Statistics Model

TASK A

The challenge of task a) was to produce a model that best explains the variation in store profits. Given were data for each of the 75 stores that were related to their business operations, such as site-location factors and people factors. [1] Based on this data, the best fit model is given by the equation

[pic 1]

with  and , yielding an explanatory power of 86.4% of all profit variation.[2] A cross check with the f test confirms that .[pic 2][pic 3][pic 4]

The downside to this model is that manager and crew tenure are not included in this model. A simple multiple regression including all data shows that ‘sales’ has the strongest explanatory power. [3] Excluding sales led to the conclusion that the second best model looks as follows:

[pic 5]

The model has an overall explanatory power of 59.4%. [4] The relationship between profit and manager tenure is that for every additional month the managers can be bound to the company (on average), the profit increases by $842.26. Also, for every additional month on the store’s the crew level (on average), the profit increases by $1003.6.

A t-test comparing the means of the subsamples ‘top 10’ and ‘bottom 10’ outcomes of manager tenure shows that there is a significantly different mean (assuming unequal variances). Therefore, the influence of manager tenure on the profit could be verified. The same analysis for crew tenure cannot uphold such hypothesis. [5]

1. We would like to remark that in order to perform a much more thorough analysis, more exhaustive data would be needed, including cost structure as well inventory turnover and ales revenues with respect to seasons, weekdays, etc.
2. See appendix 1.
3. In expression, the probability that we can reject the null hypothesis is smaller than the significance level of 5%. Therefore, we can conclude that the variables ß is not equal to zero and therefore, the variable has explanatory power to the model.
4. See appendix 2. ‘Visibility’ is excluded due to its high p value.
5. See appendix 3

TASK B

The relevance of task b) consisted in analyzing which variables have the highest influence on the model’s explanatory power. Just as in task a), sales is the variable that underlies the strongest relationship with profit. However, this relationship is rather intrinsic. Just as profit (), sales is also a metric of financial performance and depends strongly on other factors that contribute to the store’s performance.[1] In our case, it is much more interesting and valuable to analyze what the most powerful factors are that influence sales and, eventually, profit. Therefore, we removed sales from the analysis just as in task a) because otherwise, all other regressors become insignificant. [pic 6]