A big box retailer with 87 stores across Canada wants to reduce its water and electricity usage to reduce both dollar costs and its environmental footprint, and it needs to know whether these two costs are correlated. For a preliminary analysis, it collects data on five stores that sell household items and five stores that sell both household items and groceries. It expects the stores selling groceries to use more electricity for refrigeration and more water for preparing fresh food. The data are measured per square foot of retail space (for each entire store) per year and are given in the table:

a) Calculate the correlation between water and electricity usage over all 10 stores. Comment on whether this calculation is statistically sound.

b) Calculate the correlation between water and electricity usage over the five stores not selling groceries. Comment on whether this calculation is statistically sound.

c) Calculate the correlation between water and electricity usage over the five stores selling groceries. Comment on whether this calculation is statistically sound.

d) Give reasons for the differences in the correlations you just calculated. Which of these correlations would you recommend the retail chain calculate when it does a complete analysis of all its 87 retail stores in Canada?

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Water Usage Electricity Usage (Litres per sq. ft. per year) ($ per 1000 sq. ft. per year) Grocery No 109.6 695.3 No 115.2 677.5 No 77.6 817.0 98.0 No 683.8 No 93.2 797.3 Yes 339.2 2208.5 Yes 344.1 1760.2 Yes 308.6 2002.7 Yes 329.5 2078.2 2011.2 Yes 358.5