Question

Use data provided below to answer.
Gondor is facing a pandemic of Black Breath. As opposed to the previous incidences, this time the disease develops slowly in the body and in that phase the infected people are also contagious. This led to an unprecedented number of infections. The data shows the number of infected people by day. Although the hands of the king are the hands of a healer, the numbers are beyond his capacity. He is worried and he gave you the task of predicting the number of cases for next 7 days.

a.) Draw a graph of the data in Excel(Line of Scatter, your choice). How does it look like, which methods would be suitable to forecast?

b.) A wise man told you that if a variable is exponentially increasing, then the logarithm of that variable would have a linear trend. With that information, you decided to take a scatter of the logarithm of number of cases. (log(X)). You can also do the same by changing the scale of the vertical axis to log scale.(Using format axis in the graph, please Google if you don't know). You are not convinced that fitting a trend line would bring a good forecast. Why would you think so? Why fitting a trend line on logarithm may not generate good forecasts in this case?

c.) Growth rate of a variable is defined as: (X(t+1)-X(t))/X(t) Therefore, if you have a forecast for growth rate g, than you can generate a forecast for the variable using X(t+1)=X(t) x (1+g)

Calculate the daily growth rate, and scatter the growth rate of cases. How does it look like?

d.) Forecast the number of cases for the next 7 days. Choose the method based on your judgement on previous graphs.

Day	Gondor Cases of Black Breath
1	85
2	121
3	166
4	228
5	282
6	401
7	525
8	674
9	1,231
10	1,695
11	2,277
12	3,146
13	5,232
14	6,391
15	7,988
16	9,942
17	11,826
18	14,769
19	18,077
20	21,571
21	25,496
22	29,909
23	35,480
24	42,058
25	50,105
26	57,786
27	65,719
28	73,232
29	80,110
30	87,956
31	95,923

Answer 1

a)

exponential model is appropriate

b)

c)