# correlation coefficient

critical values for the correlation coefficient 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 120.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 X 4.1.19 Question Help O For the accompanying data set, (a) draw a scatter diagram of the data, (b) compute the correlation coefficient, and (c) determine whether there is a linear relation between x and y. Click the icon to view the data set. Click the icon to view the critical values table. (a) Draw a scatter diagram of the data. Choose the correct graph below. OA. B. D. У AY 10- лу 10- AY 10- 10- 3 . х х х х 0 0 0- 0 0- 0 10 10 0 10 0 10 (b) Compute the correlation coefficient. The correlation coefficient is r= I. (Round to three decimal places as needed.) complete) Score: 09.09%, 10.94 01 20 X 4.1.19 i critical values for the correlation coefficient For the accompanying data set, (a) draw a scatter diagram of the d linear relation between x and y. Click the icon to view the data set. Critical Values for Correlation Coefficient Click the icon to view the critical values table. n (a) Draw a scatter diagram of the data. Choose the correct graph b i X Х Data set х 7 6 9 00 No 3 0.997 4 0.950 5 0.878 6 0.811 0.754 8 0.707 9 0.666 100.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 у 3 7 5 Print Done Enter your answer in the answer box and then click Check Ans Print Done (c) Determine whether there is a linear relation between x and y. Because the correlation coefficient is and the absolute value of the correlation coefficient, is than the critical value for this data set, linear veen x and y. (Round to three decimal places as net negative positive (c) Determine whether there is a linear relation between x and y. Because the correlation coefficient is and the absolute value of the correlation coefficient, is than the critical value for this data set, linear relation exists between x and y. (Round to three decimal places as needed.) icient, is than the critical value for greater not greater linear relation exists between x and y. ded.) Lee de a negative nswei a positive ind then click Check Answer. no wing Cle x 4.1.17 Question Help For the accompanying data set, (a) draw a scatter diagram of the data, (b) by hand, compute the correlation coefficient, and (c) determine whether there is a linear relation between x and y. Click here to view the data set. Click here to view the critical values table. (a) Draw a scatter diagram of the data. Choose the correct graph below. A. B. лу 20- лу 20- 20- ку 20- . . : . • • х х X х 0 0- 0 0 0 0- 0 0 10 10 10 10 (b) By hand, compute the correlation coefficient. The correlation coefficient is r= (Round to three decimal places as needed.) i 1 Data set X Х n 2 4 6 6 7 ८]x 4 8 11 13 19 Print Done (c) Determine whether there is a linear relation between x and y. is greater than the critical value for Because the correlation coefficient is positive and the absolute value of the correlation coefficient, this data set, a positive linear relation exists between x and y. Round to three decimal places as needed.) 1x 4.1.25 Question Help The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Complete parts (a) through (d) below. Click the icon to view the critical values for the correlation coefficient. Commute Time (in minutes) Well-Being Score 5 69.3 17 68.3 23 67.7 36 67.4 48 66.7 72 65.9 101 63.7 (b) Draw a scatter diagram of the data. Which of the following represents the data? OA. B. C. OD. 70- 70- 110- 70- . . . . Score Score 60 0 110 Commute Time (min) 60- 0 110 Commute Time (min) 0- 60 70 Commute Time (min) 60+ 0 110 Commute Time (min) (c) Determine the linear correlation coefficient between commute time and well-being score. r= (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. x 4.1.25-T Question Help e The data in the table to the right are based on the results of a survey comparing the commute time of adults to their score on a well-being test. Complete parts (a) through (d) below. Click the icon to view the critical values for the correlation Commute Time (in minutes) Well-Being Score 7 69.9 14 68.4 67.9 33 67.6 53 66.8 75 66.6 103 63.5 coefficient. 25 (b) Draw a scatter diagram of the data. Which of the following represents the data? B. O C. D. 70 70-4• 70- 110- O Score Score Score Score 2 C 60- 0 110 Commute Time (min) 60 0 110 Commute Time (min) 60- 0 110 Commute Time (min) 0- 60 70 Commute Time (min) (c) Determine the linear correlation coefficient between commute time and well-being score. (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. % 4.1.27-T Question Help 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) below. E Click here to see the Table of Critical Values for Correlation Coefficient. Height (in.) Head Circumference (in.) . 27 17.4 25.5 16.9 26.5 17.2 25 17 27.5 17.5 26.25 17.1 26.25 17.2 26.75 17.3 TTIC Capianatory vanavic i TICIN anu WC IcSponse vanaviC is nicau II CUTTICI CICC. (b) Draw a scatter diagram. Choose the correct graph below. OA. B. C. 28- 28- 17.6- 17.6- 25+ 16.9 17.6 Circ. (in.) 음 25+ 16.9 17.6 Height (in.) 16.9+. 25 28 Height (in.) 16.9+ 25 28 Circ. (in.) (c) Compute the linear correlation coefficient between the height and head circumference of a child. (Round to three decimal places as needed.) (d) Does a linear relation exist between height and head circumference? Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. Yes, the variables height and head circumference are positively associated because r is negative and the absolute value of the correlation coefficient is greater than the critical value, . B. No, the variables height and head circumference are not linearly related because r is negative and the absolute value of the correlation coefficient is less than the critical value, C. Yes, the variables height and head circumference are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value, D. No, the variables height and head circumference are not linearly related because r is positive and the absolute value of the correlation coefficient is less than the critical value, (e) Convert the data to centimeters (1 inch = 2.54 cm), and recompute the linear correlation coefficient. What effect did the conversion have on the linear correlation coefficient? Height Head Circumference (centimeters) (centimeters) Convert the first four data values to centimeters. (Type integers or decimals. Do not round. List the terms in the same order as they appear in the original list.) Enter your answer in the edit fields and then click Check Answer. ? 63.5 43.18 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 Head Circumference (centimeters) (centimeters) Type integers or decimals. Do not round. List the terms in the same order as they appear in the original list.) nter your answer in the edit fields and then click Check Answer. ? Convert the last four data values to centimeters. Height Head Circumference made the value of r decrease. had no effect on r. reversed the sign of r. Type integers or decimals. Do not round. List the terms in the same or made the value of r increase. The conversion to centimeters The new linear correlation coefficient is r= Round to three decimal places as needed.) nter your answer in the answer box and then click Check Answer. ? and the response variable is the weight. An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weight of various cars and their gas mileage. Complete parts (a) through (d). (b) Draw a scatter diagram of the data. Choose the correct scatter plot. O A. B. 4000- 30- Weight Miles per Car (pounds) Gallon A 2655 26 B 3340 21 с 3310 19 D 3100 21 E 3180 23 Weight (lbs) : mpg . 2500+ 15 to 15+ 2500 4000 Weight (lbs) mpg Click the icon to view the critical values table. O 4000- 30- Weight (lbs) :. bdu 끝 2500+ 15 30 15 2500 4000 Weight (lbs) mpg (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. ra (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. (d) Comment on the type of relation that appears to exist between the weight of a car and its miles per gallon based on the scatter diagram and the linear correlation coefficient. Because the correlation coefficient is negative and the absolute value of the correlation coefficient, is greater than the critical value for this data set, a negative linear relation exists between the weight of a car and its miles per gallon. (Round to three decimal places as needed.) ck Answer. ? and the response variable is height. (b) Draw a scatter diagram. Which of the following represents the data? B. 17.6 28- 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) Ehrough (e) to the right. Height (in.) Head Circumference (in.) 2 27.25 17.3 25.5 16.9 26 17.2 25.75 17 27.5 17.6 26.75 17.2 25.75 17.1 26.75 17.3 Height (in) Height (in) J 16.9+ 25 28 Circ. (in) 25- 16.9 17.6 Circ. (in) C. 17.6 28- Click here to see the Table of Critical Values for Correlation Coefficient. Circ. (in) Circ. (in) 16.9 25 28 Height (in) 25- 16.9 17.6 Height (in) (c) Compute the linear correlation coefficient between the height and head circumference of a child. r= (Round to three decimal places as needed.) Inter your answer in the answer box and then click Check Answer. A pediatrician wants to determine the relation that may (Round to three decimal places as needed.) exist between a child’s height and head circumference. She randomly selects 8 children from her practice, (d) Does a linear relation exist between height and measures their height and head circumference, and head circumference? obtains the data shown in the table. Complete parts (a) (Round to three decimal places as needed.) through (e) to the right. O A. No, the variables height and head Height (in.) Head Circumference (in.) – circumference are not linearly related 27.25 17.3 because r is negative and the absolute value 25.5 16.9 of the correlation coefficient is less than the 26 17.2 critical value, 25.75 17 27.5 17.6 B. Yes, the variables height and head 26.75 17.2 circumference are positively associated 25.75 17.1 because r is negative and the absolute value 26.75 of the correlation coefficient is greater than 17.3 the critical value, : Click here to see the Table of Critical Values for O C. No, the variables height and head Correlation Coefficient. circumference are not linearly related because r is positive and the absolute value of the correlation coefficient is less than the critical value, D. Yes, the variables height and head circumference are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value, B. X One or more of your responses is incorrect. To determine if a linear relation exists, compare the linear correlation coefficient to the critical value from the table of critical values. If the linear correlation coefficient is greater than the critical value, there is a positive linear association. If the linear correlation coefficient is less than the negative of the critical value, there is a negative linear association. Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 190.456 20 0.444 21 0.433 22 0.423 23 0.413 MA ANA Print Done 8 0.707 9 0.666 100.632 110.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 n x Question Help o X Try again. between height and s as needed.) To determine if a linear relation exists, compare the linear correlation coefficient to the critical value from the table of critical values. If the linear correlation coefficient is greater than the critical value, there is a positive linear association. If the linear correlation coefficient is less than the negative of the critical value, there is a negative linear association. and head inearly related because isolute value of the less than the critical OK 17.2 17 5.75 2.5 5.75 5.75 5.75 17.6 17.2 17.1 17.3 Click here to see the Table of Critical Values for orrelation Coefficient. O B. Yes, the variables height and head circumference are positively associated because r is negative and the absolute value of the correlation coefficient is greater than the critical value, C. No, the variables height and head circumference are not linearly related because ris positive and the absolute value of the correlation coefficient is less than the critical value, 0.907 OD. Yes, the variables height and head circumference are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value, ck to select and enter your answer(s) and then click Check Answer. mx 4.1.27 Question Help IVO, le vallabies neigil allu neau circumference are not linearly related because ris positive and the absolute value of the correlation coefficient is less than the critical value, 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.) 2 27.25 17.3 25.5 16.9 26 17.2 25.75 17 27.5 17.6 26.75 17.2 25.75 17.1 26.75 17.3 D. Yes, the variables height and head circumference are positively associated because ris positive and the absolute value of the correlation coefficient is greater than the critical value, 0.707 . (e) Convert the data to centimeters (1 inch = 2.54 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. Click here to see the Table of Critical Values for Correlation Coefficient. Height Head Circumference (centimeters) (centimeters) (Type integers or decimals. Do not round. List the terms in the same order as they appear in the original list.) וייוט דט:E-ווטווין טוטוטווווווטט טו uuid טויוטwווטט (9) 1 -), 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. 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.) a 27.25 17.3 25.5 16.9 26 17.2 25.75 17 27.5 17.6 26.75 17.2 25.75 17.1 26.75 17.3 Height Head Circumference (centimeters) (centimeters) 69.215 43.942 64.77 42.926 66.04 43.688 65.405 43.18 (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. Click here to see the Table of Critical Values for Correlation Coefficient. Height Head Circumference (centimeters) (centimeters) (Type integers or decimals. Do not round. List the terms in the same order as they appear in the original list.) Enter your answer in the edit fields and then click Check Answer. 67.945 43.942 (Type integers or decimals. Do not round. List the terms in the same order as they appear in the original list.) The The new linear correlation coefficient is r= conversion to centimeters had no effect on r. (Round to three decimal places as needed.) click Check Answer Researchers initiated a long-term study of the population of American black bears. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The accompanying data represent the lengths and weights of 12 American black bears. Complete parts (a) through (d) below. Click the icon to view the data table. Click the icon to view the critical values table. i Data table B. The weight of the bear C. The number of bears (b) Draw a scatter diagram of the data. Choose the correct graph below Weigh 110 O A. B. 60 Weight (kg) 180- I ALength (cm) 180- Weight (k 180- 90 60 95 Total Length (cm) 138.0 138.0 139.0 120.5 149.0 141.0 141.0 150.0 166.0 151.5 129.5 105 40+ 100 200 Length (cm) 40 100 200 Weight (kg) 40+ 100 Length 11d 85 (c) Determine the linear correlation coefficient between weight and leng 155 The linear correlation coefficient between weight and length is r= (Round to three decimal places as needed.) 140 105 150.0 110 X Х Data table n Total Length (cm) 138.0 Weight (kg) 110 138.0 60 139.0 90 120.5 60 149.0 95 105 110 141.0 141.0 150.0 166.0 85 155 140 151.5 129.5 150.0 105 110 Print Done and then click Check Answer. . (d) Does a linear relation exist between the weight of the bear and its length? The variables weight of the bear and length of the bear are positively associated because ris positive and the absolute value of the correlation coefficient, , is greater than the critical value, (Round to three decimal places as needed.) Enter your answer in the edit fields and then click Check Answer.

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