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.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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