One uses regression analysis to find out which dependent variable connects to which independent variable. In a particular data, one can use linear regression to estimate the connection of variables by fitting an equation. The determination coefficient determines if the equation used is or is not a good fit.
For this assignment, I will use Infrastructure Index as the dependent variable. A higher Infrastructure Index score implies greater infrastructure. The independent variable includes. I will code urban and rural as binary variables. Additionally, I will create two different columns of urban, which contain (0 if otherwise, 1 if urban) and rural (0 otherwise, 1 if rural). Therefore, the numbers of imitation (dummy) variables present are two. The dummy variable is the total number of categories minus 1.
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One can use the ordinary least square technique to establish the linear association between two variables.
The equation for the multiple linear Regression is
Y = α + ∑ βi * Xi + €
Where Y is the Infrastructure Index (dependent variable)
Xi = is the number of adults within a household and area that is categorized including semi-urban, rural, and urban (independent variables)
Βi = the coefficient of independent variables
€ = Error
Output
|
Variables Entered/Removed a |
|||
| Model |
Variables Entered |
Variables Removed |
Method |
| 1 | Rural, ADULTCT: Number of adults in household, Urban b |
. |
Enter |
| a. Dependent Variable: Infrastructure Index (higher scores=greater infrastructure) | |||
| b. All requested variables entered. | |||
Model Summary b |
||||
| Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
| 1 |
.026 a |
.001 |
.001 |
3.44910 |
| 1. ADULTCT, Rural: Number of adults in the household, Urban (Constant) Predictors | ||||
| 2. Greater infrastructure =higher scores (Infrastructure Index) Dependent Variable | ||||
|
ANOVA |
||||||
| Model |
Number of Squares |
df |
Mean Square |
F |
Sig. |
|
| 1 | Regression |
329.689 |
3 |
109.896 |
9.238 |
.000 b |
| Residual |
485320.546 |
40796 |
11.896 |
|||
| Total |
485650.235 |
40799 |
||||
| a. Dependent Variable: greater infrastructure=higher scores (Infrastructure Index) | ||||||
| b. Predictors: Number of adults in the household, Urban (Constant), ADULTCT, Rural. | ||||||
|
Coefficients |
||||||
| Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
||
|
B |
Std. Error |
Beta |
||||
| 1 | (Constant) |
11.721 |
.157 |
74.571 |
.000 |
|
| ADULTCT: Number of adults in household |
.028 |
.007 |
.021 |
4.190 |
.000 |
|
| Urban |
-.488 |
.158 |
-.069 |
-3.085 |
.002 |
|
| Rural |
-.433 |
.157 |
-.061 |
-2.755 |
.006 |
|
| a. Dependent Variable: greater infrastructure=higher scores (Infrastructure Index) | ||||||
|
Coefficient Correlations |
|||||
| Model |
Rural |
ADULTCT: Number of adults in household |
Urban |
||
| 1 | Correlations | Rural |
1.000 |
-.021 |
.975 |
| ADULTCT: Number of adults in household |
-.021 |
1.000 |
-.023 |
||
| Urban |
.975 |
-.023 |
1.000 |
||
| Covariances | Rural |
.025 |
-2.294E-005 |
.024 |
|
| ADULTCT: Number of adults in household |
-2.294E-005 |
4.614E-005 |
-2.522E-005 |
||
| Urban |
.024 |
-2.522E-005 |
.025 |
||
| Dependent Variable: greater infrastructure=higher scores (Infrastructure Index) | |||||
References
Elwert and Winship (2014) “Endogenous selection bias: The problem of conditioning on a collider variable” Annual Review of Sociology
Morgan and Winship Chapter 11 Repeated Observations and the Estimation of Causal Effects
