Question

There is a disease going around in the country. As opposed to the previous cases, 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. As the king is worried, he gave you the task of predicting the number of cases for next 7 days.

Day	Number of Cases
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

a.) Draw a graph of the data in Excel. 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. 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.

Answer 1

1)

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

2)

Day	Number of Cases	LN(Day)	LN(Number of cases)	Growth
1	85	0	4.442651
2	121	0.693147	4.795791	0.423529
3	166	1.098612	5.111988	0.371901
4	228	1.386294	5.429346	0.373494
5	282	1.609438	5.641907	0.236842
6	401	1.791759	5.993961	0.421986
7	525	1.94591	6.263398	0.309227
8	674	2.079442	6.51323	0.28381
9	1,231	2.197225	7.115582	0.826409
10	1,695	2.302585	7.435438	0.376929
11	2,277	2.397895	7.730614	0.343363
12	3,146	2.484907	8.053887	0.381643
13	5,232	2.564949	8.562549	0.663064
14	6,391	2.639057	8.762646	0.221521
15	7,988	2.70805	8.985696	0.249883
16	9,942	2.772589	9.204523	0.244617
17	11,826	2.833213	9.378056	0.189499
18	14,769	2.890372	9.600286	0.248858
19	18,077	2.944439	9.802396	0.223983
20	21,571	2.995732	9.979105	0.193284
21	25,496	3.044522	10.14628	0.181957
22	29,909	3.091042	10.30591	0.173086
23	35,480	3.135494	10.47672	0.186265
24	42,058	3.178054	10.6468	0.1854
25	50,105	3.218876	10.82188	0.191331
26	57,786	3.258097	10.9645	0.153298
27	65,719	3.295837	11.09314	0.137282
28	73,232	3.332205	11.20139	0.11432
29	80,110	3.367296	11.29116	0.093921
30	87,956	3.401197	11.38459	0.09794
31	95,923	3.433987	11.4713	0.090579

Scatter of the logarithm of number of cases. (log(X)).

We are not convinced that fitting a trend line would bring a good forecast.

because it might not be able to model the specific curve that exists in your data.

Hence fitting a trend line on logarithm may not generate good forecasts in this case.

C) Daily groeth rate

Day	Growth
2	0.423529
3	0.371901
4	0.373494
5	0.236842
6	0.421986
7	0.309227
8	0.28381
9	0.826409
10	0.376929
11	0.343363
12	0.381643
13	0.663064
14	0.221521
15	0.249883
16	0.244617
17	0.189499
18	0.248858
19	0.223983
20	0.193284
21	0.181957
22	0.173086
23	0.186265
24	0.1854
25	0.191331
26	0.153298
27	0.137282
28	0.11432
29	0.093921
30	0.09794
31	0.090579

It has decline trend hence

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

Answer: growth has decline trend which we will predict using fit linear model and we get

g(D)=0.4802-0.01256*D

where D= Day

this estimated growth we will use to forecsat # of cases for next 7 days using

X(t+1)=X(t) x (1+g).

Day	g=est(g(t))	X(t+1)=X(t) x (1+g).
32	0.078024	103407
33	0.065456	110176
34	0.052888	116003
35	0.04032	120680
36	0.027752	124029
37	0.015184	125913
38	0.002616	126242