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 27.527.5 27.7527.75 25.525.5 2525 2626 Head Circumference (inches), y 17.517.5 17.617.6 17.117.1 16.916.9 17.317.3 are summarized below. Complete parts (a) through (f) below. Height (inches), x 27.527.5 27.7527.75 25.525.5 2525 2626 Head Circumference (inches), y 17.517.5 17.617.6 17.117.1 16.916.9 17.317.3 (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= (Round to four decimal places as needed.) beta 1β1almost equals≈b 1b1equals= (Round to four decimal places as needed.) (b) Use technology to compute the standard error of the estimate, s Subscript ese. s Subscript eseequals= (Round to four decimal places as needed.) (c) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine s Subscript b 1sb1. s Subscript b 1sb1equals= (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 alphaαequals= level of significance. State the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0H0: beta 0β0equals=0 Upper H 1H1: beta 0β0not equals≠0 B. Upper H 0H0: beta 0β0equals=0 Upper H 1H1: beta 0β0greater than>0 C. Upper H 0H0: beta 1β1equals=0 Upper H 1H1: beta 1β1not equals≠0 Your answer is correct. D. Upper H 0H0: beta 1β1equals=0 Upper H 1H1: beta 1β1greater than>0 Determine the P-value for this hypothesis test. P-valueequals= (Round to three decimal places as needed.) What is the conclusion that can be drawn? A. RejectReject Upper H 0H0 and conclude that a linear relation existsexists between a child's height and head circumference at the level of significance alphaαequals= Your answer is correct. B. RejectReject Upper H 0H0 and conclude that a linear relation does not existdoes not exist between a child's height and head circumference at the level of significance alphaαequals= C. Do not rejectDo not reject Upper H 0H0 and conclude that a linear relation does not existdoes not exist between a child's height and head circumference at the level of significance alphaαequals= D. Do not rejectDo not reject Upper H 0H0 and conclude that a linear relation existsexists between a child's height and head circumference at the level of significance alphaαequals= (e) Use technology to construct a 95% confidence interval about the slope of the true least-squares regression line. Lower bound: Upper bound: (Round to three decimal places as needed.) (f) Suppose a child has a height of 26.5 inches. What would be a good guess for the child's head circumference? A good estimate of the child's head circumference would be inches. (Round to two decimal places as needed.)

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 27.527.5 27.7527.75 25.525.5 2525 2626 Head Circumference (inches), y 17.517.5 17.617.6 17.117.1 16.916.9 17.317.3 are summarized below. Complete parts (a) through (f) below. Height (inches), x 27.527.5 27.7527.75 25.525.5 2525 2626 Head Circumference (inches), y 17.517.5 17.617.6 17.117.1 16.916.9 17.317.3 (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= (Round to four decimal places as needed.) beta 1β1almost equals≈b 1b1equals= (Round to four decimal places as needed.) (b) Use technology to compute the standard error of the estimate, s Subscript ese. s Subscript eseequals= (Round to four decimal places as needed.) (c) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine s Subscript b 1sb1. s Subscript b 1sb1equals= (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 alphaαequals= level of significance. State the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0H0: beta 0β0equals=0 Upper H 1H1: beta 0β0not equals≠0 B. Upper H 0H0: beta 0β0equals=0 Upper H 1H1: beta 0β0greater than>0 C. Upper H 0H0: beta 1β1equals=0 Upper H 1H1: beta 1β1not equals≠0 Your answer is correct. D. Upper H 0H0: beta 1β1equals=0 Upper H 1H1: beta 1β1greater than>0 Determine the P-value for this hypothesis test. P-valueequals= (Round to three decimal places as needed.) What is the conclusion that can be drawn? A. RejectReject Upper H 0H0 and conclude that a linear relation existsexists between a child's height and head circumference at the level of significance alphaαequals= Your answer is correct. B. RejectReject Upper H 0H0 and conclude that a linear relation does not existdoes not exist between a child's height and head circumference at the level of significance alphaαequals= C. Do not rejectDo not reject Upper H 0H0 and conclude that a linear relation does not existdoes not exist between a child's height and head circumference at the level of significance alphaαequals= D. Do not rejectDo not reject Upper H 0H0 and conclude that a linear relation existsexists between a child's height and head circumference at the level of significance alphaαequals= (e) Use technology to construct a 95% confidence interval about the slope of the true least-squares regression line. Lower bound: Upper bound: (Round to three decimal places as needed.) (f) Suppose a child has a height of 26.5 inches. What would be a good guess for the child's head circumference? A good estimate of the child's head circumference would be inches. (Round to two decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Height (inches), x	27.527.5	27.7527.75	25.525.5	2525	2626
Head Circumference (inches), y	17.517.5	17.617.6	17.117.1	16.916.9	17.317.3

are summarized below. Complete parts (a) through (f) below.

Height (inches), x	27.527.5	27.7527.75	25.525.5	2525	2626
Head Circumference (inches), y	17.517.5	17.617.6	17.117.1	16.916.9	17.317.3

(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=

(Round to four decimal places as needed.)

beta 1β1almost equals≈b 1b1equals=

(Round to four decimal places as needed.)

(b) Use technology to compute the standard error of the estimate,

s Subscript ese.

s Subscript eseequals=

(Round to four decimal places as needed.)

s Subscript b 1sb1.

s Subscript b 1sb1equals=

(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

alphaαequals=

level of significance. State the null and alternative hypotheses for this test.

Choose the correct answer below.

Upper H 0H0:

beta 0β0equals=0

Upper H 1H1:

beta 0β0not equals≠0

Upper H 0H0:

beta 0β0equals=0

Upper H 1H1:

beta 0β0greater than>0

Upper H 0H0:

beta 1β1equals=0

Upper H 1H1:

beta 1β1not equals≠0

Your answer is correct.

Upper H 0H0:

beta 1β1equals=0

Upper H 1H1:

beta 1β1greater than>0

Determine the P-value for this hypothesis test.

P-valueequals=

(Round to three decimal places as needed.)

What is the conclusion that can be drawn?

RejectReject

Upper H 0H0

and conclude that a linear relation

existsexists

between a child's height and head circumference at the level of significance

alphaαequals=

Your answer is correct.

RejectReject

Upper H 0H0

and conclude that a linear relation

does not existdoes not exist

between a child's height and head circumference at the level of significance

alphaαequals=

Do not rejectDo not reject

Upper H 0H0

and conclude that a linear relation

does not existdoes not exist

between a child's height and head circumference at the level of significance

alphaαequals=

Do not rejectDo not reject

Upper H 0H0

and conclude that a linear relation

existsexists

between a child's height and head circumference at the level of significance

alphaαequals=

(e) Use technology to

construct

a 95% confidence interval about the slope of the true least-squares regression line.

Lower bound:

Upper bound:

(Round to three decimal places as needed.)

(f) Suppose a child has a height of 26.5 inches. What would be a good guess for the child's head circumference?

A good estimate of the child's head circumference would be

inches.

(Round to two decimal places as needed.)

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