regression analysis

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

220 238.1 182.7222.7 240.9 183223.8 245.8 184.4230.2 248.8 187

234 253.3 189.4236.2 256.1 192.2236 255.9 193.8

234.1 255.9 194.8233.4 254.4 197.3236.4 254.8 197239 257 200.3

243.2 260.9 204.2248.7 263 207.6253.7 271.5 209.4259.9 276.5 211.1261.8 281.4 213.2263.2 282 214.1263.7 286.2 216.5263.4 287.7 217.3266.9 291 217.3268.9 291.1 218.2270.4 294.6 218.5273.4 296.1 219.8272.1 293.3 219.5268.9 291.3 220.5270.9 292.6 222.7274.4 299.9 225278.7 302.1 229.4283.8 305.9 232.2289.7 312.5 235.2290.8 311.3 237.2

292.8 313.2 237.7295.4 315.4 238299.5 320.3 238.4298.6 321 240.1299.6 320.1 243.3297 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 PConstant -10.627 3.273 -3.25 0.003C2 0.68166 0.07098 9.60 0.000C3 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 PRegression 2 23165 11583 3724.45 0.000Residual Error 35 109 3Total 37 23274

Source DF Seq SSC2 1 23119C3 1 46

(i) The regression model will beConsumption = -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 = 0.988P-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 isC1 = - 12.2 + 0.657 C2 + 0.413 C3

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

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



Source DF Seq SSC2 1 21595C3 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 isC2 = - 5.64 + 1.34 C3

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

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



Unusual ObservationsObs 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




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



Unusual Observations

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


Excluding liquid asset




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



Unusual Observations

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


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.

regression analysis

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