Question

Annual high temperatures in a certain location have been tracked for several years. Let Xrepresent the year and Ythe high temperature. Based on the data shown below, calculate the correlation coefficient (to three decimal places) between Xand Y.

x	y
4	23.3
5	21.7
6	19
7	20.1
8	16.8
9	12.3
10	12.6
11	8.4
12	6.4
13	6.8

r=

Answer 1

Solution,

X	Y	XY	X^2	Y^2
4	23.3	93.2	16	542.89
5	21.7	108.5	25	470.89
6	19	114	36	361
7	2.1	14.7	49	4.41
8	16.8	134.4	64	282.24
9	12.3	110.7	81	151.29
10	12.6	126	100	158.76
11	8.4	92.4	121	70.56
12	6.4	76.8	144	40.96
13	6.8	88.4	169	46.24

n	10
sum(XY)	959.10
sum(X)	85.00
sum(Y)	129.40
sum(X^2)	805.00
sum(Y^2)	2129.24
Numerator	-1408.00
Denominator	1937.04
r	-0.7269
r square	0.5284
Xbar(mean)	8.5000
Ybar(mean)	12.9400
SD(X)	1.7078
SD(Y)	3.5734
b	-1.7067
a	27.4467

r = -0.7269