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Men in a statistics course had their body fat index measured. After taking a resting heart rate in beats per minute (bpm), the men walked two laps of the A building including going up and down stairs. Then they measured their heart rate again. The difference in the heart rates was recorded as a rise in heart rate. The data thus provides a potential look at the possibility of a relationship between body fat index and heart rate increase after light exercise. Although the data is real data, the sample is not a random sample, the heart rates were self-measured, and the body fat index is from a Tanita body composition unit.
| body fat index | heart rate rise after exercise |
|---|
| 18.4 | 8 |
| 31.5 | 6 |
| 17.5 | 2 |
| 20.4 | 17 |
| 23.4 | 13 |
| 23.6 | 9 |
| 17.2 | 23 |
| 20.9 | -2 |
| 18.6 | 28 |
| 14.5 | 15 |
| 21.3 | 10 |
| 21.5 | 7 |
| 17.1 | 18 |
| 10.8 | 9 |
| 29.0 | 14 |
| 36.5 | 22 |
| 25.2 | 8 |
| 32.3 | 11 |
| 37.7 | 37 |
| 20.1 | 25 |
| 20.6 | 15 |
| 24.2 | 20 |
| 13.9 | 3 |
- Calculate the sample size n.
- Calculate the slope of the linear regression. For entry into Schoology, round to two decimal places.
- Calculate the y-intercept of the linear regression. For entry into Schoology, round to two decimal places.
- Is the relation between the variables positive, negative, or neutral?
- Calculate the correlation coefficient r for the data. For entry into Schoology, round to two decimal places.
- Is the correlation none, weak, moderate, strong, or perfect?*
- Determine the coefficient of determination. For entry into Schoology, round to two decimal places.
- What percent in the variation in body fat index "explains" the variation in heart rate rise?
- Use the slope and intercept to calculate the predicted heart rate rise for a body fat index of 35. In the calculation use the unrounded slope and intercept. Round the final answer to two decimal places.
- Use the slope and intercept to calculate the predicted body fat index for a heart rate rise of 12 beats per minute.In the calculation use the unrounded slope and intercept. Round the final answer to two decimal places.
* The fully correct answer to this also involves taking into account the sample size n, but at this point in the course that involves understanding concepts that have not yet been introduced.