The Honeybee Waggle Dance When honeybee scouts find a food source or a nice site for a new home, they communicate the location to the rest of the swarm by doing a ''waggle dance."¹ They point in the direction of the site and dance longer for sites farther away. The rest of the bees use the duration of the dance to predict distance to the site. Table 1 shows the distance, in meters, and the duration of the dance, in seconds, for seven honeybee scouts.²

Duration		Distance
0.40		200
0.45		250
0.95		500
1.30		950
2.00		1950
3.10		3500
4.10		4300

Table 1 Duration of a honeybee waggle dance to indicate distance to the source

a) Use technology to find the correlation between the two variables. Round your answer to three decimal places.

(b) Use technology to find the regression line to predict distance from duration. Round your answers to the nearest integer.

c) Interpret the slope of the line in context.

The slope tells the expected duration if the distance is 1 meter more.

The slope tells the expected distance if the duration is 1 second more.

The slope tells the expected change in distance if the duration is 1 second more.

The slope tells the expected change in duration if the distance is 1 meter more.

(d) Round your answers to the nearest integer. Predict the distance to the site if a honeybee does a waggle dance lasting 1 second. Predict the distance to the site if a honeybee does a waggle dance lasting 3 seconds.