PHYS5032 Techniques for Sustainability Analysis
Total points: 15
Homework Sheet 3: Multiple Linear Regression
There is increasing evidence that the continuing replacement of natural environments by human developments has adverse effects on human health. For this homework sheet, you will be looking at the linkages between deforestation and malaria cases in developing countries.
Current practice is to prevent malaria with insecticide-treated mosquito nets (ITN), and to treat patients with artemisinin-based combination therapies (ACT). This has shown positive effects on the development of malaria cases. Additionally, it has been shown that the deforestation of primary forests in malaria-plagued countries contributes to the spread of the disease. The tree cover loss (TCL) is expected to have significant effects on the occurrence of malaria.
Your task is to build a linear regression model to investigate how much the loss of tree cover contributes to the malaria cases, and to simulate the malaria occurrence if ITN and ACT were not available.
1. Please download the data sheet on the Canvas homework page. The data sheet contains data for the whole of Africa.
2. (A) (3 points) Perform. a linear regression using LINEST for the whole of Africa data set. The explanatory variables (denoted with x_i in the lecture) are year, TCL, ITN, and ACT. The explained variable (denoted with y in the lecture) is Malaria Cases. Write down the model in the form used in the lecture explicitly.
3. (A) (2 points) Perform t-test for the three significance levels 0.1, 0.05, and 0.01 and indicate for which variable and which significance level you reject/accept the null hypothesis.
4. (A) (1.5 points) Is there any statistical proof that tree cover loss (TCL) has an effect on the malaria cases? If yes, what is the highest significance level for which you reject the null hypothesis? Does this give you strong evidence that there is a relationship?
5. (A) (0.5 point) The research team requires a goodness offit of at least 0.9 to accept the model. Can you confirm a goodness offit of 0.9 for your model? (1 point)
6. (A) (2 points) The research team decides to use your model for scenario analysis. Use your model to determine how many malaria cases there would be if
a) TCL and ITN were the same as in the last year of the measurements, but there were no treatment options (ACT = 0) in the final year.
b) there were no mosquito nets or treatment options in the final year.
7. In your own words (A): (3 points) Assume your r-squared value was too low. How would you improve the model? Are you be able to prove how effective are your suggestions?
8. In your own words (A): (3 points) Provide your reflections on how the multi-regression model is applied in the sustainability field. Talk about at least one specific application; It could be from papers covered in the lecture or any applications that interest you. Make sure you describe research questions, model framework, and conclusions for the chosen application, together with your own reflections. (within 400 words)