Question

An emergency service wishes to see whether there a relationship exists between the outside temperature and the number of emergency calls it receives. The data is shown below. Temperature x | 68 74 82 88 93 99 101 Number of calls | 5 5 7 8 11 12 13

Answer 1

Calculat Correlation Coefficient To see whether there a relationship exists between the outside temperature and the number of emergency calls

Therefor,

x: outside temperature

y: number of emergency calls

Formua for Calculat Correlation Coefficient is,

First, calculate mean of x and y,

Mean of x = (68+74+82+88+93+99+101) / 7

= 605 / 7

= 86.42

Mean of y = (5+5+7+8+11+12+13) / 7

= 61 / 7

= 8.71

Construct a table for get required sum,

Where, Meanx = Mean of x and Meany = Mean of y

S.N.	x	y	xi - Meanx	yi - Meany	(xi - Meanx) * (yi - Meany)	(xi - Meanx)2	(yi - Meany)2
1	68	5	-18.42	-3.71	68.34	339.30	13.76
2	74	5	-12.42	-3.71	46.08	154.26	13.76
3	82	7	-4.42	-1.71	7.56	19.54	2.92
4	88	8	1.58	-0.71	-1.12	2.50	0.50
5	93	11	6.58	2.29	15.07	43.30	5.24
6	99	12	12.58	3.29	41.39	158.26	10.82
7	101	13	14.58	4.29	62.55	212.58	18.40
Total	605	61	0.06	0.03	239.86	929.71	65.43

By Using Above Formula,

r = 239.86 / sqrt (929.71) * sqrt(65.43)

= 239.86 / 246.63

r = 0.97 i.e. 97%

The Correlation is 97%, that means Highly Correlated.

Conclusion:

There is Relationship Exists between the outside temperature and the number of emergency calls it receives.