Question

Does the number of years that a woman is on birth control (X) have an effect on how long it takes for her to become pregnant (Y) once she ceases to use it and tries to have children? A curious researcher collected the following data for a sample of pregnant women who had previously used birth control:

Years on Birth Control (X)	Time Until Pregnant (Y)
7.5	25
10.0	31
3.5	42
4.0	36
7.0	13
2.5	22
5.0	56

a) Draw a scatter plot of the data
b) Calculate the regression slope and Y-intercept
c) Draw a regression line on the scatter plot
d) Can you predict how long it will take for a woman who was on birth control for eight years to get pregnant once she stops using it?
e) Find the coefficients of determination and nondetermination. What do they mean?
f) Construct an analysis of variance table and perform an F test on the significance of the regression.

Answer 1

a.

b.

c.

d.

f.

Coefficients:
Estimate Std. Error t value Pr(>|t|)  
(Intercept) 39.577 14.292 2.769 0.0394 *
x -1.317 2.324 -0.567 0.5953  
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 15.03 on 5 degrees of freedom
Multiple R-squared: 0.06039, Adjusted R-squared: -0.1275
F-statistic: 0.3214 on 1 and 5 DF, p-value: 0.5953

Df Sum Sq Mean Sq F value Pr(>F)
x 1 72.65 72.646 0.3214 0.5953
Residuals 5 1130.21 226.042

Since p-value=0.5953>0.05, hence regression equation of Y on X is not significant at 5% level.