Question

In: Statistics and Probability

Can you be 95% confident that your independent variables are explaining variance in the dependent variable...

  1. Can you be 95% confident that your independent variables are explaining variance in the dependent variable among the population?
  2. Can you be 99% confident that your independent variables are explaining variance in the dependent variable among the population
Model Summary (Number of children)
R R Square Adjusted R Square Std. Error of the Estimate
.28 .08 .07 1.39
ANOVA (Number of children)
Sum of Squares df Mean Square F Sig.
Regression 99.37 4 24.84 12.87 .000
Residual 1163.52 603 1.93
Total 1262.89 607
Coefficients (Number of children)
Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B
B Std. Error Beta t Sig. Lower Bound Upper Bound
(Constant) .58 7294153.92 .00 .00 1.000 -14325031.14 14325032.29
Year of birth .00 3618.13 .00 .00 1.000 -7105.67 7105.67
Age of respondent .03 3618.13 .27 .00 1.000 -7105.64 7105.70
General happiness .17 .10 .07 1.78 .076 -.02 .37
Respondents sex -.14 .11 -.05 -1.20 .230 -.36 .09
Coefficient Correlations (Number of children)
Model Year of birth Age of respondent General happiness Respondents sex
Covariances Age of respondent 13090878.47 13090878.47 .00
General happiness 13090878.47 13090878.47 .00
Respondents sex .00 .00 .01
Model Summary (Respondents income)
R R Square Adjusted R Square Std. Error of the Estimate
.27 .07 .06 5.41
ANOVA (Respondents income)
Sum of Squares df Mean Square F Sig.
Regression 1336.59 4 334.15 11.44 .000
Residual 17619.40 603 29.22
Total 18955.99 607
Coefficients (Respondents income)
Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B
B Std. Error Beta t Sig. Lower Bound Upper Bound
(Constant) 47.84 28384680.13 .00 .00 1.000 -55744792.19 55744887.87
Year of birth -.01 14079.70 -.03 .00 1.000 -27651.22 27651.20
Age of respondent .00 14079.70 .00 .00 1.000 -27651.21 27651.21
General happiness -1.16 .38 -.12 -3.03 .003 -1.90 -.41
Respondents sex -2.66 .44 -.24 -6.06 .000 -3.52 -1.80
Coefficient Correlations (Respondents income)
Model Year of birth Age of respondent General happiness Respondents sex
Covariances Age of respondent 198238020.98 198238020.98 .00
General happiness 198238020.98 198238020.98 .00
Respondents sex .00 .00 .15
Model Summary (Spouse's highest degree)
R R Square Adjusted R Square Std. Error of the Estimate
.17 .03 .02 1.58
ANOVA (Spouse's highest degree)
Sum of Squares df Mean Square F Sig.
Regression 43.78 4 10.95 4.40 .002
Residual 1501.69 603 2.49
Total 1545.47 607
Coefficients (Spouse's highest degree)
Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B
B Std. Error Beta t Sig. Lower Bound Upper Bound
(Constant) .38 8286643.39 .00 .00 1.000 -16274187.25 16274188.00
Year of birth .00 4110.44 .00 .00 1.000 -8072.51 8072.51
Age of respondent .02 4110.44 .17 .00 1.000 -8072.49 8072.53
General happiness .00 .11 .00 .02 .987 -.22 .22
Respondents sex -.07 .13 -.02 -.52 .606 -.32 .19
Coefficient Correlations (Spouse's highest degree)
Model Year of birth Age of respondent General happiness Respondents sex
Covariances Age of respondent 16895702.12 16895702.12 .00
General happiness 16895702.12 16895702.12 .00
Respondents sex .00 .00 .01
Model Summary (Abortion if woman wants for any reason)
R R Square Adjusted R Square Std. Error of the Estimate
.05 .00 .00 .50
ANOVA (Abortion if woman wants for any reason)
Sum of Squares df Mean Square F Sig.
Regression .40 4 .10 .40 .809
Residual 150.80 603 .25
Total 151.20 607
Coefficients (Abortion if woman wants for any reason)
Unstandardized Coefficients Standardized Coefficients 95% Confidence Interval for B
B Std. Error Beta t Sig. Lower Bound Upper Bound
(Constant) .45 2626004.47 .00 .00 1.000 -5157225.15 5157226.05
Year of birth .00 1302.58 .02 .00 1.000 -2558.15 2558.15
Age of respondent .00 1302.58 -.01 .00 1.000 -2558.15 2558.15
General happiness -.02 .04 -.03 -.66 .510 -.09 .05
Respondents sex -.03 .04 -.03 -.82 .411 -.11 .05
Coefficient Correlations (Abortion if woman wants for any reason)
Model Year of birth Age of respondent General happiness Respondents sex
Covariances Age of respondent 1696718.78 1696718.78 .00
General happiness 1696718.78 1696718.78 .00
Respondents sex .00 .00 .00

Solutions

Expert Solution

  1. Can you be 95% confident that your independent variables are explaining variance in the dependent variable among the population?

The hypothesis being tested is:

H0: β1 = β2 = β3 = 0

H1: At least one βi ≠ 0

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

Thus, we can be 95% confident that your independent variables are explaining variance in the dependent variable among the population.

  1. Can you be 99% confident that your independent variables are explaining variance in the dependent variable among the population

The hypothesis being tested is:

H0: β1 = β2 = β3 = 0

H1: At least one βi ≠ 0

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

Thus, we can be 99% confident that your independent variables are explaining variance in the dependent variable among the population.


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