MATH 220 Matrices : Use of Multiple Regression Analysis
Answer:
Introduction
In the present assignment we study the use of Multiple Regression Analysis using Dummy Variables.
Scenario
For the study of multiple
regression we use the Afrobarometer data set. The chosen dependent variable of study is “Q3b your present living condition.” The four regions of Africa are chosen and three dummy variables are created. North Africa is taken as the reference variable. We test the hypothesis that there is no difference in the present living conditions of the four regions of Africa.
- Null Hypothesis: The present living conditions of the people does not depend on the region of Africa
- Alternate Hypothesis: The present living conditions of the people depends on the region of Africa
|
Table 1: Model Summaryb | |||||
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
Durbin-Watson |
|
1 |
.171a |
.029 |
.029 |
1.159 |
1.621 |
|
a. Predictors: (Constant), Region South, Region East, Region West | |||||
|
b. Dependent Variable: Q3b. Your present living conditions | |||||
The model summary table 1 we find that 2.9% of the present living conditions can be predicted through the three regions of Africa. The Durbin-Watson value (1.621) shows that there is positive auto-correlation amongst the regions.
|
Table 2: ANOVAa | ||||||
|
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. | |
|
1 |
Regression |
2068.350 |
3 |
689.450 |
513.559 |
.000b |
|
Residual |
68981.331 |
51383 |
1.342 |
|
| |
|
Total |
71049.681 |
51386 |
|
|
| |
|
a. Dependent Variable: Q3b. Your present living conditions | ||||||
|
b. Predictors: (Constant), Region South, Region East, Region West | ||||||
From the ANOVA table 2 we find that there are significant differences in the present living conditions of the four regions of Africa F(3,51383) = 513.559, p < .001, less than a= 0.05, level of significance.
|
Table 3: Coefficientsa | ||||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
Collinearity Statistics | |||
|
B |
Std. Error |
Beta |
Tolerance |
VIF | ||||
|
1 |
(Constant) |
2.706 |
.015 |
|
180.281 |
.000 |
|
|
|
Region West |
.055 |
.017 |
.023 |
3.216 |
.001 |
.378 |
2.644 | |
|
Region East |
-.501 |
.020 |
-.157 |
-25.497 |
.000 |
.496 |
2.015 | |
|
Region South |
.038 |
.017 |
.015 |
2.205 |
.027 |
.383 |
2.610 | |
|
a. Dependent Variable: Q3b. Your present living conditions | ||||||||
Table 3 shows the regression confidents of the test. The equation for the present living condition of the people as compared to North Africa can be written as
Thus compared to North Africa there is a difference of .055 with West Africa. Similarly when comparing North and East Africa there is a difference of negative .501. Further when comparing North Africa with South Africa there is a difference of .038. Furthermore the b-Unstandardized coefficients are statistically significant.
Thus from the multiple regression analysis we can say that present living conditions of region of West and South Africa is better as compared to North African region. Further The present living condition of region of East Africa is poorer that North Africa.
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