From 2005 through 2016, the numbers of new cases of a waterborne disease in a small city increased in a pattern that was approximately linear (see figure). Find the least squares regression line y = at + b for the data shown in the figure by solving the system below using matrices. Let t represent the year, with t = 0 corresponding to 2005.

Use the result to predict the number of new cases of the waterborne disease in 2020. Is the estimate reasonable? Explain.

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12b + 66a 66b + 506a = 5643 831 120 100 - 80 www... 60 - 40- 20- +++++ 3 4 5 6 7 Year (0 + 2005) 1 2 8 9 10 11 Number of new cases