Question

4) Listed below data from a preschool with the ages of children and the mean number of diaper changes for each child per day in that age group. Compute the correlation coefficient. Show your work. 1 Age (years) 2 Diaper Changes 3.5 2.3 3 4 5 1.8 0.65 0

Answer 1

	X	Y	X^2	Y^2	XY
	1	3.5	1	12.25	3.5
	2	2.3	4	5.29	4.6
	3	1.8	9	3.24	5.4
	4	0.65	16	0.4225	2.6
	5	0	25	0	0
SUM	15	8.25	55	21.2025	16.1
n	5
Mean	3	1.65
SSxx	10	Sum(x^2) - ((Sum(x))^2 /n)	SSR	7.48225	slope * Ssxy	MSR	7.48225	SSR/k-1
Ssyy	7.59	Sum(y^2) - ((Sum(y))^2 /n)	SSE	0.10775	SST-SSR	MSE	0.035917	SSE/n-k
Ssxy	-8.65	Sum(xy) - (Sum(x)*Sum(y)/n)	SST	7.59	Ssyy	F	208.3225	MSR/MSE
slope	-0.865	Ssxy/SSxx
intercept	4.245	Mean Y - Mean X * Slope
Se	0.189517	SQRT(SSE/(n-2))
Sb1	0.059931	Se/SQRT(SSxx)
r	-0.99288	SSxy/SQRT(SSxx*SSyy)
r^2	0.985804

Correlation coefficient (r) = -0.9929

There is a negative and strong correlation between X and Y variables