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.€ 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 2.36 shows the distance, in meters, and the duration of the dance, in seconds, for seven honeybee scouts. This information is also given in HoneybeeWaggle.

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

(a) Which is the explanatory variable? Which is the response variable?
(b) Figure 2.69 shows a scatterplot of the data. Does there appear to be a linear trend in the data? If so, is it positive or negative?

Figure 2.69

(c) Use technology to find the correlation between the two variables.
(d) Use technology to find the regression line to predict distance from duration.
(e) Interpret the slope of the line in context.
(f) Predict the distance to the site if a honeybee does a waggle dance lasting 1 second. Lasting 3 seconds.

Transcribed Image Text:

4000 3000 2000 1000 2 3 4 Duration Distance