Question

How do I draw a scatterplot of each of the following, while giving a realistic example of each: A weak positive correlation A weak negative correlation

Answer 1

The magnitude of a weak correlation is between 0 to 0.3.

A positive correlation occurs when the two variables are directly related (or you can say that the slope of the line is positive) and a negative correlation occurs when the two variables are inversly related (or you can say that the slope of the line is negative).

-------------------------------------------

An example of the weak positive correlation would be the relation between 'Age' and 'Number of sickies of that age'.

Now a general intution says that older people are more prone to diseases than younger people. But that is not strongly correlated because infants and children also have high disease rate. Only the teenagers and people in 30s are less prone to disease as body is efficient to fight against diseases. A random data for this is given below -

Age	Number of Sickies
2	6
3	6
4	8
5	9
6	10
8	10
9	8
10	7
12	11
13	9
14	12
15	12
16	13
17	11
18	6
19	8
20	5
21	6
22	4
23	2
24	3
25	2
26	4
27	4
28	4
29	2
30	3
31	4
32	5
33	6
34	5
35	4
36	1
37	2
38	3
39	7
40	6
41	5
42	4
43	8
44	9
45	7
46	7
48	8
50	10
52	11
54	9
56	8
58	12
60	12
62	13
64	12
66	11
68	13
70	14

And the correlation of this data is = 0.267284

And the scatter plot of the data is -

_______________________________________________

And an example of weak negative correlation would be 'per capita income' and 'population' of a given country. Generally one would expect the per capita income of a highly populated country like China to be small compared to a less populated country like Japan, but that is not so strongly supported by the data. Although there is a negative correlation but a very weak one.

A random data is as shown -

Country	Population (Thousands)	Per Capita Income
Afghanistan	35530.08	$139,100
Albania	2873.46	$124,500
Algeria	41318.14	$115,700
American Samoa	55.64	$111,600
Andorra	76.97	$106,300
Angola	29784.19	$99,400
Antigua and Barbuda	102.01	$84,600
Argentina	44271.04	$78,200
Armenia	2930.45	$75,500
Australia	24598.93	$70,800
Austria	8809.21	$67,700
Bangladesh	164669.75	$61,400
Barbados	285.72	$61,400
Belgium	11372.07	$58,600
Bhutan	807.61	$52,500
Brazil	209288.28	$50,300
Bulgaria	7075.99	$49,900
Cambodia	16005.37	$46,200
Canada	36708.08	$44,300
Chile	18054.73	$42,800
Colombia	49065.61	$41,800
Cuba	11484.64	$37,000
France	67118.65	$27,800
Germany	82695	$26,300
Greece	10760.42	$25,300
Hungary	9781.13	$19,300
Iceland	341.28	$19,200
Iran	81162.79	$18,700
Iraq	38274.62	$18,100
Ireland	4813.61	$17,900
Israel	8712.4	$17,700
Italy	60551.42	$17,500
Japan	126785.8	$17,000
Mauritius	1264.61	$11,500
Mexico	129163.28	$11,300
Nepal	29305	$8,900
Pakistan	197015.95	$7,200
Philippines	104918.09	$6,200
Portugal	10293.72	$5,800
Romania	19586.54	$5,700
Russia	144495.04	$5,600
Saudi Arabia	32938.21	$3,900
Singapore	5612.25	$3,700
South Africa	56717.16	$3,400
Spain	46572.03	$3,200
Sri Lanka	21444	$3,200
Switzerland	8466.02	$2,700
Thailand	69037.51	$2,300
Turkey	80745.02	$2,000
United Arab Emirates	9400.15	$1,700
United Kingdom	66022.27	$1,600
United States	325719.18	$1,600
Uruguay	3456.75	$1,600
Zimbabwe	16529.9	$700

The scatter plot of the data is as shown -

And the correlation coefficient of the data is = -0.23614

--------------------------------

If you include the data of India and China, this value goes down to -0.08.