Question 1 [40 marks] A paramo is a high altitude ecosystem above the forestline but below the snowline. A study was conducted in a chain of paramo 'islands' in the Andes of Venezuela, Colombia and Ecuador. Consider a regression model with abundance of bird species in paramo 'islands' as explained by the geography of the 'islands.' The data is available in the le paramo.dat on iLearn. Each row records the abundance of birds observed and geographic information for a single 'island' in the paramo chain. The variables are dened below. N Number of species of bird present AR Area of the island in square km EL Elevation in thousands of metres DEC Distance from Ecuador in kilometres DNI distance to the nearest other island in kilometre a. [6 marks] Produce a scatterplot and correlation matrix of the data and comment on possible relationships between the response and predictors and relationships between the predictors themselves. b. [14 marks] Fit a model using all the predictors to explain the N abundance number response. Conduct an F -test for the overall regression i.e. is there any relationship between the response and the predictors. In your answer: a Write down the mathematical multiple regression model for this situation, dening all appropriate parameters 0 Write down the Hypotheses for the Overall ANOVA test of multiple regression 0 Produce an ANOVA table for the overall multiple regression model (One combined regression SS source is sufcient) o Compute the F statistic for this test a State the Null distribution 0 Compute the P-Value 0 State your conclusion (both statistical conclusion and contextual conclusion) C. [9 marks] Validate the full model using all the predictors and comment on whether it is appropriate to a multiple regression model to explain the N abundance value. (:1. [2 marks] Find the R2 and comment on what it means in the context of this dataset. e. [3 marks] Using model selection procedures used in the course, nd the best multiple regression model that explains the data. State the nal tted regression model. f. [2 marks] Comment on the R2 and Adjusted R2 in the full and nal model you chose in part e. In particular explain why those goodness of tness measures change but not in the same way. g. [4 marks] Compute a 95% condence interval for the AR regression parameter and explain what it means in the context of this data