MATH $401$ Homework assignment $4$ Long$-$term wildlife monitoring programs provide us data sets which allow us retrospective analysis of temporal change in population parameters of species of our interest. North American Breeding Bird Survey $($BBS$)$ is a nation$-$wide $($some survey routes are in Canada and Mexico$)$ annual bird count survey started in $1996.$ In this assignment, you will analyze data sets for Harmony route in Maine obtained from the BBS database using logistic regression and Poisson regression. In both analyses, consider $1967$ as year $0.$ Exclude the years when the survey was not conducted $($the years with $-$ symbol in the count column$).$ Part I: Analyzing BBS data using logistic regression Vesper swallow $($Pooecetes gramineus$)$ is a widely distributed species in North America. This species is commonly observed in open grasslands during a breeding season. It is known that the Vesper swallow quickly responds to habitat change and abandon the sites when their habitats are converted. In this exercise, you will analyze temporal pattern in vesper swallow presence along this route. Download data set $($assignment$4\_$data$1.$csv$),$ which contains year and species presence and absence $(1=$ presence, $0=$ absence$)$ and analyze it as instructed. Question $1.$ Fit the logistic regression model to predict the presence of Vesper swallow from year in Harmony route using R$.$ Report the estimated logistic equation in a form, logit$($y$)=$ b$0+$ b$1$ x$,$ where x is the year $($starts from $0)$ and y is the presence or absence of Vesper swallow. $(20\%)$ Question $2.$ Based on the results you obtained, is there a temporal pattern in presence and absence of the Vesper swallow along this route? If so$,$ what is the pattern? Report the test statistic and p$-$value to support your answer. Part II: Analyzing BBS data using Poisson regression The barn swallow $($Hirundo rustica$)$ is a globally distributed species which is typically observed in open areas with low vegetations. This species was observed frequently in early years of the BBS survey in $1960$s along the Harmony route. In this exercise, you will analyze the historical counts of the barn swallow at the route to examine the temporal trend of species abundance. Download the data set $($assignment$4\_$data$2.$csv$),$ which contains year and bird count for each year, and analyze it as instructed.Question $3.$ Create a scatter plot to examine the association between year $($x$-$axis$)$ and bird count $($y$-$axis$)$ and describe the association between the two variables. $(20\%)$ Question $4.$ Fit the Poisson regression model to predict the number of barn swallows from year using R$.$ Report the estimated Poisson regression equation in a form, log$($y$)=$ b$0+$ b$1$ x$,$ where x is the year $($starts from $0)$ and y is the count of the barn swallow. $(20\%)$ Question $5.$ Based on the results you have, is there any temporal pattern in barn swallow count in this route? If so$,$ what is the pattern? Report the test statistic and p$-$value to support your answer. $(10\%)$ Question $6.$ Attach the R code and outputs to this assignment. $(20\%)$