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PREDICTION OF FUTURE RATINGS OF COMPANIES, THOSE ARE RATED BY BROKER FIRMS

Fig: 1 Fig: 2

Fig: 3 In these three figures the linearity relationship between the

Star rating and independent variables are shown. Based on

the observations the relationship between star rating and

range of offerings is strong, where as the relation between the

rating and ease of use is very low. Linearity relationship

varies from -1 to +1. None of the relationship is perfectly

positive but rating and range has 0.827, which is highest

among them.

5.04.03.02.01.0

TradeEx

4.0

3.5

3.0

2.5

2.0

Rat

ing

R Sq Linear = 0.556

4.54.03.53.02.5

Ease

4.0

3.5

3.0

2.5

2.0

Rat

ing

R Sq Linear = 0.176

5.04.54.03.53.02.5

Range

4.0

3.5

3.0

2.5

2.0

Rat

ing

R Sq Linear = 0.685

In the above figures of scatter plot between the rating and other variables are interesting because the range of offerings in figure 3 shows better relationship and again it is noticeable that all the variables are positively correlated to the ratings.

Correlations

1 .746* .420 .827**.013 .227 .003

10 10 10 10.746* 1 .229 .434.013 .524 .210

10 10 10 10.420 .229 1 .301.227 .524 .397

10 10 10 10.827** .434 .301 1.003 .210 .397

10 10 10 10

Pearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)N

Rating

TradeEx

Ease

Range

Rating TradeEx Ease Range

Correlation is significant at the 0.05 level (2-tailed).*.

Correlation is significant at the 0.01 level (2-tailed).**.

5.04.54.03.53.02.5

Range

4.0

3.5

3.0

2.5

2.0

Rat

ing

R Sq Linear = 0.685

5.04.54.03.53.02.5

Range

4.0

3.5

3.0

2.5

2.0

Rat

ing

R Sq Cubic =0.85

If rating and range is linearly related then the R 2 value is 0.685, which is increased to 0.85 by considering the relationship as cubic. Hence the transformation of value of rating and range can improve the relationship. Transforming the value of range the relationship increases from 0.685 to 0.762. Even transforming the value of rating and range both the relationship goes stronger to 0.767. Correlation between rating and range is 0.827 which improves after transformation to 0.873 between rating and inverse of range and to 0.876 between squire of rating and inverse of range.

0.300.280.260.240.220.200.180.16

invRn

4.0

3.5

3.0

2.5

2.0

Rat

ing

R Sq Linear = 0.762

0.300.280.260.240.220.200.180.16

invRn

16.00

14.00

12.00

10.00

8.00

6.00

4.00

sqRt

R Sq Linear = 0.767

Model 1: Star rating = 0.864+0.647*Range of offeringsModel 2: Star rating = 6.393 -14.376/ (1+Range of offerings)

Model 3: (Star rating) 2 = 29.651 -86.045/ (1+Range of offerings)Any one may follow the model 2 because model 1 can not relate star rating to the range of offerings. In model 1, if the range of offerings is 4 then rating will be 3.452, where as model 2 can rate 3.518. But with further improvement through transformation can help to build up model 3. Model3 can rate 3.527 for range of offerings of 4. This improvement is possible because of the improvement in correlation between the rating and range.

Model Summary b

.876a .767 .738 1.79269 1.779Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Durbin-Watson

Predictors: (Constant), invRna.

Dependent Variable: sqRtb.

ANOVAb

84.640 1 84.640 26.337 .001a

25.710 8 3.214110.350 9

RegressionResidualTotal

Model1

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), invRna.

Dependent Variable: sqRtb.

Coefficients a

29.659 3.766 7.874 .000-86.045 16.767 -.876 -5.132 .001 1.000 1.000

(Constant)invRn

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig. Tolerance VIFCollinearity Statistics

Dependent Variable: sqRta.

Regressing the Star rating with the independent variables like Trade execution, Ease of use and range of offering this model could be build. Based on the observations on 10 brokers’s this regression model can be developed for predicting the Star rating in the nest year.

210-1-2

Regression Standardized Predicted Value

4.0

3.5

3.0

2.5

2.0

Rating

Dependent Variable: Rating

Scatterplot

R Sq Linear = 0.886

Star rating = 0.345 + 0.255*(Trade Execution) + 0.132*(Ease of use) + 0.459*(Range of offerings)

Correlations

1.000 .746 .420 .827.746 1.000 .229 .434.420 .229 1.000 .301.827 .434 .301 1.000

. .007 .114 .002.007 . .262 .105.114 .262 . .199.002 .105 .199 .

10 10 10 1010 10 10 1010 10 10 1010 10 10 10

RatingTradeExEaseRangeRatingTradeExEaseRangeRatingTradeExEaseRange

Pearson Correlation

Sig. (1-tailed)

N

Rating TradeEx Ease Range

Star rating is positively related to ratings for trade execution, ease of use and range of offerings. Out of these three qualities, range of offerings is highly correlated to Star ratings (0.827 and statistically significant in 95% confidence) where as the ease of use is insignificant in correlation with star rating and these are reflected in the model also.

Model Summary b

.941a .886 .828 .2431 1.923Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Durbin-Watson

Predictors: (Constant), Range, Ease, TradeExa.

Dependent Variable: Ratingb.

Higher value of R2 (0.886) of this model signifies the goodness of fit or the sample regression line is fitting well with the observations on 10 broker platform.

ANOVAb

2.745 3 .915 15.485 .003a

.355 6 .0593.100 9

RegressionResidualTotal

Model1

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), Range, Ease, TradeExa.

Dependent Variable: Ratingb.

In this model the explained sum squire (ESS) is 2.745 and residual sum of squire is 0.355 which is the reason for goodness of fit. Here R2 is equal to ESS/TSS and TSS=ESS+RSS, TSS is total sum squire. Analysis of variance or ANOVA is useful for testing the significance of the model as Star rating has three independent variables. In the f-test for this model the degree of freedom for numerator is 3 because it has three independent variables and denominator has 10 – four variables = 6, degree of freedom. Hence from the f table it could be found the standard value is 4.76. But the model has 15.485 of f-test value which is in the critical or significance zone with p value of 0.003. As the p value is less than 0.05, hence the whole model is significant. But if the model is looked in to detail that the easy of use has insignificant correlation with the Star rating as well as the p value of t-test is lower than the 0.05. Hence the null hypothesis of assumption that the coefficients are equal and zero can be rejected.

Coefficients a

.345 .531 .650 .540

.255 .086 .460 2.978 .025 .801 1.249

.132 .140 .138 .944 .382 .897 1.114

.459 .123 .586 3.722 .010 .768 1.302

(Constant)TradeExEaseRange

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig. Tolerance VIFCollinearity Statistics

Dependent Variable: Ratinga.

Three independent variables have standard t value of 1.943 at the 6 degree of freedom. In this model trade execution and range of offerings have t-test value of 2.978 and 3.722, which is higher than the 1.943 or p value is lower than 0.05. Hence for these two variables the hypothesis of considering the coefficient with zero value can be rejected. Star rating = 0.345 + 0.255*(Trade Execution) + 0.132*(Ease of use) + 0.459*(Range of offerings)

In this model if the trade execution drops by -2 then the effect on star rating will be – (0.255*2) = -0.51. Or the star rating will be decreased by 0.51. Where as the decrease in range of offerings by -3 will impact on Star rating by 0.459*3= 1.377. Or the star rating will be decreased by 1.337. Change in range of offerings will be impacted more for this model.

This regression model has fewer diseases (Low Multicollinerity as VIF is nearly 1, no auto regression as DW is nearly 2) but can be improved by Increasing the sample sizeInclusion of more variablesTransforming variables.Transforming all four variables it can be observed that the correlation is significantly improved.

Correlations

1.000 .746 .420 .827.746 1.000 .229 .434.420 .229 1.000 .301.827 .434 .301 1.000

. .007 .114 .002.007 . .262 .105.114 .262 . .199.002 .105 .199 .

10 10 10 1010 10 10 1010 10 10 1010 10 10 10

RatingTradeExEaseRangeRatingTradeExEaseRangeRatingTradeExEaseRange

Pearson Correlation

Sig. (1-tailed)

N

Rating TradeEx Ease Range

Correlations

1.000 -.876 .813 .505-.876 1.000 -.636 -.288.813 -.636 1.000 .149.505 -.288 .149 1.000

. .000 .002 .068.000 . .024 .210.002 .024 . .341.068 .210 .341 .

10 10 10 1010 10 10 1010 10 10 1010 10 10 10

sqRtinvRninvTrsqEsqRtinvRninvTrsqEsqRtinvRninvTrsqE

Pearson Correlation

Sig. (1-tailed)

N

sqRt invRn invTr sqE

210-1-2

Regression Standardized Predicted Value

16.00

14.00

12.00

10.00

8.00

6.00

4.00

sqRt

Dependent Variable: sqRt

Scatterplot

R Sq Linear = 0.956

In this model the R2 value or goodness of fit is now increased to 0.956. And all the three variables are significant from t-test.

Coefficients a

24.261 2.399 10.112 .000-49.867 11.312 -.508 -4.408 .005 .558 1.793-20.291 5.063 -.447 -4.008 .007 .595 1.681

.242 .074 .292 3.253 .017 .915 1.093

(Constant)invRninvTrsqE

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig. Tolerance VIFCollinearity Statistics

Dependent Variable: sqRta.

(Star rating) 2 = 24.261 -20.291/ (1+Trade Execution) + 0.242(Ease of use) 2 -49.867/ (1+Range of offerings) This improved model is built up by transforming the variables and excluding the other possibilities of improvement a model.