2.73 Least-squares regression for radioactive decay. Refer to Exercise 2.32 (page 99) for the data on radioactive decay of barium-137m. Here are the data:

Time 1 3 5 7
Count 578 317 203 118

  1. (a) Using the least-squares regression equation

  2. count = 602.8 − (74.7 × time)

  3. find the predicted values for the counts.

  4. (b) Compute the differences, observed count minus predicted count. How many of these are positive; how many are negative?

  5. (c) Square and sum the differences that you found in part (b).

  6. (d) Repeat the calculations that you performed in parts (a), (b), and (c) using the equation

  7. count = 500 − (100 × time)

  8. (e) In a short paragraph, explain the least-squares idea using the calculations that you performed in this exercise.