Pricing House Cleaning Assignments

HCA Statistical Analysis with Practical Applications

8.Other Definitions

Man-minutes: measures the total man-minutes spent on that particular assignment. It can be calculated as the number of team members multiplied by the elapsed cleaning time (measured from the moment the team arrives outside an address, to the moment it departs from the address). The cleaning time does not include driving time. For the dataset, Man-minutes has a mean value of 372, and ranges from 156 to 1,002 minutes.
Hourly Rates: The operator establishes standard hourly rates for regular cleanings (applies to both weekly and bi-weekly), and initial cleanings. The hourly rate can be adjusted and saved via the Member Desktop Pricer; such prices determine the results of all HCA Pricing Tools.
Minimum Prices per Visit: The Member Desktop Pricer allows an operator to fix minimum prices per visit for three types of cleanings: Initial Cleaning; Weekly Cleaning; and Bi-weekly Cleaning. These minimum prices result in a floor being applied to prices resulting from all HCA Pricing Tools.
Scenarios: refer to the set of observed variables for a household. They are defined (and saved) by the operator of a house cleaning company via the Member Version of the Desktop Pricer. Scenarios can include a mix of hypothetical assignments as well as actual assignments. An operator can adjust the results of the HCA Pricing Tools and then analyze the results based on multiple scenarios which he defines himself. “Big Dirty House” might include a large square footage, high number of bathrooms, and high scores for usage variables. Scenarios allow a company to analyze the effect on the clean times and prices associated with actual customer households, which arise from tweaking one or more variable coefficients via the Member Desktop Pricer.
Companies with different scope definitions and operating configurations will experience different results in terms of man-minutes to complete a given assignment. The scenarios provide a means for the operator to customize the HCA Pricing Tools to reflects these configurations and arrive at the desired Man-minute estimates.
Scenarios provide a means for an operator to customize the HCA Pricing Tools to meet the Company’s own needs. Allowing operators to adjust the results of the HCA Pricing Tools allows HCA to accommodate any number of different operating profiles of professional house cleaning companies.

9.Correlation between Factors

Despite the definitions being reasonably well defined, our analysis shows that some of the variables are not entirely independent and, in fact, some are highly correlated. In terms of predicting total man-minutes, including correlated explanatory variables does not impair the overall predictive value of the model. However, in terms of associating the coefficients with a break down of man-minutes by variable, multicollinearity limits the ability to do so.
Square Footage and Number of Toilets: Architects add more bathrooms to their plans as the size of the house increases, so it is not surprising that a correlation exists between these two variables. We use the number of toilets as a proxy for number of bathrooms, so as to avoid ambiguities associated with “half baths”, “powder rooms”, etc. Our study shows that these two variables, Square Footage and Number of Toilets are highly correlated, with a correlation coefficient of 0.86.
Number of Inhabitants and Number of Showers in Use: these are found to be highly and positively correlated. Roughly, we have found that the number of showers in use is approximately the number of inhabitants minus one. This is not surprising, since many newer homes are designed for a couple to share a master bathroom, with a separate bathing facility for each additional person. The correlation coefficient between this pair of variables is 0.71.
Lifestyle Factor and Clutter Factor: Even though defined separately, these two measurements of the residents’ behavior were found to be highly correlated. For example, a pack ratter who drips a spot of ketchup on the floor might be tempted not to wipe up the spot. The correlation between this pair of variables is 0.64. Due to the high correlation between these variables, combined with the fact that the Clutter Factor was found to have a low predictive value, the Clutter Factor has been dropped from the equation and is not used in the HCA Pricing Tools. While the concept seems to have merit based on experience, we have found it difficult to convince all users about the difference between to the two definitions; this may contribute.

Number of Toilets and Number of Showers in Use: It is naturally common to have a toilet and a shower in use in the same room. In our model, this will count as one toilet and one shower. It is also common that there is a toilet in a room without a shower in use, and this will count as one toilet, zero showers. However, it is very unusual to have only a shower in a room without a toilet, so the interfaces for Pricing Tools validate inputs to exclude this option.
The inputs for these two variables are combined in the formulae to calculate toilets without showers, so as to avoid the problem associated with estimating the coefficients, since a higher number of showers in use can only occur when there exists a sufficiently high number of toilets, but the opposite is not true. Therefore, the coefficient of showers in use could never be statistically significant because of this close relationship. We avoid this problem by applying a derived variable in the formulae:

The number of toilets without showers in use =

number of toilets – number of showers in use

Then we substituted the number of toilets and the number of showers in use by the newly-created “number of toilets without showers in use” and “number of toilets with showers in use” into the model. Doing so makes those two variables independent of each other and allows us to include both variables in estimating man-minutes.

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