Sampling Distributions for Linear Regression Question 6

The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river.

Which of the following statements is a correct interpretation of the value 19.0 in the output?

On average there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in concentration of zinc found in the fish.

On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish.

The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc.

Approximately 19% of the variability in zinc concentration is predicted by its linear relationship with lead concentration.

Approach

The coefficient values correspond to $\alpha$ and $\beta$ :

\hat{y}=\alpha + \beta x

\hat{y}=16.3+19.0x

The slope $\left(\dfrac{19.0}{1}\right)$ represents the change in $\hat{y}$ for every change of $x$ . So for every 19.0 change in zinc, there is a change of 1 in lead.