Question

please help with step by step calculations

Variables Entered/Removed Variables Removed Model Variables Entered) Method contraception use (%) Enter a. All requested variables entered. b. Dependent Variable: fertility rate per woman Model Summary

Answer 1

The regression model that is being estimated is

$\text{Fertility Rate}=\beta_0+\beta_1\text{contraception use}+\text{error}$

a) Using this

LUCILIUS Standardized Coefficients 95% Confidence interval for B Unstandardized Coefficients Std. Error Model Beta Lower Bound Upper Bound 6.391 7.503 1 (Constant) 6.947 contraception use (%) -.030 a. Dependent Variable: fertility rate per Wohan 261 .014 - 4691 -.060 .001

we can get

the estimate of intercept is

$\hat{\beta}_0=6.947$

The estimate of slope is

$\hat{\beta}_1=-0.030$

The simple linear regression line to predict the fertility rate is

$\widehat{\text{Fertility Rate}}=6.947-0.030\times \text{contraception use}$

b) Using this

ANOVA Model Sum of Squares Mean Square Regression Residual 2.177 2.177 7.725 9.902 15 .515 Total 161 a. Predictors: (Constant), contraception use b. Dependent Variable: fertility rate per woman

we get

The Total Sum of Square (SST) is

$SST=9.902$

Regression Sum of Square (SSR) is

$SSR=2.177$

Residual Sum of Square (SSE) is

$SSE=7.725$

The total sum of squares is equal to the sum of regression sum of squares and residual sum of squares

That is

$SST=SSR+SSE=2.177+7.725=9.902$

c) Using the following

Std. Error of the Estimate R Adjusted R Square .168 Model .469 220 .71764 Predictors: (Constant), cohiaception use (%)

we get

the coefficient of determination is

$R^2=0.220$

This indicates that 22.0% of variation in fertility rate per woman is explained by the regression model (or is explained by the dependent variable contraceptive use )