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).

Answer 1

I don’t have the image, but if your regression equation was V = kP^(−1) (i.e. V = k/P), then all four statements are true (statement 3 looks like a typo of statement 2).

Why:
- V = k/P is an inverse relationship, so as pressure P increases, volume V decreases (statement 1).
- Multiplying both sides by P gives P·V = k, so P·V is approximately the same constant for all data pairs (statements 2 and 3).
- Statement 4 simply restates the regression form V = kP^(−1), so it is true.

If your actual fitted equation differed significantly from V = k/P, then PV would only be approximately constant depending on the fit.