A company based in Kingston, Ontario, has been installing solar modules on residential roofs in Kingston and Ottawa and is planning to expand its operation in the smaller communities along Highway 401 toward Toronto to the southwest of Kingston. One reason for expansion in this direction is that Kingston and the other communities along Highway 401 have less snow than Ottawa and other communities to the north and east of Kingston. Snow often accumulates on solar modules in Ottawa, reducing electricity generation. An ideal roof for installing solar modules faces south, thus capturing the greatest amount of solar energy throughout the year. The company has installed modules on roofs facing slightly east and slightly west of south in both Kingston and Ottawa and has monitored the value of the average electricity generated per year (see ch19_MCSP_solar). It needs to know how much reduction in value occurs as a result of the orientation of the modules, since the communities along Highway 401 are built on regular grids of roads with the majority of houses facing the same direction (for example, see the map of Napanee, where most houses face 35 degrees east of south or 55 degrees west of south). The company would not want to market its services in a community where the orientation of the roads and houses results in a significant drop in the value of electricity generated.

Model the value of electricity generated as a function of orientation of roof, identifying data groupings, outliers, and influential points. What value of annual electricity generation do you estimate for the following communities?

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Belleville -70 Napanee Peterborough Ottawa Perth 35 30 Orientation east of south (degrees) 0 40