243.252 0.432 5.448 2.68R R denotes an observation with a large standardized residual. m = 0.9953-((0.9953-0.9829)+(0.9953-0.9933)) = 0.9809 Since m is not equal to zero ,hence we can say that multicollinearity exists.
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