The article The Role of Niche Breadth, Resource Availability and Range Position on the Life History of Butterflies (A. Komonen, A. Grapputo, et al., Oikos,

The article €œThe Role of Niche Breadth, Resource Availability and Range Position on the Life History of Butterflies€ (A. Komonen, A. Grapputo, et al., Oikos, 2004:41€“54) describes a study of several species of butterflies found in Finland. The following table presents the mean wingspan (in mm) and the flight period, defined as the mean number of days of appearance in the winged state, for 23 species in the family Lycaenidae.

a. Compute the least-squares line for predicting the flight period (y) from wingspan (x).

b. Compute 95% confidence intervals for β₀ and β₁.

c. Two butterflies differ in wingspan by 2 mm. By how much do you estimate that their flight periods will differ?

d. Can you conclude that species of butterflies with larger wingspans have shorter flight periods on average? Explain.

e. Can you conclude that the mean flight period for butterflies with a wingspan of 30 mm is less than 28 days?

f. A certain butterfly species has a wingspan of 28.5 mm. Find a 95% prediction interval for its flight period.

Flight Flight Period Flight Period Flight Period Wingspan 35.5 30.6 Wingspan 25.9 Wingspan Wingspan Period 32.5 27.5 19.8 28.8 35.9 25.9 28.1 25.9 28.8 18.5 32.3 17.3 31.3 23.1 30.0 27.5 23.0 31.0 37.4 22.6 23.0 24.6 53.1 29.1 32.3 23.9 22.4 26.3 23.7 38.8 36.5 24.0 31.4 28.5 37.0 40.7 28.1 25.4 33.7 27.7 18.3 27.1 23.1