Question 3 (10 marks) Timmy is a herpetologist specialising in the giant snakes on the exotic island of Cosmanda. He believes there is a relationship between the age of Cosmandan snakes and their length. Timmy has just completed a 5-year collaboration with Cosmandan Wildlife Preservation, and has collected data on the age of various snakes (in years) and their corresponding length (in metres). A plot of the data is included below. 12 10 Length (metres) 2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Age (years) a) Let A and L, denote the age and length of snake s. State which one of these is the dependent variable, and which is the independent variable. [1 mark) b) Timmy has applied a linear regression to this data. He has found that = 1.2637, B = 1.5935, and a = 0.550676. Clearly state the function of each of a, b, and 8%. [2 marks] c) Timmy has calculated SE(X) = 0.13289, and SE() = 0.04894. Perform any relevant calculations, then comment on the significance of & and . [1 mark] d) For this model, R2 = 0.843305. State what this means, with reference to the graph above. [1 mark] e) Vicky, one of Timmy's colleagues, has found a snake during her surveyance, but was not able to measure the length of this snake. However, she was able to tell that the snake was 3.5 years old based on the patterns on its scales. Estimate the length, in metres, of this snake based on Timmy's results, and also give a 95% confidence interval for this estimate. [2 marks] f) State the formula for the linear regression model, and any associated assumptions. Then, by using the included graph above, comment on the appropriateness of this model. In particular, discuss whether the assumptions hold true. Question 3 (10 marks) Timmy is a herpetologist specialising in the giant snakes on the exotic island of Cosmanda. He believes there is a relationship between the age of Cosmandan snakes and their length. Timmy has just completed a 5-year collaboration with Cosmandan Wildlife Preservation, and has collected data on the age of various snakes (in years) and their corresponding length (in metres). A plot of the data is included below. 12 10 Length (metres) 2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Age (years) a) Let A and L, denote the age and length of snake s. State which one of these is the dependent variable, and which is the independent variable. [1 mark) b) Timmy has applied a linear regression to this data. He has found that = 1.2637, B = 1.5935, and a = 0.550676. Clearly state the function of each of a, b, and 8%. [2 marks] c) Timmy has calculated SE(X) = 0.13289, and SE() = 0.04894. Perform any relevant calculations, then comment on the significance of & and . [1 mark] d) For this model, R2 = 0.843305. State what this means, with reference to the graph above. [1 mark] e) Vicky, one of Timmy's colleagues, has found a snake during her surveyance, but was not able to measure the length of this snake. However, she was able to tell that the snake was 3.5 years old based on the patterns on its scales. Estimate the length, in metres, of this snake based on Timmy's results, and also give a 95% confidence interval for this estimate. [2 marks] f) State the formula for the linear regression model, and any associated assumptions. Then, by using the included graph above, comment on the appropriateness of this model. In particular, discuss whether the assumptions hold true
