2.74 Least-squares regression for the log counts. Refer to Exercise 2.33 (page 99), where you analyzed the radioactive decay of barium-137m data using log counts. Here are the data:
| Time | 1 | 3 | 5 | 7 |
| Log count | 6.35957 | 5.75890 | 5.31321 | 4.77068 |
(a) Using the least-squares regression equation
log count = 6.593 − (0.2606 × time)
find the predicted values for the log counts.
(b) Compute the differences, observed count minus predicted count. How many of these are positive; how many are negative?
(c) Square and sum the differences that you found in part (b).
(d) Repeat the calculations that you performed in parts (a), (b), and (c) using the equation
log count = 7 − (0.2 × time)
(e) In a short paragraph, explain the least-squares idea using the calculations that you performed in this exercise.