A poll uses responses to several questions to calculate a "Happiness" index that measures overall happiness. An article included the happiness index for the 7 years between 2008 and 2016. Also included in the article were the percentages of people who responded "somewhat agree" or "strongly agree" to the following statements.Statement 1 (happy with life) 1: At this time, I'm generally happy with my life.Statement 2 (won't benefit): I won't get much benefit from the things that I do anytime soon.YearHappinessIndexHappy withLife Statement(percentagesomewhat orstrongly agree)Won't BenefitStatement(percentagesomewhat orstrongly agree)2008327835200934813920103478352011348137201330774520153178392016328440(a)Calculate the value of the correlation coefficient for Happiness index and the response to the Happy with life statement. (Round your answer to four decimal places.) (b)Calculate the value of the correlation coefficient for Happiness index and the response to the Won't benefit statement. (Round your answer to four decimal places.)

The sample correlation coefficient is denoted with 'r' and the formula for 'r' is defined as shown…

Answered: A poll uses responses to several…

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 12PPS

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Question

A poll uses responses to several questions to calculate a "Happiness" index that measures overall happiness. An article included the happiness index for the 7 years between 2008 and 2016. Also included in the article were the percentages of people who responded "somewhat agree" or "strongly agree" to the following statements.

Statement 1 (happy with life) 1: At this time, I'm generally happy with my life.
Statement 2 (won't benefit): I won't get much benefit from the things that I do anytime soon.

Year	Happiness Index	Happy with Life Statement (percentage somewhat or strongly agree)	Won't Benefit Statement (percentage somewhat or strongly agree)
2008	32	78	35
2009	34	81	39
2010	34	78	35
2011	34	81	37
2013	30	77	45
2015	31	78	39
2016	32	84	40

(a)

Calculate the value of the correlation coefficient for Happiness index and the response to the Happy with life statement. (Round your answer to four decimal places.)

(b)

Calculate the value of the correlation coefficient for Happiness index and the response to the Won't benefit statement. (Round your answer to four decimal places.)

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