One of the first steps in analysis of the data is to make a comparison of the 10 most profitable stores and the 10 least profitable stores. Hart claimed that the manager and crew tenure in the most profitable stores was almost four times the level of that in the least profitable stores. This analysis is however based solely on the summary statistics for those ten stores in each category. Taking a closer look at the results for the individual stores would suggest that the relationship is not so simple. For example looking at store 47, which is at the bottom of the ten most profitable list, both the crew and manager tenure are very low in comparison to the other stores in the list. This means that it would not be expected that store 47 would be so profitable if the manager and crew tenure were the only influencing factor on profitability. In fact, the levels of tenure in this store are lower the average of those from the ten lowest profit stores, which would indicate that very low levels of profit would be expected from the store. A more in-depth analysis is therefore required.
There is further evidence that neither manager tenure nor employee tenure alone significantly influences the profitability of each store. This may seen in the scatter-plots which are included below as Figure 1 and Figure 2. It appears clear from Figure 1 that most managers have been at their store for less than 50 months, and the mean which is given for manager tenure is 45.3. This mean may however be slightly higher than the median would be given that there are several exceedingly high values which would influence the calculation of the mean. A similar pattern may be seen in Figure 2, where it is clear that most employees have lower than 20 months retention, with the mean given as 13.9 months.
What is also apparent from these plots is that neither variable may significantly explain variability in the profitability of a store. This is evident in the r-squared value, which indicates that only 19.6% of variation in profitability may be explained by manager tenure alone. Similarly, only 6.7% of this variation may be explained by employee tenure alone. It therefore is apparent that there are multiple variables which may influence profitability.
In order to assess whether a manager and employee tenure combine to influence profitability a multiple regression model may be formed using these two variables. The results of this regression may be seen in Table 1.
Figure 1: Correlation between manager tenure and store profitability
Figure 2: Correlation between employee tenure and store profitability
From Table 1 it may be seen that when considering both manager and employee tenure there is still only 21.7% of variation in profitability which these variables may explain. This therefore indicates that there must be other factors which exert an influence. It would therefore be suitable to construct a multiple regression model which takes into account other variables for which data is available. Although it was originally believed that the relationship may be non-linear, this still does not significantly increase the r-squared value.
Table 1: Regression model in which manager tenure and employee tenure are included |Regression Statistics |
|Multiple R |0.465617551 |
|R Square |0.216799704 |
|Adjusted R Square |0.19504414 |
|Standard Error |80212.7404 |
|Observations |75 |
Multiple Regression Model
The first multiple regression model which is included is that which includes all of the variables for which data are available. These variables are:
X1: Manager tenure
X2: Employee tenure
X3: Population near store
X4: Competition near store
X5: Visibility of store
X6: Pedestrian count
X7: Residential or industrial area
X8: 24 hour access
The results of the regression model may be seen in Table 2 below. This shows that using the model with all eight variables included 63.8% of the variation in profitability may be explained. This suggests that the model may be valid in explaining the impact on profitability. In addition to this, from Table 3 it may be seen that the value of the F-test statistic is 14.53, with a significance of less than 0.05 which also shows that the model is significant. However by looking at the results in Table 4 it may be seen that not all of the variables which are included in the model may be significantly contributing to the model. As the variable X5, which is the visibility of the store, has a p-value of more than 0.05 this suggests that the variable is not contributing significantly to the model.
This would suggest that removing this variable may further improve the model. In addition to this it would be necessary to remove any variables which were collinear as this could interfere with the results of the regression. After using the program PHStat to analyse the variable inflation factors (VIFs) of the variables these are all below 5, which shows that there is no collinearity between variables. Therefore the improved model would be one which included all variables except X5.
The Impact of Increasing Crew Tenure
From the regression equation which is calculated from the multiple regression model it may be seen that increasing both manager and employee tenure is significant in increasing profitability of stores. Specifically, the model predicts that for every month increase in manager tenure there would be an increase in profits of around $787 if all other factors were kept constant. Also, for every increase of one month in employee tenure there is predicted to be an increase in profitability of around $963 if all other factors were kept constant. It was suggested that the relationship between tenure and profitability may be dependent on the length of tenure, i.e. a non-linear relationship. However the fitting of a trend line to the scatter-plot suggests that a non-linear relationship does not fit the data significantly better than a linear trend line. Therefore it would be predicted that an increase in employee tenure of 1.38 months would result in an increase in profitability of around $1330.
Validity of the Data
The data on which the above analyses are based contains information taken from 2000, which is now eight years old. Therefore it is possible that the financial implications of increasing crew tenure have changed somewhat. It would however be considered valid to use the data to provide an estimate of the financial implications as the factors which would influence the regression model used would be largely the same. Although the data also included only the data from 75 of the 82 stores, this is a large enough sample to be considered representative of the chain as a whole. It would therefore be expected that while these other stores may not follow the model precisely, it should still provide an indication of the influence of tenure on profitability of these stores.
Based on the analysis of the data it would be recommended that increasing both manager and employee tenure may significantly increase profitability of stores. In particular, the current bonus plan would be profitable to the company if the amount of bonus offered were less than around $1330, as this is the increase in profitability which would result. However, it is also possible that offering these bonuses would increase manager tenure, which would then further increase profitability. It would however be suggested that this alone may not be sufficient to largely increase the profitability of some stores, as the overall profitability of stores is a result of an interplay of both site-location and people factors.
Berenson, M.L., Levine, D.M. & Krehbiel, T.C. (2008) Basic Business Statistics. 11th Edition. Philadelphia, PA: Prentice Hall.
Kazmier, L.J. (2003) Schaum’s Outline of Business Statistics. New York: McGraw-Hill.
Levine, D.M., Stephan, D.F., Krehbiel, T.C. & Berenson, M.L. (2007) Statistics for Managers Using Microsoft Excel. Philadelphia, PA: Prentice Hall.