Calculating the phi-coefficient CENGAGE MINDTAPProblem Set: Chapter 14 Correlation and RegressionComplete the bottorm two rows of the researcher's data.AgeListens to Classical Musicou = 01= yes0= < 18 years old1 = 18+ years old1.2.0.3.1.4.1.5.6.1.7.1.1.1.8.9.10.The phi correlation is the appropriate correlation for this experiment becauseThe phi correlation isGrade It NowSave & ContinueContinue without savingaType here to searchdy Problem Set: Chapter 14 Correlation and RegressionSuppose a researcher is interested in examining the relationship between a person's age and whether he or she listens to classical music. She collectsa sample of n = 10 people and asks them whether they listen to dassical music. The following table summarizes the results.Does Not Listen to Classical MusicListens to Classical Music< 18 Years Old3.2.18+ Years old2.The researcher wants to calculate the correlation between a person's age and whether he or she listens to classical music. To do so, the researcherfirst creates a table of the data by converting each variable to a numerical value. She assigns 0 to "< 18 years old" and 1 to "18+ years old." She thenassigns 0 to "does not listen to classical music" and 1 to "listens to classical music."Complete the bottom two rows of the researcher's data.AgeListens to Classical Music0= < 18 years oldou = 01 = yes1 = 18+ years old1.2.3.1.4.Type here to searchdyH.

Here the given characteristics are Age of the person and habit of listening music. The data represents the number of people in a given age group having habit of listening music and not having habit of listening music. The data is in a 2×2 contingency table i.e., dichotomous classification.Phi coefficient is used to determine the association between two categorical variables in a dichotomous classification. This value is lies between -1 and +1. For a 2×2 table a b c d The phi coefficient is computed by the formula φ = (ad - bc)(a+b)(c+d)(a+c)(b+d) Here we have Does not listen to music listens to music Total < 18 years a = 3 b = 2 a+b =5 18+ years c = 2 d = 3 c+d = 5 Total a+c = 5 b+d = 5 N = 10 φ = (ad - bc)(a+b)(c+d)(a+c)(b+d) = (3×3 -2×2) 5×5×5×5 = 525 = 15 = 0.2 There is a positive correlation between the two variables.