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. Data Set x 2 4 6 6 7 y 4 8 12 14 18 Critical values fir the 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 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 By hand, compute the correlation coefficient. The correlation coefficient is r = 0.972 Determinewhether the correlation coefficient is a linear relation between x and y. Answer the following: Because the correlation coefficient is ___ ( positive or negative) and the absolute value of the correlation coefficient, , is _ (not greater than or greater) than the critical value for this data set, _, ________ (a negative, a positive, or no) linear relation exists between x and y. (round to three decimal places as needed).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 11PPS

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Related questions

Question

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.

Data Set

x 2 4 6 6 7

y 4 8 12 14 18

Critical values fir the correlation coefficient

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

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

By hand, compute the correlation coefficient. The correlation coefficient is r = 0.972

Determinewhether the correlation coefficient is a linear relation between x and y.

Answer the following:

Because the correlation coefficient is _______ ( positive or negative) and the absolute value of the correlation coefficient, ____, is _______ (not greater than or greater) than the critical value for this data set, ___, ________ (a negative, a positive, or no) linear relation exists between x and y.
(round to three decimal places as needed).

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