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).
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 |
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.
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
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