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 Head Circumference (inches), y| 26.5 25.5 25 27 260 17.5 17.3 17.1 16.9 17.3 (a) Treating height as the explanatory variable, x, use technology to determine the estimates of Po and B,. Bo bo = B, b, = (Round to four decimal places as needed.) (Round to four decimal places as needed.) (b) Use technology to compute the standard error of the estimate, 8q. (Round to four decimal places as needed.) Se (c) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine sp. (Round to four decimal places as needed.) (d) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between height and head circumference at the a = 0.01 level of significance. State the null and alternative hypotheses for this test. lew C Choose the correct answer below. w Qu OA Hg: B 0 OB. Ho: P 0 lew Qu OC. Ho: Po -0 H: Po0 OD. Ho: Po 0 or to bu Click to select your answer(s).

Answer 1

Given

- Fax F8 A 0.923076923076922 D B C 26.5 SUMMARY OUTPUT 17.3 17.1 16.9 17.5 17.3 26 Regression Statistics Multiple R 0.970725343 R Square 0.942307692 Adjusted R Square 0.923076923 Standard Error 0.063245553 Observations ANOVA df F significance F 490.005986256 1 Regression Residual Total SSMS 0.196 0.196 0.012 0.004 0.208 w Intercept Coefficients Standard Error 9.94 1.040384544 0.28 0.04 Stat P-value 9.55416 0.002432346 7 0.005986256 Lower 95% Upper 95% Lower 99.0% Upper 99.0% 6.629032051 13.2509679 3.86320823 16.01679177 0.152702148 0.40729785 0.046363628 0.513636372

a) b0 = 9.94
b1 = 0.28

b) se = 0.0632

c) sb1 = 0.04

d) Correct answer: Option (A)

P-value = 0.006

Correct answer: Option (B) Reject H0 and conclude that a linear relation exists between a child's height and head circumference at the level of significance alpha = 0.01

e) Lower Bound: 0.153
and Upper bound : 0.407

f) The regression equation is
y = 9.94 + 0.28 x
Given X = 26.5
then y-hat = 9.94 + 0.028(26.5) = 17.36
Answer: 17.36 inches