An emerging technology known as concentrating photovoltaics (CPV) has recently been introduced into the market. Morgan Solar of Toronto specializes in CPV. The cost of new technology is related to cumulative volume deployed since the industry gains more experience of the technology as it is deployed, resulting in cost reductions. The corresponding data for CPV are:

a) Check the conditions for fitting a linear regression model to this data.

b) An experience curve is often used for new technology to represent the relationship between cost and cumulative volume deployed. It relates the logarithm of cost to the logarithm of cumulative volume and is used to estimate costs after a certain cumulative volume has been deployed. Fit an experience curve to the CPV data above, using a linear model with log(cumulative volume) as the explanatory variable and log(cost) as the dependent variable. Comment on the conditions.

c) Forecast the cost of CPV when cumulative volume is 400 MW using your answer to (b).

d) The CEO of a CPV manufacturer disagrees with the idea that cumulative volume determines cost. “It’s the cost that determines the volume deployed,” he says, “and the lower the cost, the more will be deployed.” Fit a different linear model to represent this CEO’s view, again using log(cost) and log(cumulative volume) as your variables. Comment on the conditions.

e) Using your answer to (d), estimate how much cumulative volume will be deployed by the time the cost reaches $1.50/W.

f) What fraction of the variability in the data is explained by these two models? Why is the answer the same for each model?

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Cumulative Cumulative Volume to Volume to Cost ($/W) Cost ($/W) Date (MW) Date (MW) 5.15 8.5 1.5 28 8.5 3.3 4.66 29.2 10.2 4.72 8.5 46 86.75 9.4 13 3.9 8.5 91.2 13 3.08 3.54 108 5.75 15.6 15.6 3.8 2.3 160 5.76 17.7 160 3.02 4.85 18 2.62 275 9.63 20