Question

Look back at your data and your regression equation. (Sample data is shown to the right, with x = pressure and y = volume.) Check all statements that are true.

As the pressure of the gas increased, the volume of the gas decreased.

For all pairs of data of pressure and volume, P • V was appoximately the same.

For all pairs of data of pressure and volume, P • V mr001-1.jpg k for the same value k.

The regression equation was of the form V = kP–1 (which is the same as V = k/P).
A graph with pressure as the horizontal axis and volume as the vertical axis. A line extends through the points, listed in a table titled Data with 2 columns and 6 rows next to the graph. Column 1 is labeled Pressure P and has entries 1.03, 1.08, 1.18, 1.27, 1.37, 1.47. Column 2 is labeled Volume V and has entries 50, 47.5, 43.5, 40.5, 37.5, 35.0. Beneath the table text reads Power Regression y = 51.387 x Superscript negative 0.999.

Answer 1

Check: 1, 2, and 4 are true; 3 is not exactly true.

Reasoning:
- As P increases (1.03 → 1.47) V decreases (50 → 35), so statement 1 is true.
- Compute P·V: 1.03·50 = 51.50, 1.08·47.5 = 51.30, 1.18·43.5 = 51.33, 1.27·40.5 = 51.44, 1.37·37.5 = 51.38, 1.47·35 = 51.45. These are all approximately the same (about 51.4), so statement 2 is true.
- The power regression shown is y = 51.387 x^(−0.999), which is essentially V ≈ 51.387·P^(−1) = 51.387/P, so statement 4 is true.
- Statement 3 (that P·V equals the same exact k for all pairs) is not exactly true for the raw data (it’s only approximately constant), so it should not be taken as exactly correct.