Data were collected on the distance a baseball will travel when hit by a baseball bat at a certain speed. The speed, s, is measured in miles per hour, and distance, y, is measured in yards. The regression line is given by ŷ = 4.17 + 52.45s.

Question

Identify the slope and y-intercept of the regression line. Interpret each value in context.

The slope, 52.45, indicates that the distance increases by 52.45 yards for every one mile per hour of speed. The y-intercept, 4.17, is the distance estimated by this model if the speed is zero miles per hour.
The slope, 4.17, indicates that the distance increases by 4.17 yards for every one mile per hour of speed. The y-intercept, 52.45, is the distance estimated by this model if the speed is zero miles per hour.
The slope, 4.17, indicates that the distance decreases by 4.17 yards for every one mile per hour of speed. The y-intercept, 52.45, is the distance estimated by this model if the speed is one mile per hour.
The slope, 52.45, indicates that the distance decreases by 52.45 yards for every one mile per hour of speed. The y-intercept, 4.17, is the distance estimated by this model if the speed is one mile per hour.

Answer 1

The correct interpretation of the regression line ŷ = 4.17 + 52.45s is as follows:

• The slope is 52.45. This indicates that the distance the baseball travels increases by 52.45 yards for every one mile per hour increase in speed.

• The y-intercept is 4.17. This is the distance estimated by the model if the speed is zero miles per hour. In this context, it suggests that if the baseball is not hit (0 mph), it is expected to travel 4.17 yards (though practically, this might not make sense as a baseball would not travel significantly when not hit).

Thus, the correct choice is:

The slope, 52.45, indicates that the distance increases by 52.45 yards for every one mile per hour of speed. The y-intercept, 4.17, is the distance estimated by this model if the speed is zero miles per hour.