Question: Report the regression results below using 2 formats: In equation form
ID: 3053711 • Letter: Q
Question
Question: Report the regression results below using 2 formats:
In equation form
In table form
Data:
A study was conducted in Botswana to evaluate the effect of education and age on female fertility. Use the results below to answer the questions related to the problem.
The variables used in the regression model were:
children = # of children
education = number of years of schooling
age = age in years
Children
Age
Education
Mean
2.268
27.405
3.469
Min
0.000
15.000
0.000
Max
13.000
49.000
20.000
Std Dev
2.222
8.685
4.294
Total Sum of squares
21527.176
328889.043
80400.102
Regression of children on age and education (i.e., children is the dependent variable)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.742
R Square
0.550
Adjusted R Square
0.550
Standard Error
1.491
Observations
4361.000
ANOVA
df
SS
MS
F
Significance F
Regression
2.000
11842.083
5921.042
2664.290
0.000
Residual
4358.000
9685.093
2.222
Total
4360.000
21527.176
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-2.541
0.080
-31.736
0.000
-2.698
-2.384
age
0.183
0.003
69.727
0.000
0.178
0.188
education
-0.061
0.005
-11.410
0.000
-0.071
-0.050
Children
Age
Education
Mean
2.268
27.405
3.469
Min
0.000
15.000
0.000
Max
13.000
49.000
20.000
Std Dev
2.222
8.685
4.294
Total Sum of squares
21527.176
328889.043
80400.102
Explanation / Answer
The equation of Regression analysis:
General form - y=ax+b
Here the number of children is the x-variable; age and education are y- variables. Therefore there are two regression models as shown below.
The regression model to predict age:
Age = 0.183*(#number of children ) - 2.541
The regression model to predict education:
Education = -0.061*(#number of children) - 2.541
Multiple R
0.742
R Square
0.550
Adjusted R Square
0.550
Standard Error
1.491
Observations
4361.000
ANOVA
df
SS
MS
F
Significance F
Regression
2.000
11842.083
5921.042
2664.290
0.000
Residual
4358.000
9685.093
2.222
Total
4360.000
21527.176
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-2.541
0.080
-31.736
0.000
-2.698
-2.384
age
0.183
0.003
69.727
0.000
0.178
0.188
education
-0.061
0.005
-11.410
0.000
-0.071
-0.050
Regression StatisticsMultiple R
0.742
R Square
0.550
Adjusted R Square
0.550
Standard Error
1.491
Observations
4361.000
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