Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24
Cardiologists use the short-
| Short | Long |
| 0.54 | 0.55 |
| 1.02 | 0.79 |
| 1.4 | 0.81 |
| 0.88 | 0.9 |
| 1.68 | 1.05 |
| 1.16 | 1.05 |
| 0.82 | 1.05 |
| 0.93 | 1.07 |
| 1.26 | 1.1 |
| 1.18 | 1.19 |
| 0.81 | 1.19 |
| 0.81 | 1.2 |
| 1.28 | 1.23 |
| 1.18 | 1.23 |
| 0.71 | 1.24 |
Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text.
A. Compute the least-squares line for predicting the long-term measurement from the short-term measurement. Round the answers to three decimal places.
y = + x
B. Find a 95% confidence interval for the mean long-term measurement for those with short-term measurements of 1.2. Round the answers to three decimal places.
The 95% confidence interval is ( , ).
C. Find a 95% prediction interval for the long-term measurement for a particular individual whose short term measurement is 1.2. Round the answers to three decimal places.
The 95% prediction interval is ( , ).
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