Applying Quantitative Reasoning Skills
The Australian paper giant Auspaper has a long history of success in production of paper products. The company is an affiliated franchise of Pinnon Paper Industries. The historical backdrop of the company is very encouraging, and they used to produce almost equal amount of paper products compared to the total products all the similar companies. The major customers belonged to two different market sectors. The company used to sell their products to the magazine and newspaper sectors through direct sales or through dealer. The company also exported paper products to various countries of Asia, Middle East, USA, and Europe and in different provinces of India as well as Africa.
The future problem areas were identified by the research and development wing of Auspaper and some of the concerns bothered the management. The expansion of social media, along with increasing market of electronic gadgets was two of the most important factors for probable future decline in sale. The company indented to perform a market research and they approached the research team manager Hugo Barra, a PhD in Data Science and a Master in Digital Marketing at ANALYTICS7. The job of analysing the project was given to the scholar after a long conversation on the scope of the research.
The key factor was identified as edification of strategic alliance in a business to business environment with respect to the customer satisfaction with Auspaper’s functioning and products. The likelihood of the customers was also evaluated with a logistic model for further understanding the trend of strategic alliance. Furthermore a forecasting for last three quarters of sales was conducted for the year 2017.
The first task was to assess the dependent factor of the collected data fields of 200 customers. The descriptive values of strategic alliance were found for satisfaction level of the customers. The job was performed using Microsoft Excel Tool pack facility. The average satisfaction score was found as 6.95 in scale of 10. Indication of almost 70% likely future purchase of Auspaper products was observed. The deviation of satisfaction score of 1.24 was also noticed. This factor was a very disturbing figure as 12% deviation in the negative side could deter the future planning of the company. The median was 7.05 and a Gaussian nature of the distribution of satisfaction score was seen with a very minor skewness of 0.09. The mode of the data was at 5.4; this indicated the satisfaction level for most of the customers. This trend was not at all encouraging for the company. The range of the satisfaction was noted to be 5.2 with minimum satisfaction level at 4.7 and maximum at 9.9. Total 200 samples were analyzed for this study and the standard error was calculated as 0.08, which provided an approximate estimate for the population mean. The 95% confidence interval for the satisfaction score was between 6.77 and 7.12, the compactness of the confidence interval was a useful result to analyse the customer likelihood for the paper products of Auspaper.
The entire data was split into two subcategories based on the strategic alliance choice of the customers. The first part consisted of 86 customers who preferred to continue future alliance with the company. The average satisfaction level for those customers was found to be 7.94, which was expectedly greater than that of the total data set. The median was at 7.9 and the mode at 7.6. Almost perfect normal distribution for the satisfaction curve was seen with a negligible skewness of -0.08. The consistency and homogeneity for the customers was evident from the descriptive figures. The 95% confidence interval was calculated as [7.75, 8.13]. The second section of customers with preference of discontinuing their strategic alliance with Auspaper was 114 in numbers. It was noticed that most of the customers were unhappy with services in the collected sample data. The average satisfaction was 6.2 and the median was at 6.3, the most important observation was for the median which was 5.4 for the data set. The distribution had a skewness of 0.26 with kurtosis of -0.77.
Correlation Analysis
Identifying Factors Influencing Customer Satisfaction
The satisfaction of customers was the dependent variable and it was cross checked with the independent factors. Multiple correlation technique was used for the purpose and association levels among the factors were noticed.
The probable dependent variable was customer satisfaction score, which was continuous in nature. The strategic alliance was a binary dependent variable. Initially correlation with these dependent variables was noticed. In order to narrow down on the search of independent factors, and finalize the list for most significant independent factors multiple correlation matrix was constructed using the excel tool pack using this set of 15 variables.
For the purpose of visual influence, initially scatter diagrams were drawn. The diagrams represented the trend of the dependent factor based on the independent factors. The delivery speed was found to have a high positive (R = 0.63) correlation with customer satisfaction; price flexibility had a low level of correlation (R = 0.03) with satisfaction. The dependent variable had a high positive correlation (R = 0.54) with billing, image (R = 0.48), product line (R = 0.65), complaint readdress (R = 0.59) and product quality (R = 0.51). Some of the variables such as e-commerce (R = 0.34) and technical support (R = 0.2) also had low level of positive correlation with satisfaction of customers. The scatter diagrams clearly reflected the trend of these associations. Pricing was the only factor which was negatively (R = -0.28) correlated with the dependent variable. The purchase intention of the customers was hampered by the higher prices of paper products of Auspaper compared to other rival companies. On the positive side the fast delivery of the paper products, product line variability, complaint readdress system and correct billing were the major factors for customer retention research work. The sales channel ways of distribution, the different regions, the industry types did not come into the correlation analysis.
Regression Analysis
After the correlation analysis, the scholar went ahead with multiple regression technique using excel tool pack. The first model consisted of fourteen variables including the strategic alliance of the customers with the company. It was observed that advertising was not a significant factor for the regression model with p value of 0.98 and coefficient of -0.001. The model was restructured by removing advertisement factor and warranty on products was found to be insignificant with a p value of 0.85 and likelihood coefficient of -0.015. The model was reconstructed again without the factor warranty, and gradually, delivery speed of the company (p value of 0.66), billing transparency (p value of 0.58), new product launching in market (p value of 0.21), technical support for customers (p value of 0.22), pricing of paper products (p value of 0.09), and complaint readdress system (p value of 0.06) were also eliminated from the model due to level of insignificance levels. The final model consisted of six factors, which were product quality, e-commerce, and product line variability, image of the company, price flexibility and type of future strategic alliance possibility with the customers. The multiple-linear regression model was finalized as below (Ton & Raman, 2010).
Building a Statistical Model to Predict Customer Satisfaction
The dependent variable Y was the satisfaction level of the customers and the independent variables were as follows.
X1 = Product quality
X2 = E-commerce
X3 = Product line
X4 = Image
X5 = Price flexibility
X6 = Strategic alliance level
The model described the fact that for one unit level of increase in product quality (keeping other factors same) will increase the satisfaction level of the customers by 34%. The similar decision was possible for other five factors (Woodside, 2013).
Outside ANZ Model
For outside ANZ region a regression model with previously identified variables was found, and five variables were found to be significantly correlated to customer satisfaction. Product quality, complaints readdress system, image of the company, pricing of paper products, and strategic alliance type were used to build up the new regression model. The final model was as below,
Y = Customer satisfaction
X1 = Product quality
X2 = Complaint readdress system
X3 = Image
X4 = Price of products
X5 = Strategic alliance level
The course coordinator of the scholar and an analytical expert at ANALYTICS7, Dr. Hugo Barra analyzed and predicted that Product Line, Product Quality, Price Flexibility, Competitive Pricing, and Personnel Image were the important and decisive factors for strategic alliance of the customers with the firm. The scholar was guided to cross check the likelihood estimation for the above predictive factors. The scholar used a logistic regression model as the factor strategic alliance was binary in nature. Due to incapability of linear regression model to handle binary factors the scholar went ahead with his proposed logistic model. The logistic regression model with Dr. Hugo’s prescribed variables revealed that competitive pricing of the paper products was not a significant factor of the study (p value of 0.06). The model was restructured with remaining four variables. The model was finalized with Product Line, Product Quality, Price Flexibility, and Personnel Image. The equation of the model has been provided below as,
Where the dependent variable was Y = strategic alliance and the independent factors were as follows.
X1 = Product quality
X2 = Product line
X3 = Image
X4 = Price flexibility
The model described the fact that for one unit level of increase in product quality (keeping other factors same) will increase the satisfaction level of the customers by almost 100%. The similar decision was possible for other three factors (Kleinbaum et al., 2013).
Maximum Likelihood
The maximum likelihood probabilities for the continuous variables were evaluated and are reported in table 11 in appendix. The four significant variables Product Line, Product Quality, Price Flexibility, and Personnel Image from the logistic model were used to find the likelihood estimate probabilities. The likelihood function was constructed. Initially the constant term and coefficients of the models were assumed to be 0.5. The values were then multiplied with the four factors and the constant term was added to find the likelihood function. The exponential value was evaluated for each value of the likelihood function as an intermediate step. The likelihood probabilities were evaluated as the ratio where L was the likelihood functional values (Kleinbaum & Klein, 2010). The Logloss vales for each subject were valuated from the probabilities. The sum of the Logloss value was found. Afterwards excel solver was used to minimize the value of the Logloss value by changing the initial values of the factors of the logistic regression model. The solver values were taken and a new model was prescribed for predicting the likelihood estimates of the factors (Pascal et al., 2008). The final model has been given below as,
Where the dependent variable was Y = strategic alliance and the independent factors were as follows.
X1 = Product quality
X2 = Product line
X3 = Image
X4 = Price flexibility
The model was able to described the increase the satisfaction level of the customers due to increase in product quality (keeping other factors same). The slope of the model indicated that customer satisfaction will touch level zero and hypothetical negative customer satisfaction level will be attained if all the four factors were made zero
Predicted probability visualization
Here the scholar evaluated the probabilities for the association strategic alliance level as prescribed by Dr. Hugo Barra. The personal image and variability of product lines were considered fixed at level 5. The intention was to keep the neutral responses of the customers on these two factors. Then the probabilities for the purpose were evaluated for three levels of price flexibility. The three levels of price flexibility were zero (Non flexible price level), five (moderate flexible price level) and ten (highly flexible price level). The ten levels of product quality of the paper product were used against three levels of price flexibility. The association alliance probabilities were plotted in figure 1 for three levels of price flexibility.
Figure 1: Product quality versus Predicted probability
For the price flexibility of level zero it was observed that the predicted probabilities for strategic alliance of the customers with the firm were almost zero. Therefore it was observed that irrespective of high level of finished paper products, the probability of association of the customers did not exist. For the second tier of flexibility (Price_Flex = 5) the trend showed that customers started to respond from level 6 of the product quality. Hence for lower product levels mediocre price flexibility was a non responsive factor. The probability sharply increased for high level of products even for price flexibility of level 5. The third tier of price flexibility (Price_Flex = 10) was an eye catcher for customers. Irrespective of the quality of product customers were inclined to buy the products of Auspaper. The trends were in line with earlier research works and general customer behavior of the Australian market. People preferred to buy the products for a lower price level but the increase rate in the trend flattened out for higher end products.
Hence the scholar concluded that people were inclined for low priced products, but there were some customers who were also inclined towards high end paper products for moderate price flexibility (Silva & Tenreyro, 2010).
For this purpose the scholar developed a time series model and later adjusted the seasonal variation. It is a well know tool to forecast future trend and therefore seasonal adjustments were also performed. The quarterly turnover for 37 quarters for previous ten years (2008-2017) was used to find average sales for time series and then seasonal indices were calculated for the entire time frame (De Livera, Hyndman & Snyder, 2011). The seasonal adjusted values for sales turnover was recalculated using seasonal indices. The trend was smoothed out that way and future forecast for last three quarters were done. Mean absolute percentage error (MAPE) was 2.68 % (Brockwell & Davis, 2016).
Figure 2: Time Series data for forecasting turnover of Auspaper
The trend forecasted the turnover figures for last three quarters of 2017 as $ 4575.44, $ 5043.32, $ 5099.46 (Box et al., 2015).
Conclusion
The key findings of the scholar for future business prospect of Auspaper were submitted to Dr. Hugo Barra. Some of them were as follows,
- Auspaper should increase their price flexibility for their paper products.
- The company should maintain the higher range of quality products as a market segment was identified, who preferred to buy good quality products for mediocre price flexibility also.
- Outside ANZ sales depended on product quality and pricing as well, though image of the company and customer satisfaction were important. Hence, Auspaper was advised to think on those lines, by not compromising on quality and customer need satisfaction.
- The descriptive for customer satisfaction revealed that more customers preferred non alliance with the company. The main reason was later identified as low price flexibility (Black, 2009).
- Overall Auspaper should increase the quality of customer handling utilities with flexibility in price of finished products
References
Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M., 2015. Time series analysis: forecasting and control. John Wiley & Sons.
Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. springer.
De Livera, A.M., Hyndman, R.J. and Snyder, R.D., 2011. Forecasting time series with complex seasonal patterns using exponential smoothing. Journal of the American Statistical Association, 106(496), pp.1513-1527.
Black, K., 2009. Business statistics: Contemporary decision making. John Wiley & Sons.
Kleinbaum, D.G., Kupper, L.L., Nizam, A. and Rosenberg, E.S., 2013. Applied regression analysis and other multivariable methods. Cengage Learning.
Ton, Z. and Raman, A., 2010. The effect of product variety and inventory levels on retail store sales: A longitudinal study. Production and Operations Management, 19(5), pp.546-560.
Silva, J.S. and Tenreyro, S., 2010. On the existence of the maximum likelihood estimates in Poisson regression. Economics Letters, 107(2), pp.310-312.
Kleinbaum, D.G. and Klein, M., 2010. Maximum likelihood techniques: An overview. In Logistic regression (pp. 103-127). Springer, New York, NY.
Pascal, F., Chitour, Y., Ovarlez, J.P., Forster, P. and Larzabal, P., 2008. Covariance structure maximum-likelihood estimates in compound Gaussian noise: Existence and algorithm analysis. IEEE Transactions on Signal Processing, 56(1), pp.34-48.
Woodside, A.G., 2013. Moving beyond multiple regression analysis to algorithms: Calling for adoption of a paradigm shift from symmetric to asymmetric thinking in data analysis and crafting theory.
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