The performance of a solar cell can deteriorate when atmospheric dust accumulates on the solar panel surface. In the International Journal of Energy and Environmental Engineering (Dec. 2012), researchers at the Renewable Energy Research Laboratory, University of Lucknow (India) estimated the relationship between the dust thickness and the efficiency of a solar cell. The thickness of dust (in millimeters) collected on a solar cell was measured three times per month over a year-long period. Each time the dust thickness was measured, the researchers also determined the percentage difference (before minus after dust collection) in efficiency of the solar panel. Data (monthly averages) for the 10 months where there was no rain are listed in the table.

a. Fit the linear model, E(y) = β_o + β₁x to the data where y = Efficiency and x = average dust thickness.

b. Find an estimate of σ, the true standard deviation of the error, ∈.

c. Give a practical interpretation of the result, part b.

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SOLARCELL Month Efficiency (% change) Average Dust Thickness (mm) January 1.5666 0.00024 February 1.9574 0.00105 March 1.3707 0.00075 April 1.9563 0.00070 May 1.6332 0.00142 June 1.8172 0.00055 July 0.9202 0.00039 October 1.8790 0.00095 November 1.5544 0.00064 December 2.0198 0.00065