Two species of predatory Birds-collard flycatchers and tits-compete for nest holes during breeding season on the island of Gotland, Sweden. Frequently, dead flycatchers are found in nest boxes occupied by tits. A field study examined whether the risk of mortality to flycatchers is related to the degree of competition between the two bird species for nest sites (The Condor, May 1995). The table (p. 647) gives data on the number y of flycatchers killed at each of 14 discrete locations (plots) on the island, as well as on the nest box tit occupancy x (i.e., the percentage of nest boxes occupied by tits) at each plot. Consider the simple linear regression model E(y) = β0 + β1 x.

a. Plot the data in a scatterplot. Does the frequency of flycatcher casualties per plot appear to increase linearly with increasing proportion of nest boxes occupied by tits?
b. Use the method of least squares to find the estimates of β0 and β1. Interpret their values.
c. Test the utility of the model, using α = .05.
d. Find r and r2 and interpret their values.
e. Find s and interpret the result.
f. Do you recommend using the model to predict the number of flycatchers killed? Explain.

Transcribed Image Text:

Number of Nest Box Tit Occupancy x (%) Plot Flycatchers Killed y 24 33 34 43 50 35 35 38 40 31 43 55 57 64 10 11 12 13 14 -223 45