In Example 7.5, we implied that each of the five observations was from one period of time, such as a particular week. Suppose instead that each is an average over several weeks. For example, the 4.7 million exposures corresponding to 1 ad might really be an average over 15 different weeks where 1 ad was shown in each of these weeks. Similarly, the 90.3 million exposures corresponding to 50 ads might really be an average over only 3 different weeks where 50 ads were shown in each of these weeks. If the observations are really averages over different numbers of weeks, then simply summing the squared prediction errors doesn’t seem appropriate.

For example, it seems more appropriate that an average over 15 weeks should get 5 times as much weight as an average over only 3 weeks. Assume the five observations in the example are really averages over 15, 10, 4, 3, and 1 weeks, respectively. Devise an appropriate fitting function, to replace sum of squared errors or RMSE, and use it to find the best fit.