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. Complete parts​ (a) through​ (f) below.

Height​ (inches), x	27.7527.75	2525	26.7526.75	27.527.5	25.525.5
Head Circumference​ (inches), y	17.617.6	16.916.9	17.317.3	17.517.5	17.117.1

​(a) Treating height as the explanatory​ variable, x, use technology to determine the estimates of

beta 0β0

and

beta 1β1.

beta 0β0almost equals≈b 0b0equals=nothing

​(Round to four decimal places as​ needed.)

beta 1β1almost equals≈b 1b1equals=nothing

​(Round to four decimal places as​ needed.)

Answer 1

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. Complete parts​ (a) through​ (f) below.

Height​ (inches), x	27.75	25	26.75	27.5	25.5
Head Circumference​ (inches), y	17.6	16.9	17.3	17.5	17.1

​(a) Treating height as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.

b0 = 11.0779

​(Round to four decimal places as​ needed.)

b1 = 0.2340

​(Round to four decimal places as​ needed.)

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis

Regression Analysis
	r²	0.981	n	5
	r	0.991	k	1
	Std. Error	0.045	Dep. Var.	Head Circumference​ (inches), y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	0.3218	1	0.3218	155.93	.0011
Residual	0.0062	3	0.0021
Total	0.3280	4
Regression output					confidence interval
variables	coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	11.0779	0.4971	22.285	.0002	9.4959	12.6599
Height​ (inches), x	0.2340	0.0187	12.487	.0011	0.1744	0.2937