Exercise 2 – Cluster and Multiple Regression 1. Run a 2 Group cluster analysis using X22 – Purchase Level. We identify a single solution with two new cluster using X22- Purchase Level using...



Exercise 2 – Cluster and Multiple Regression



1.

Run a 2 Group cluster analysis using X22 – Purchase Level.


We identify a single solution with two new cluster using X22- Purchase Level using Hierarchical Cluster analysis in SPSS. Word’s method was selected in this case because of its tendency to generate clusters that are homogeneous and relatively equal in size (Hair, Black, Babin, and Anderson (2018). Then we run Compare Means to determine the level of purchase and recoded and labeled the new group to (low purchase- high purchase) in SPSS.



Case processing Summary table describes the sample number (N=100) and cases missing (0) in this model. The agglomeration schedule below is a numerical summary of the cluster solution and shows each cluster combined in a specific step. It helps to identify at what point two clusters being combined are considered too different to form a homogeneous group. In this case, it suspected the first two pairs to get joined in the cluster analysis procedure are 37 and 100. The Coefficients value represent the distance (or similarity) statistic used to form the cluster.



















































































































































































































































































































































































































































































































































































































































































































































































































































































































































Agglomeration Schedule



Stage



Cluster Combined



Coefficients



Stage Cluster First Appears



Next Stage



Cluster 1



Cluster 2



Cluster 1



Cluster 2



1



37



100



.000



0



0



54



2



78



99



.000



0



0



22



3



92



98



.000



0



0



9



4



87



97



.000



0



0



14



5



67



96



.000



0



0



31



6



90



95



.000



0



0



11



7



93



94



.000



0



0



8



8



3



93



.000



0



7



50



9



32



92



.000



0



3



29



10



70



91



.000



0



0



28



11



10



90



.000



0



6



39



12



56



89



.000



0



0



39



13



85



88



.000



0



0



16



14



51



87



.000



0



4



33



15



69



86



.000



0



0



29



16



30



85



.000



0



13



81



17



40



83



.000



0



0



52



18



11



82



.000



0



0



78



19



76



81



.000



0



0



23



20



63



80



.000



0



0



34



21



43



79



.000



0



0



50



22



41



78



.000



0



2



43



23



62



76



.000



0



19



77



24



45



75



.000



0



0



48



25



73



74



.000



0



0



26



26



53



73



.000



0



25



79



27



59



71



.000



0



0



37



28



13



70



.000



0



10



47



29



32



69



.000



9



15



55



30



65



68



.000



0



0



33



31



6



67



.000



0



5



67



32



48



66



.000



0



0



45



33



51



65



.000



14



30



74



34



31



63



.000



0



20



57



35



16



61



.000



0



0



75



36



50



60



.000



0



0



43



37



2



59



.000



0



27



44



38



46



58



.000



0



0



47



39



10



56



.000



11



12



80



40



34



55



.000



0



0



56



41



33



54



.000



0



0



57



42



49



52



.000



0



0



44



43



41



50



.000



22



36



51



44



2



49



.000



37



42



65



45



23



48



.000



0



32



80



46



20



47



.000



0



0



65



47



13



46



.000



28



38



66



48



1



45



.000



0



24



63



49



28



44



.000



0



0



59



50



3



43



.000



8



21



68



51



41



42



.000



43



0



84



52



12



40



.000



0



17



71



53



24



39



.000



0



0



63



54



5



37



.000



0



1



76



55



32



36



.000



29



0



81



56



15



34



.000



0



40



77



57



31



33



.000



34



41



73



58



27



29



.000



0



0



60



59



19



28



.000



0



49



62



60



22



27



.000



0



58



75



61



18



26



.000



0



0



66



62



19



25



.000



59



0



83



63



1



24



.000



48



53



79



64



17



21



.000



0



0



67



65



2



20



.000



44



46



78



66



13



18



.000



47



61



85



67



6



17



.000



31



64



72



68



3



14



.000



50



0



82



69



8



9



.000



0



0



76



70



4



7



.500



0



0



87



71



12



35



1.250



52



0



90



72



6



77



2.083



67



0



86



73



31



72



2.917



57



0



93



74



51



64



3.750



33



0



92



75



16



22



4.950



35



60



88



76



5



8



6.150



54



69



83



77



15



62



7.650



56



23



84



78



2



11



9.206



65



18



89



79



1



53



11.081



63



26



89



80



10



23



12.956



39



45



85



81



30



32



14.956



16



55



86



82



3



57



18.384



68



0



88



83



5



19



24.073



76



62



90



84



15



41



30.823



77



51



94



85



10



13



37.881



80



66



94



86



6



30



45.981



72



81



92



87



4



84



54.148



70



0



93



88



3



16



64.519



82



75



91



89



1



2



78.971



79



78



96



90



5



12



98.255



83



71



95



91



3



38



126.179



88



0



96



92



6



51



162.221



86



74



95



93



4



31



202.721



87



73



97



94



10



15



263.390



85



84



98



95



5



6



478.187



90



92



97



96



1



3



706.748



89



91



98





4



5



1355.637



93



95



99



98



1



10



2429.401



96



94



99



99



1



4



7773.000



98



97



0




From the descriptive table below, we compare the number of cluster 1 and cluster 2. It tells us that the sample had more cluster 1 (n = 57) than cluster 2 (n = 43). We compare the mean of cluster 1 and cluster 2, too. The mean of cluster 1 was (64.749) and the mean of cluster 2 was (49.984), which was about14.765 cluster 1 higher than cluster 2.




























































Descriptives



X22 - Purchase Level





N



Mean



Std. Deviation



Std. Error



95% Confidence Interval for Mean



Minimum



Maximum



Lower Bound



Upper Bound



1



57



64.749



5.0727



.6719



63.403



66.095



58.1



77.1



2



43



49.984



4.8512



.7398



48.491



51.477



37.1



57.1



Total



100



58.400



8.8609



.8861



56.642



60.158



37.1



77.1




The ANOVA table below indicates which variables contribute the most to the cluster solution. In this case where one case solution with two clusters, we found F values provide the greatest separation between the two clusters (215.556) and statistically significant at (.000).













































ANOVA



X22 - Purchase Level





Sum of Squares



df



Mean Square



F



Sig.



Between Groups



5343.599



1



5343.599



215.556



.000



Within Groups



2429.401



98



24.790







Total



7773.000



99











# Post hoc tests are not performed for X22 - Purchase Level because there are fewer than three groups.


Then, we recode 2 groups based on mean of each. The cluster with higher mean = High Purchase, we recode it 1. In this case cluster group 1 is higher (mean=64.749). recode it 1=1. The second cluster group (mean=49.984), recode it 2=0 (Lower Purchase).



- Using Recode option to recode the groups:



click Transform -à Record into different variables--à move Clu2-1 from left to right and name (Purchase 1) label (Purchase 1) ---à add ---à OK.


After recoding the two groups, we go to the Variable View in the SPSS file and look for the Values column. Using the Values column, click on None beside the newly created (recoded) variable and add labels so we identify the Higher Purchase and Lower Purchase groups.




Then we run multiple regression models using the outputs from the first section.




2.

Use the newly created two group purchase level variable (after recoding) to Select Cases so you can run two separate multiple regression models. Remember, the Select Cases option is under the Data Tab.


We run two separate multiple regression models.



Case 1 (Higher Purchase):


To select cases: click Data-à Select Cases -à If-à move Purchase 1 to left and add =0.



Then, we run regression Dependent variable (Loyalty) = sum of X19, X20, X21, and IVs are the Four Factors.





























Variables Entered/Removeda



Model



Variables Entered



Variables Removed



Method



1



Product_Value, Marketing, Technical_Support, Customer_Servicesb



.



Enter



a. Dependent Variable: Loyalty



b. All requested variables entered.































Model



R



R Square



Adjusted R Square



Std. Error of the Estimate



1



.576a



.332



.280



.63596



a. Predictors: (Constant), Product_Value, Marketing, Technical_Support, Customer_Services





















































ANOVAa



Model



Sum of Squares



df



Mean Square



F



Sig.



1



Regression



10.432



4



2.608



6.449



.000b



Residual



21.031



52



.404







Total



31.463



56









a. Dependent Variable: Loyalty



b. Predictors: (Constant), Product_Value, Marketing, Technical_Support, Customer_Services










































































Coefficientsa



Model



Unstandardized Coefficients



Standardized Coefficients



t



Sig.



B



Std. Error



Beta



1



(Constant)



7.395



.130





56.815



.000



Customer_Services



.289



.134



.294



2.153



.036



Marketing



.376



.082



.555



4.564



.000



Technical_Support



.011



.095



.013



.114



.910



Product_Value



.322



.105



.412



3.075



.003



a. Dependent Variable: Loyalty







Case 2 (Lower Purchase):






























Variables Entered/Removeda



Model



Variables Entered



Variables Removed



Method



1



Product_Value, Technical_Support, Customer_Services, Marketingb



.



Enter



a. Dependent Variable: Loyalty



b. All requested variables entered.






























Model Summary



Model



R



R Square



Adjusted R Square



Std. Error of the Estimate



1



.612a



.374



.308



.62452



a. Predictors: (Constant), Product_Value, Technical_Support, Customer_Services, Marketing




















































ANOVAa



Model



Sum of Squares



df



Mean Square



F



Sig.



1



Regression



8.860



4



2.215



5.679



.001b



Residual



14.821



38



.390







Total



23.681



42









a. Dependent Variable: Loyalty



b. Predictors: (Constant), Product_Value, Technical_Support, Customer_Services, Marketing





































































Coefficientsa



Model



Unstandardized Coefficients



Standardized Coefficients



t



Sig.



B



Std. Error



Beta



1



(Constant)



6.985



.149





46.850



.000



Customer_Services



.395



.106



.493



3.719



.001



Marketing



.126



.133



.128



.951



.347



Technical_Support



.148



.090



.218



1.634



.111



Product_Value



.362



.128



.389



2.832



.007



a. Dependent Variable: Loyalty






















3.

Run the separate regression models again. Keep the Four Factors as IVs but this time add variables X1 to X5, and X23 to the regression models as IVs.



Case 1 (Higher Purchase):


First, we run regression model after selecting case 1 (High Purchase) following the same steps as Q2. We add the same DV (Loyalty= Sum score) as in second exercise, but we add more IV. Then we run regression.



First time we run regression using method: Enter.





























Variables Entered/Removeda



Model



Variables Entered



Variables Removed



Method



1



X23 - Consider Strategic Alliance, Product_Value, X2 - Industry Type, Marketing, Technical_Support, X5 - Distribution System, X3 - Firm Size, Customer_Services, X1 - Customer Type, X4 - Regionb



.



Enter



a. Dependent Variable: Loyalty



b. All requested variables entered.






























Model Summary



Model



R



R Square



Adjusted R Square



Std. Error of the Estimate



1



.896a



.803



.760



.36749



a. Predictors: (Constant), X23 - Consider Strategic Alliance, Product_Value, X2 - Industry Type, Marketing, Technical_Support, X5 - Distribution System, X3 - Firm Size, Customer_Services, X1 - Customer Type, X4 - Region




















































ANOVAa



Model



Sum of Squares



df



Mean Square



F



Sig.



1



Regression



25.251



10



2.525



18.698



.000b



Residual



6.212



46



.135







Total



31.463



56









a. Dependent Variable: Loyalty



b. Predictors: (Constant), X23 - Consider Strategic Alliance, Product_Value, X2 - Industry Type, Marketing, Technical_Support, X5 - Distribution System, X3 - Firm Size, Customer_Services, X1 - Customer Type, X4 - Region





















































































































Coefficientsa



Model



Unstandardized Coefficients



Standardized Coefficients



t



Sig.



B



Std. Error



Beta



1



(Constant)



5.646



.341





16.548



.000



Customer_Services



.089



.086



.091



1.044



.302



Marketing



.181



.057



.267



3.147



.003



Technical_Support



.146



.062



.178



2.371



.022



Product_Value



.177



.090



.226



1.972



.055



X1 - Customer Type



.328



.131



.249



2.512



.016



X2 - Industry Type



.122



.107



.081



1.133



.263



X3 - Firm Size



.501



.144



.334



3.469



.001



X4 - Region



.287



.157



.193



1.824



.075



X5 - Distribution System



.421



.117



.283



3.609



.001



X23 - Consider Strategic Alliance



.611



.115



.376



5.295



.000



a. Dependent Variable: Loyalty






Then we run it again using method: Backward and look for the Excluded Variables table.


























































































































Excluded Variablesa



Model



Beta In



t



Sig.



Partial Correlation



Collinearity Statistics



Tolerance



2



Customer_Services



.091b



1.044



.302



.152



.566



3



Customer_Services



.085c



.973



.336



.140



.568



X2 - Industry Type



.077c



1.070



.290



.154



.833



4



Customer_Services



.007d



.091



.928



.013



.729



X2 - Industry Type



.071d



.973



.335



.139



.835



Product_Value



.164d



1.624



.111



.228



.422



5



Customer_Services



.050e



.675



.503



.096



.849



X2 - Industry Type



.043e



.583



.562



.083



.877



Product_Value



.112e



1.112



.272



.157



.453



X4 - Region



.157e



1.608



.114



.224



.469



a. Dependent Variable: Loyalty



b. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, Product_Value, X2 - Industry Type, Marketing, Technical_Support, X5 - Distribution System, X3 - Firm Size, X1 - Customer Type, X4 - Region



c. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, Product_Value, Marketing, Technical_Support, X5 - Distribution System, X3 - Firm Size, X1 - Customer Type, X4 - Region



d. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, Marketing, Technical_Support, X5 - Distribution System, X3 - Firm Size, X1 - Customer Type, X4 - Region



e. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, Marketing, Technical_Support, X5 - Distribution System, X3 - Firm Size, X1 - Customer Type







Then we to run regression again and use method: Enter again, but before that we remove the Excluded Variables from the IVs block.






























Variables Entered/Removeda



Model



Variables Entered



Variables Removed



Method



1



X23 - Consider Strategic Alliance, X1 - Customer Type, Technical_Support, X5 - Distribution System, X3 - Firm Size, Marketingb



.



Enter



a. Dependent Variable: Loyalty



b. All requested variables entered.






























Model Summary



Model



R



R Square



Adjusted R Square



Std. Error of the Estimate



1



.878a



.770



.742



.38039



a. Predictors: (Constant), X23 - Consider Strategic Alliance, X1 - Customer Type, Technical_Support, X5 - Distribution System, X3 - Firm Size, Marketing




















































ANOVAa



Model



Sum of Squares



df



Mean Square



F



Sig.



1



Regression



24.229



6



4.038



27.908



.000b



Residual



7.235



50



.145







Total



31.463



56









a. Dependent Variable: Loyalty



b. Predictors: (Constant), X23 - Consider Strategic Alliance, X1 - Customer Type, Technical_Support, X5 - Distribution System, X3 - Firm Size, Marketing





















































































Coefficientsa



Model



Unstandardized Coefficients



Standardized Coefficients



t



Sig.



B



Std. Error



Beta



1



(Constant)



5.614



.271





20.688



.000



Marketing



.194



.053



.287



3.690



.001



Technical_Support



.139



.063



.169



2.210



.032



X1 - Customer Type



.424



.097



.322



4.358



.000



X3 - Firm Size



.569



.116



.380



4.898



.000



X5 - Distribution System



.482



.109



.324



4.419



.000



X23 - Consider Strategic Alliance



.661



.116



.407



5.677



.000



a. Dependent Variable: Loyalty








Case 2 (Lower Purchase):



First, we run regression model after selecting case 2 (Lower Purchase) following the same steps as Q2. We add the same DV (Loyalty= Sum score) as in second exercise, but we add more IV. Then we run regression.



First time we run regression using method: Enter.































Variables Entered/Removeda



Model



Variables Entered



Variables Removed



Method



1



X23 - Consider Strategic Alliance, X3 - Firm Size, Technical_Support, X2 - Industry Type, Marketing, X1 - Customer Type, Product_Value, Customer_Services, X5 - Distribution System, X4 - Regionb



.



Enter



a. Dependent Variable: Loyalty



b. All requested variables entered.






























Model Summary



Model



R



R Square



Adjusted R Square



Std. Error of the Estimate



1



.912a



.832



.779



.35264



a. Predictors: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, Technical_Support, X2 - Industry Type, Marketing, X1 - Customer Type, Product_Value, Customer_Services, X5 - Distribution System, X4 - Region




















































ANOVAa



Model



Sum of Squares



df



Mean Square



F



Sig.



1



Regression



19.702



10



1.970



15.844



.000b



Residual



3.979



32



.124







Total



23.681



42









a. Dependent Variable: Loyalty



b. Predictors: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, Technical_Support, X2 - Industry Type, Marketing, X1 - Customer Type, Product_Value, Customer_Services, X5 - Distribution System, X4 - Region





















































































































Coefficientsa



Model



Unstandardized Coefficients



Standardized Coefficients



t



Sig.



B



Std. Error



Beta



1



(Constant)



5.602



.320





17.506



.000



Customer_Services



.019



.083



.023



.224



.824



Marketing



-.017



.082



-.018



-.213



.833



Technical_Support



.035



.054



.052



.650



.520



Product_Value



-.220



.140



-.236



-1.565



.127



X1 - Customer Type



.420



.169



.260



2.480



.019



X2 - Industry Type



-.159



.117



-.107



-1.355



.185



X3 - Firm Size



.819



.149



.548



5.503



.000



X4 - Region



-.566



.239



-.342



-2.369



.024



X5 - Distribution System



.911



.213



.593



4.281



.000



X23 - Consider Strategic Alliance



.482



.212



.208



2.275



.030



a. Dependent Variable: Loyalty






Then we run it again using method: Backward and look for the Excluded Variables table.





































































































































































Excluded Variablesa



Model



Beta In



t



Sig.



Partial Correlation



Collinearity Statistics



Tolerance



2



Marketing



-.018b



-.213



.833



-.038



.766



3



Marketing



-.019c



-.228



.821



-.040



.768



Customer_Services



.024c



.240



.812



.042



.493



4



Marketing



-.028d



-.346



.731



-.059



.790



Customer_Services



.027d



.270



.788



.046



.494



Technical_Support



.055d



.725



.473



.123



.853



5



Marketing



-.026e



-.320



.751



-.054



.790



Customer_Services



.035e



.342



.734



.058



.495



Technical_Support



.065e



.847



.403



.142



.860



X2 - Industry Type



-.113e



-1.485



.146



-.243



.850



6



Marketing



.003f



.033



.974



.006



.829



Customer_Services



.043f



.417



.679



.069



.497



Technical_Support



.094f



1.268



.213



.207



.940



X2 - Industry Type



-.079f



-1.033



.308



-.170



.896



Product_Value



-.215f



-1.624



.113



-.261



.287



a. Dependent Variable: Loyalty



b. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, Technical_Support, X2 - Industry Type, X1 - Customer Type, Product_Value, Customer_Services, X5 - Distribution System, X4 - Region



c. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, Technical_Support, X2 - Industry Type, X1 - Customer Type, Product_Value, X5 - Distribution System, X4 - Region



d. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, X2 - Industry Type, X1 - Customer Type, Product_Value, X5 - Distribution System, X4 - Region



e. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, X1 - Customer Type, Product_Value, X5 - Distribution System, X4 - Region



f. Predictors in the Model: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, X1 - Customer Type, X5 - Distribution System, X4 - Region





Then we to run regression again and use method: Enter again, but before that we remove the Excluded Variables from the IVs block.





























Variables Entered/Removeda



Model



Variables Entered



Variables Removed



Method



1



X23 - Consider Strategic Alliance, X3 - Firm Size, X1 - Customer Type, X4 - Region, X5 - Distribution Systemb



.



Enter



a. Dependent Variable: Loyalty



b. All requested variables entered.






























Model Summary



Model



R



R Square



Adjusted R Square



Std. Error of the Estimate



1



.897a



.805



.778



.35355



a. Predictors: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, X1 - Customer Type, X4 - Region, X5 - Distribution System




















































ANOVAa



Model



Sum of Squares



df



Mean Square



F



Sig.



1



Regression



19.056



5



3.811



30.491



.000b



Residual



4.625



37



.125







Total



23.681



42









a. Dependent Variable: Loyalty



b. Predictors: (Constant), X23 - Consider Strategic Alliance, X3 - Firm Size, X1 - Customer Type, X4 - Region, X5 - Distribution System













































































Coefficientsa



Model



Unstandardized Coefficients



Standardized Coefficients



t



Sig.



B



Std. Error



Beta



1



(Constant)



5.399



.231





23.412



.000



X1 - Customer Type



.542



.134



.335



4.043



.000



X3 - Firm Size



.699



.130



.468



5.388



.000



X4 - Region



-.336



.174



-.203



-1.938



.060



X5 - Distribution System



.780



.182



.508



4.298



.000



X23 - Consider Strategic Alliance



.565



.190



.244



2.965



.005



a. Dependent Variable: Loyalty






















Oct 30, 2021
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