Statistics case study analysis

¶ … Employee and Manager Tenure and Store Performance

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

Square

Adjusted R. Square

Standard Error

Observations

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:

Y: Profitability

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.

Table 2: Regression model in which all explanatory variables are included

Regression Statistics

Multiple R

Square

Adjusted R. Square

Standard Error

Observations

Using the improved model which includes all of the variables except X5, the regression equation is given as:

47508.5 + 787.3X1 + 962.6X2 + 3.8X3-25578.8X4 + 32523X6 + 93009.2X7 + 64718.3X8

There are a number of conclusions which may be drawn from this equation. First of all is that the location of the store being in a residential area and 24-hour access are both associated with increased profitability. Also, lower levels of competition and higher levels of pedestrian access are important for profitability. In terms of tenure this model also shows that both manager and employee tenure are important to profitability, although employee tenure results in greater changes in profitability.

Table 3: ANOVA table from the multiple regression with all variables included df

SS

MS

Significance F

Regression

3.77314E+11

5.38241E-12

Residual

2.14174E+11

5.91489E+11

Table 4: Analysis of the fit of the individual variables within the multiple regression model

Coefficients Standard Error't Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 7610.041452 66821.99424 0.113885279 0.909674466 -125804.3731 141024.4561 -125804.3731 141024.4561 X Variable 1 760.9927338 127.0856393 5.98803089 9.7159E-08-507.2580711 1014.727397 507.2580711 1014.727397 X Variable 2 944.9780259 421.6874239 2.240944293 0.028399552 103.051929 1786.904123 103.051929 1786.904123 X Variable 3-3.666606265 1.466307821 2.500570625 0.014890457 0.739028275 6.594184254 0.739028275 6.594184254 X Variable 4 -25286.88666 5491.93698 -4.604365774 1.93838E-05 -36251.8925 -14321.88082 -36251.8925 -14321.88082 X Variable 5 12625.44705 9087.619601 1.389301886 0.169410559 -5518.570694 30769.46479 -5518.570694 30769.46479 X Variable 6 34087.35879 9073.1961 3.756929577 0.000366441 15972.13849 52202.57908 15972.13849 52202.57908 X Variable 7 91584.67523 39231.28297 2.334480759 0.022623199 13256.89244 169912.458 13256.89244 169912.458 X Variable 8 63233.30716 19641.11429 3.219435834 0.001993586 24018.55766 102448.0567 24018.55766 102448.0567

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 $1,330.