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
| r² | 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
| R² | 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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significance and R2. What are the limitations of your specification
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Quantity
Price
84
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80
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85
54
83
61
81
64
84
58
87
48
78
68
82
63
76
70
79
65
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80
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Quantity
Price
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59
80
65
85
54
83
61
81
64
84
58
87
48
78
68
82
63
76
70
79
65
75
80
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Obs
Y
X
(X-)
(Y-)
(X-)(Y-)
(X-)2
(Y-)2
U
U2
u(-1)
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1
10
4
2
50
3
3
10
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30
1
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ANOVA
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