Question

In: Statistics and Probability

b. Write down potential questions that you could answer using regression analysis for the Happiness_2011.xls dataset...

b. Write down potential questions that you could answer using regression analysis for the Happiness_2011.xls dataset

c. Perform one simple regression using any two reasonable variables from the Happiness_2011.xls file (two quantitative variables) and show the analysis result

d. Interpret the findings from the simple regression analysis

e. Add one or more quantitative variable (including dummy variable that have values of 0 and 1) to the analysis in #b, perform one multiple regression analysis

f. Interpret your findings from the multiple regression analysis

Age Children Education_Year Sibling Income Happiness (3 levels) EQ (3 levels) Health (4 levels)
52 5 6 1 9 Not too Happy Below Average Very poor Health
61 3 12 2 18 Pretty Happy Average Poor Health
50 3 13 2 18 Not too Happy Average Poor Health
56 0 17 1 18 Pretty Happy Average Poor Health
64 3 12 1 8 Pretty Happy Below Average Poor Health
51 2 10 2 9 Pretty Happy Below Average Poor Health
56 6 9 2 5 Not too Happy Below Average Poor Health
61 3 15 2 16 Pretty Happy Below Average Poor Health
68 2 12 0 16 Pretty Happy Below Average Poor Health
69 4 11 2 17 Not too Happy Below Average Poor Health
46 3 9 2 3 Not too Happy Below Average Poor Health
42 1 13 2 9 Not too Happy Below Average Poor Health
36 4 9 2 11 Not too Happy Below Average Poor Health
24 0 12 2 16 Not too Happy Below Average Poor Health
57 0 19 3 25 Pretty Happy Above Average Healthy
41 2 12 3 21 Pretty Happy Above Average Healthy
24 0 16 1 22 Very Happy Above Average Healthy
39 0 16 1 22 Not too Happy Above Average Healthy
55 4 16 3 22 Pretty Happy Above Average Healthy
19 0 13 3 23 Pretty Happy Above Average Healthy
46 2 12 0 19 Pretty Happy Average Healthy
41 3 12 3 18 Pretty Happy Average Healthy
40 0 16 3 18 Not too Happy Average Healthy
48 1 13 3 11 Pretty Happy Below Average Healthy
41 2 14 0 15 Pretty Happy Below Average Healthy
66 2 12 3 16 Pretty Happy Below Average Healthy
24 1 14 3 13 Very Happy Below Average Healthy
38 0 12 0 13 Pretty Happy Below Average Healthy
59 0 6 3 15 Pretty Happy Below Average Healthy
38 0 17 1 15 Not too Happy Below Average Healthy
36 6 11 3 16 Not too Happy Below Average Healthy
19 0 13 3 17 Pretty Happy Below Average Healthy
24 0 16 3 11 Pretty Happy Below Average Healthy
51 0 11 1 13 Very Happy Below Average Healthy
29 0 12 3 15 Pretty Happy Below Average Healthy
19 0 11 3 16 Pretty Happy Below Average Healthy
33 0 12 1 17 Very Happy Below Average Healthy
31 0 14 3 17 Pretty Happy Below Average Healthy
60 2 12 4 23 Pretty Happy Above Average Very Healthy
44 2 16 4 21 Pretty Happy Above Average Very Healthy
37 3 12 4 23 Pretty Happy Above Average Very Healthy
50 1 17 4 20 Not too Happy Average Very Healthy
63 2 17 4 18 Pretty Happy Average Very Healthy
42 4 10 4 20 Pretty Happy Average Very Healthy
43 0 20 4 20 Not too Happy Average Very Healthy
46 1 17 4 19 Pretty Happy Average Very Healthy
65 0 18 4 18 Very Happy Average Very Healthy
24 0 12 4 20 Pretty Happy Average Very Healthy
46 3 16 4 2 Very Happy Below Average Very Healthy
50 2 12 4 15 Pretty Happy Below Average Very Healthy
20 0 13 4 10 Pretty Happy Below Average Very Healthy
36 1 12 4 13 Very Happy Below Average Very Healthy
61 0 16 4 17 Very Happy Below Average Very Healthy
61 4 12 1 14 Pretty Happy Below Average Very poor Health
54 3 10 2 21 Very Happy Above Average Poor Health
54 0 16 2 24 Very Happy Above Average Poor Health
49 2 12 2 22 Pretty Happy Above Average Poor Health
29 0 12 0 22 Not too Happy Above Average Poor Health
56 2 12 2 18 Pretty Happy Average Poor Health
28 1 12 0 17 Very Happy Below Average Poor Health
54 2 12 2 17 Pretty Happy Below Average Poor Health
64 3 14 0 2 Pretty Happy Below Average Poor Health
53 2 12 2 13 Pretty Happy Below Average Poor Health
82 3 12 0 15 Not too Happy Below Average Poor Health
65 3 12 2 13 Pretty Happy Below Average Poor Health
49 2 14 3 21 Very Happy Above Average Healthy
33 4 12 1 22 Pretty Happy Above Average Healthy
82 3 18 3 25 Very Happy Above Average Healthy
53 2 13 3 22 Pretty Happy Above Average Healthy
35 2 18 0 23 Pretty Happy Above Average Healthy
52 2 11 3 21 Pretty Happy Above Average Healthy
38 0 12 0 21 Pretty Happy Above Average Healthy
27 1 14 3 25 Very Happy Above Average Healthy
45 2 19 3 25 Pretty Happy Above Average Healthy
35 4 18 0 19 Very Happy Average Healthy
44 4 12 3 19 Pretty Happy Average Healthy
64 1 12 3 18 Pretty Happy Average Healthy
67 2 11 3 19 Very Happy Average Healthy
46 2 12 3 19 Very Happy Average Healthy
44 3 12 0 19 Pretty Happy Average Healthy
63 3 12 3 19 Pretty Happy Average Healthy
30 0 16 3 20 Very Happy Average Healthy
44 3 16 3 20 Very Happy Average Healthy
57 0 12 3 18 Pretty Happy Average Healthy
35 3 16 0 20 Very Happy Average Healthy
35 3 12 3 20 Pretty Happy Average Healthy
24 0 14 3 12 Very Happy Below Average Healthy
65 3 18 4 21 Very Happy Above Average Very Healthy
66 2 16 4 23 Pretty Happy Above Average Very Healthy
65 2 14 4 22 Very Happy Above Average Very Healthy
31 1 18 4 22 Very Happy Above Average Very Healthy
34 2 16 4 25 Pretty Happy Above Average Very Healthy
55 3 12 4 18 Pretty Happy Average Very Healthy
36 2 11 4 19 Very Happy Average Very Healthy
37 2 16 4 20 Very Happy Average Very Healthy
23 0 16 4 17 Pretty Happy Below Average Very Healthy
79 3 12 4 14 Pretty Happy Below Average Very Healthy
28 0 16 4 15 Not too Happy Below Average Very Healthy
36 0 13 4 16 Very Happy Below Average Very Healthy
68 5 12 4 16 Pretty Happy Below Average Very Healthy
33 2 14 4 12 Pretty Happy Below Average Very Healthy

Solutions

Expert Solution

b. Write down potential questions that you could answer using regression analysis for the Happiness_2011.xls dataset

Is there a relationship between Children and Age?

c. Perform one simple regression using any two reasonable variables from the Happiness_2011.xls file (two quantitative variables) and show the analysis result

0.174
r   0.417
Std. Error   1.393
n   101
k   1
Dep. Var. Children
ANOVA table
Source SS   df   MS F p-value
Regression 40.4522 1   40.4522 20.84 1.44E-05
Residual 192.1815 99   1.9412
Total 232.6337 100  
Regression output confidence interval
variables coefficients std. error    t (df=99) p-value 95% lower 95% upper
Intercept -0.1523
Age 0.0423 0.0093 4.565 1.44E-05 0.0239 0.0606

d. Interpret the findings from the simple regression analysis

There is a significant relationship between Children and Age.

e. Add one or more quantitative variable (including dummy variable that have values of 0 and 1) to the analysis in #b, perform one multiple regression analysis

0.177
Adjusted R² 0.160
R   0.421
Std. Error   1.398
n   101
k   2
Dep. Var. Children
ANOVA table
Source SS   df   MS F p-value
Regression 41.1915 2   20.5957 10.54 .0001
Residual 191.4422 98   1.9535
Total 232.6337 100  
Regression output confidence interval
variables coefficients std. error    t (df=98) p-value 95% lower 95% upper
Intercept -0.0895
Age 0.0426 0.0093 4.581 1.36E-05 0.0242 0.0611
Dummy -0.1719 0.2794 -0.615 .5399 -0.7264 0.3826

f. Interpret your findings from the multiple regression analysis

There is a significant relationship between Children and Age.


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