Question

Many attempts have been made to relate happiness with various factors. One such study relates happiness...

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 40's ( The Economists December 16, 2010). The accompanying data shows a respondent's age and his or her perception of well being on a scale from 0 to 100.

pt1

1) Calculate and interpret covariance using Excel (10 points)

2)Use Excel to calculate and interpret the correlation coefficient between age and happiness. (10 points)

pt2

3)Use Excel to estimate a simple regression model with happiness as the response variable and age as the explanatory variable. (Excel product should look similar to p519) (10 points)

4) Construct the simple regression model (the equation) and round to two digits after the decimal for the y-intercept and slope.a) Interpret the slope coefficient. b) Use the estimate to predict happiness when age equals 25,45,60. (Show work typed)(10 points)

5)Find the coefficient of determination (R2) on the simple regression model and interpret the output about the data happiness and age? (p530-531) (5 points)

Age Happiness
51 62
53 66
43 67
67 71
86 87
43 60
85 86
18 78
37 59
60 63
17 77
86 90
75 70
32 62
84 93
23 72
51 58
72 73
65 63
30 66
73 78
46 60
89 95
70 72
0 0
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Answer #1

a)

The covariance comes out to be 147.6. It signifies the relationship between the movement of two variables, which are age and happiness here.

b)

The correlation comes out to be 0.6, which shows a medium positive correlation between the two variables.

c)

We will be applying the Linear regression model here, it can be done by using the function =LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of Happiness here and x_values have Age values.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.    

The equation comes out to be -
Happiness = 56 + 0.28*Age  

d)

For every unit increase in the age, which is for every year increase in age, happiness increases by 0.28 units.

When Age = 25, Happiness = 56 + 0.28*25 = 63.08

When Age = 45, Happiness = 56 + 0.28*45 = 68.75

When Age = 60, Happiness = 56 + 0.28*60 = 72.99

e)

The coefficient of determination comes out to be 0.33, which means that the change in happiness can be 33 percent explained by the age.

A C D E F H 1 K L M N o P covariance correlation 147.6 COVARIANCE.S(A2:A25,B2:B25) 0.6 CORREL(A2:A25,B2:B25) Age 51 53 43 67

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