Question

A pediatrician wants to determine the relation that may exist between a? child's height and head circumference. She randomly selects 8 children from her? practice, measures their height and head? circumference, and obtains the data shown in the table. Complete parts? (a) through? (e) to the right. Height? (in.) Head Circumference? (in.) 27 17.4 25.5 17.2 26 17.2 25.75 17 27.75 17.5 26.5 17.2 26.25 17.2 26.75 17.4 LOADING... Click here to see the Table of Critical Values for Correlation Coefficient. ?(a) If the pediatrician wants to use height to predict head? circumference, determine which variable is the explanatory variable and which is the response variable. The explanatory variable is height and the response variable is head circumference. The explanatory variable is head circumference and the response variable is height. ?(b) Draw a scatter diagram. Which of the following represents the? data? A. 16.9 17.6 25 28 Circ. (in) Height (in) A scatter diagram has a horizontal axis labeled “Circumference (inches)” from 16.9 to 17.6 in increments of 0.1 and a vertical axis labeled “Height (inches)” from 25 to 28 in increments of 0.5. The following 8 points are plotted, listed here from left to right: (17, 25.8); (17.2, 25.5); (17.2, 26); (17.2, 26.3); (17.2, 26.5); (17.4, 26.8); (17.4, 27); (17.5, 27.8). All vertical coordinates are approximate. The points generally rise from left to right at a constant rate. B. 16.9 17.6 25 28 Height (in) Circ. (in) A scatter diagram has a horizontal axis labeled “Height (inches)” from 16.9 to 17.6 in increments of 0.1 and a vertical axis labeled “Circumference (inches)” from 25 to 28 in increments of 0.5. The following 8 points are plotted, listed here from left to right: (17, 25.8); (17.2, 25.5); (17.2, 26); (17.2, 26.3); (17.2, 26.5); (17.4, 26.8); (17.4, 27); (17.5, 27.8). All vertical coordinates are approximate. The points generally rise from left to right at a constant rate. C. 25 28 16.9 17.6 Height (in) Circ. (in) A scatter diagram has a horizontal axis labeled “Height (inches)” from 25 to 28 in increments of 0.5 and a vertical axis labeled “Circumference (inches)” from 16.9 to 17.6 in increments of 0.1. The following 8 points are plotted, listed here from left to right: (25.5, 17.2); (25.8, 17); (26, 17.2); (26.3, 17.2); (26.5, 17.2); (26.8, 17.4); (27, 17.4); (27.8, 17.5). All horizontal coordinates are approximate. The points generally rise from left to right at a constant rate. D. 25 28 16.9 17.6 Circ. (in) Height (in) A scatter diagram has a horizontal axis labeled “Circumference (inches)” from 25 to 28 in increments of 0.5 and a vertical axis labeled “Height (inches)” from 16.9 to 17.6 in increments of 0.1. The following 8 points are plotted, listed here from left to right: (25.5, 17.2); (25.8, 17); (26, 17.2); (26.3, 17.2); (26.5, 17.2); (26.8, 17.4); (27, 17.4); (27.8, 17.5). All horizontal coordinates are approximate. The points generally rise from left to right at a constant rate. ?(c) Compute the linear correlation coefficient between the height and head circumference of a child. requals nothing ?(Round to three decimal places as? needed.) ?(d) Does a linear relation exist between height and head? circumference? ?(Round to three decimal places as? needed.) A. ?Yes, there appears to be a positive linear association because r is positive and is greater than the critical? value, nothing. B. ?Yes, there appears to be a negative linear association because r is negative and is less than the negative of the critical? value, nothing. C. ?No, there is no linear association since r is positive and is less than the critical? value, nothing. D. ?Yes, there appears to be a positive linear association because r is positive and is less than the critical? value, nothing. ?(e) Convert the data to centimeters? (1 inchequals2.54 ?cm), and recompute the linear correlation coefficient. What effect did the conversion have on the linear correlation? coefficient? Convert the first four data values to centimeters. Height? (centimeters) Head Circumference? (centimeters) nothing nothing nothing nothing nothing nothing nothing nothing ?(Type integers or decimals. Do not round. List the terms in the same order as they appear in the original? list.) Convert the last four data values to centimeters. Height? (centimeters) Head Circumference? (centimeters) nothing nothing nothing nothing nothing nothing nothing nothing ?(Type integers or decimals. Do not round. List the terms in the same order as they appear in the original? list.) The new linear correlation coefficient is requals nothing. The conversion to centimeters ? made the value of r decrease. had no effect on r. reversed the sign of r. made the value of r increase.

Answer 1

a)

The explanatory variable is height and the response variable is head circumference.

b) Option C is correct

A scatter diagram is obtained in excel by following the step,

Select the data > INSERT > Recommended Charts > All Charts > Scatter X Y.

c)

The correlation coefficient can be obtained using the excel function =CORREL(array1, array2)

Correlation coefficient, r=0.866237

d) Option A is correct.

The critical value of correlation coefficient for degree of freedom = n -2 = 8 - 2 = 6 and significance level = 0.05 is,

Yes, there appears to be a positive linear association because r is positive and is greater than the critical

e)

The data values after conversion are,

Sample	Height	Head Circumference
1	68.58	44.196
2	64.77	43.688
3	66.04	43.688
4	65.405	43.18
5	70.485	44.45
6	67.31	43.688
7	66.675	43.688
8	67.945	44.196

The correlation coefficient is obtained using the excel function =CORREL(array1, array2)

Correlation coefficient, r=0.866237.

There is no change in correlation coefficient after conversion (r unchanged)