Question

A pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Complete parts​ (a) and​ (b) below.

Height_(inches)_-_x   Head_Circumference_(inches)_-_y
26   17.3
25.5   17.1
27.5   17.5
24.5   17.1
27.75   17.6

​(a) Use technology to determine s Subscript b 1sb1.

s Subscript b 1sb1equals=   ​(Round to four decimal places as​ needed.)

Determine the​ P-value for this hypothesis test.

​P-value equals=? ​(Round to three decimal places as​ needed.)

What is the conclusion that can be​ drawn?

Answer 1

Solution :

Regression Statistics
Multiple R	0.960768923
R Square	0.923076923
Adjusted R Square	0.897435897
Standard Error	0.073029674
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.192	0.192	36	0.009273
Residual	3	0.016	0.005333
Total	4	0.208
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	13.12	0.700761	18.72249	0.000333	10.88986	15.35014	10.88986	15.35014
X Variable 1	0.16	0.026667	6	0.009273	0.075135	0.244865	0.075135	0.244865

a)

Sb1 = 0.0267

P-value = 0.009

P-value < alpha

0.009 < 0.05

Reject H0.