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An assignment forEC51001 Applied Business and Marketing Research Submitted To Dr. Andrzej Kwiatkowski University of Dundee Submitted On 26 March, 2012 By Swapnil Mali 120004897
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1.0 Introduction1.1 Survey name- Chicken Survey.1.2 Objectives- The objective of this survey was to characterize consumers of chicken.1.3 Aim- Aim is to find out what factors discriminate between those who buy chicken at the who do not.1.4 Key Findings- This survey did help to understand the buying behaviour of customers. Thosewhose expenditure on chicken in week is more, whose age is more, and who feel that chicken at hop. But who have more trust on1.5 Methodology- This survey was done by asking various questions to customers at supermarket pping, income, family,etc. Then this data has been analysed by SPSS and statistic model is generated. Prediction is doneon the basis of this statistical model.EC51001 Applied Business and Marketing Research Page 1
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2.0 Analysis partOn the basis of the result in tables by SPSS, logistic regression analysis has been carried out,which elaborated in detail below. Case Processing Summary Unweighted Casesa N Percent Selected Cases Included in 420 84.0 Analysis Missing Cases 80 16.0 Total 500 100.0 Unselected Cases 0 .0 Total 500 100.0 a. If weight is in effect, see classification table for the total number of cases.The table above shows that there are few missing cases. But most of the data (84%) is beencovered under analysis. It is a good model for the analysis. By default, the tool logisticregression in SPSS performs a listwise deletion of missing data, which means if there is missingvalue for any variable in the model; the entire case will be excluded from the analysis. Dependent Variable Encoding Original Value Internal Value no 0 yes 1This shows the internal value representation for the dependent variable. Those who not buy at Block 0: Beginning Block o Classification Tablea,b Predicted Butcher Percentage Observed no yes Correct Step 0 Butcher no 277 0 100.0 yes 143 0 .0 Overall Percentage 66.0EC51001 Applied Business and Marketing Research Page 2
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a. Constant is included in the model. b. The cut value is .500Step 0: No predictors and just the intercept at this stage.It is recognising 100 % which is ideal butin the case of it is not doing the same. 66% of the total dependent variables were correctlypredicted in the given model (277/ 420 = 0.66). So any random calculation for most frequentcategory for all cases will yield the same correct present i.e. 66 %. o Variables in the Equation B S.E. Wald df Sig. Exp(B) Step 0 Constant -.661 .103 41.228 1 .000 .516In the null model B is the coefficient for the constant. In this table significant value indicates thatnull hypothesis can be neglected (as value less than 0.05). Exp(B) is nothing but the odds ratiowhich can be can calculated as 43/277. Block 1: Method = Enter o Omnibus Tests of Model Coefficients Chi-square df Sig. Step 1 Step 71.655 4 .000 Block 71.655 4 .000 Model 71.655 4 .000This help in deciding the significance of the independent variables in the model. As significantvalues are less than 0.05 we can say that all predictors are statistically significant. o Model Summary -2 Log Cox & Snell R Nagelkerke R Step likelihood Square Square a 1 467.079 .157 .217 a. Estimation terminated at iteration number 5 because parameter estimates changed by less than .001.EC51001 Applied Business and Marketing Research Page 3
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Variation in the dependent variable changes only by 15.7 % due to independent variuables.Nagelkerke R value is 0.217 which shows variance observed is equal to 21.7% between thepredictors and the prediction. o Hosmer and Lemeshow Test Step Chi-square df Sig. 1 3.030 8 .932The difference between observed and expected values should be the minimum. The H-Lgoodness-of- -Significant value (more than 0.05) shows that there is very less or no difference between observedand expected values. o Classification Tablea Predicted Butcher Percentage Observed no yes Correct Step 1 Butcher no 243 34 87.7 yes 89 54 37.8 Overall Percentage 70.7 a. The cut value is .500This table is about the prediction of model. This is a good model with overall 70.7% correctlypredicted variables. o Variables in the Equation B S.E. Wald df Sig. Exp(B) a Step 1 q5 .085 .028 8.975 1 .003 1.088 q51 .022 .007 8.988 1 .003 1.022 q21d .441 .077 32.888 1 .000 1.554 q43b -.269 .074 13.327 1 .000 .764 Constant -3.169 .615 26.539 1 .000 .042 a. Variable(s) entered on step 1: q5, q51, q21d, q43b.With the B values we can form logistic regression equation.Log(p/1-p)= -3.169 + 0.085 x q5 + 0.022 x q51 + 0.441 x q21d + (-0.269) x q43bEC51001 Applied Business and Marketing Research Page 4
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Supermarkets - 0.236 0.246 From the butcher 0.554 Series1 Age 0.022 In a typical week how much do you spend on 0.088 0 0.1 0.2 0.3 0.4 0.5 0.6 Fig. 1: Exp(B) values against different independent variables If score expenditure on chicken in a standard week of increases by 0.088 %. If score age of the respondent buying chicken at increases by 0.022 % whether a respondent agrees (on a seven-point ranking scale) that butchers sell safe chicken increases by 0.554 % I trust (on a seven-point ranking scale) towards supermarkets unit probability of 236 % Classification plot Step number: 1 Observed Groups and Predicted Probabilities 16 + + I I I IF I y y IR 12 + n y +E I n y y n y IQ I y n y y n y y y IU I y n y yn nyy ny y y y yy IE 8 + n nyyn yy nn y nyy ny y y n y yy +N I n nnnny nynnn y ynnn ny y yy y n yy yy IC I nn nnnnnynnnnnyy n y ynnn nn nyy yyy yyn yy yy IY I nnn nnnnnynnnnnnyyn nnnnnnynnynynyyyyyyyn yn yn yy y y y I 4 + nnnynnnnnnnnnnnnnnyn nnnnnnynnynnnnynyynyn yn nn yn n y yy y n + I nnnnnnnnnnnnnnnnnnnnyynnnnnnnnnynnnnynnynynynnynn yn nyyy yy y y n I I n nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnynnnnynnnnynnyyn nyyn yyyy y y yn y y I I nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnynnnnnnnnnnnnyynnnnnn ynny n nynnn yyn y y y y IPredicted ---------+---------+---------+---------+---------+---------+---------+---------+---------+---------- Prob: 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 Group: nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy Predicted Probability is of Membership for yes The Cut Value is .50EC51001 Applied Business and Marketing Research Page 5
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On X axis probabilities are scaled from 0 to 1. Y axis shows the frequency of occurrence. Thisplot is widely spread so predictions are not sharp. But it clearly indicates that more frequencies arethere towards the lower probability values.3.0 Comparison Logistic regression allows one to predict a discrete outcome such as group membership from aset of variables that may be continuous, discrete, dichotomous, or a mix. The goal of thediscriminant function analysis is to predict group membership from a set of predictors. Thelogistic regression is much more relaxed and flexible in its assumptions than the discriminantanalysis. Unlike the discriminant analysis, the logistic regression does not have the requirementsof the independent variables to be normally distributed, linearly related, nor equal variancewithin each group. ell, 1996, p575).A logistic regression and discriminant analysis produces nearly similar results. Both methodscalculate statistical significant coefficients similarly. Logistic regression estimated largercoefficients overall. Either can be helpful in predicting the possibility of who buy chicken at the .Total 71.2% of original grouped cases correctly classified in discriminant analysis, while inlogistic analysis for all cases yield 70.07 % correctly. Whether a respondent agrees (on a seven-point ranking scale) that butchers sell safe chicken is dominant factor in logistic regression aswell as in discriminant analysis.Thought logistic analysis can predict model with slightly more value of probability than that oflogistic regression, both gives the same result. In both the cases probability of customer buy reduces if there is higher value of trust towards supermarkets . Boththe analysis produces same results for other factors as well.4.0 Conclusions i) Expenditure on chicken in a standard week to higher value. ii) Age of the respondent shop d to higher value. iii) Whether a respondent agrees (on a seven-point ranking scale) that butchers sell safe chicken d to higher value.2) Customer i) Trust (on a seven-point ranking scale) towards supermarkets to higher value.3) Logistic regression and discriminant analyses were similar in the model analysis. In order todecide which method should be used, we must consider the assumptions for the application ofeach one.EC51001 Applied Business and Marketing Research Page 6
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ReferencesTabachnick, B.G. and Fidell, L.S. , 1996 , Using Multivariate Statistics. NY: HarperCollins.AppendixLOGISTIC REGRESSION VARIABLES q8d /METHOD=ENTER q5 q51 q21d q43b /CLASSPLOT /PRINT=GOODFIT SUMMARY /CRITERIA=PIN(0.05) POUT(0.10) ITERATE(20) CUT(0.5).Logistic Regression[DataSet3] C:UsersSMMaliDownloadsASSIGNMENT_II.sav Case Processing Summary Unweighted Casesa N Percent Selected Cases Included in 420 84.0 Analysis Missing Cases 80 16.0 Total 500 100.0 Unselected Cases 0 .0 Total 500 100.0 a. If weight is in effect, see classification table for the total number of cases. Dependent Variable EncodingOriginalValue Internal ValueNo 0yes 1Block 0: Beginning Block Classification Tablea,b Predicted Butcher Percentage Observed no yes CorrectStep 0 Butcher No 277 0 100.0 Yes 143 0 .0 Overall Percentage 66.0a. Constant is included in the model.b. The cut value is .500 Variables in the EquationEC51001 Applied Business and Marketing Research Page 7
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B S.E. Wald df Sig. Exp(B)Step 0 Constant -.661 .103 41.228 1 .000 .516 Variables not in the Equation Score df Sig.Step 0 Variables q5 9.903 1 .002 q51 10.968 1 .001 q21d 37.676 1 .000 q43b 9.718 1 .002 Overall Statistics 65.001 4 .000Block 1: Method = Enter Omnibus Tests of Model Coefficients Chi-square df Sig.Step 1 Step 71.655 4 .000 Block 71.655 4 .000 Model 71.655 4 .000 Model Summary -2 Log Cox & Snell R Nagelkerke RStep likelihood Square Square1 467.079a .157 .217a. Estimation terminated at iteration number 5 becauseparameter estimates changed by less than .001. Hosmer and Lemeshow TestStep Chi-square df Sig.1 3.030 8 .932EC51001 Applied Business and Marketing Research Page 8
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Contingency Table for Hosmer and Lemeshow Test Butcher = no Butcher = yes Observed Expected Observed Expected TotalStep 1 1 39 39.037 3 2.963 42 2 36 36.728 6 5.272 42 3 35 34.575 7 7.425 42 4 32 32.047 10 9.953 42 5 32 29.184 10 12.816 42 6 29 27.151 13 14.849 42 7 21 24.497 21 17.503 42 8 20 21.929 22 20.071 42 9 20 19.095 22 22.905 42 10 13 12.756 29 29.244 42 Classification Tablea Predicted Butcher Percentage Observed no yes CorrectStep 1 Butcher no 243 34 87.7 yes 89 54 37.8 Overall Percentage 70.7a. The cut value is .500 Variables in the Equation B S.E. Wald df Sig. Exp(B) aStep 1 q5 .085 .028 8.975 1 .003 1.088 q51 .022 .007 8.988 1 .003 1.022 q21d .441 .077 32.888 1 .000 1.554 q43b -.269 .074 13.327 1 .000 .764 Constant -3.169 .615 26.539 1 .000 .042a. Variable(s) entered on step 1: q5, q51, q21d, q43b.EC51001 Applied Business and Marketing Research Page 9
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Step number: 1 Observed Groups and Predicted Probabilities 16 ++ I I I IF I y y IR 12 + n y +E I n y y n y IQ I y n y y n y y y IU I y n y yn nyy ny y y y yy IE 8 + n nyyn yy nn y nyy ny y y n y yy +N I n nnnny nynnn y ynnn ny y yy y n yy yy IC I nn nnnnnynnnnnyy n y ynnn nn nyy yyy yyn yy yy IY I nnn nnnnnynnnnnnyyn nnnnnnynnynynyyyyyyyn yn yn yy y y y I 4 + nnnynnnnnnnnnnnnnnyn nnnnnnynnynnnnynyynyn yn nn yn n y yy y n + I nnnnnnnnnnnnnnnnnnnnyynnnnnnnnnynnnnynnynynynnynn yn nyyy yy y y n I I n nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnynnnnynnnnynnyyn nyyn yyyy y y yn y y I I nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnynnnnnnnnnnnnyynnnnnn ynny n nynnn yyn y y y y IPredicted ---------+---------+---------+---------+---------+---------+---------+---------+---------+---------- Prob: 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 Group: nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy Predicted Probability is of Membership for yes The Cut Value is .50 Symbols: n - no y - yes Each Symbol Represents 1 Case. EC51001 Applied Business and Marketing Research Page 10
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