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...
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.
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.
Recommendations
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 $1,330, 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…
