Question

Many attempts have been made to relate happiness with various factors. One such study relates happiness with age and finds that holding everything else constant, people are least happy when they are in their mid-40s (The Economist, December 16, 2010). Data are collected on a respondent’s age and his/her perception of well-being on a scale from 0 to 100; the data is presented below.

Age	Happiness
49	62
51	66
41	67
65	71
84	87
41	60
83	86
18	78
36	59
61	63
15	77
86	90
73	70
32	62
84	93
23	72
52	58
72	73
63	63
30	66
72	78
47	60
88	95
69	72

Create a scatterplot in R to evaluate your interpretation of the calculated sample correlation value.

• The interpretation is reliable given that for the majority of observations, a direct relationship exists.

• The interpretation is reliable given that for the majority of observations, an inverse relationship exists.

• The interpretation is flawed given the linear relationship that seems to exist between these two variables.

• The interpretation is flawed given the non-linear relationship that seems to exist between these two variables.

1.Interpret the sample correlation coefficient between age and happiness.

• The correlation between age and happiness is positive and moderate.

• The correlation between age and happiness is negative and moderate.

• There is no correlation between age and happiness.

Answer 1

Create a scatterplot in R to evaluate your interpretation of the calculated sample correlation value.

Solution:

The scatterplot is:

The correct option is:

The interpretation is flawed given the non-linear relationship that seems to exist between these two variables.

1. Interpret the sample correlation coefficient between age and happiness.

Answer:

Correlation coefficient is $\dpi{100} r=\sqrt{R^2}=\sqrt{0.3267}=0.5716$

Therefore, the correlation between age and happiness is positive and moderate.