1.A 1993 paper by Robey, et.al. in Scientific American was concerned with the declining fertility rate in developing countries.In particular, they were looking at effect that contraceptive use had on fertility rate.Conduct a simple linear regression analysis for this data set.

contprev = percentage of married women in the country using contraception

fertrate = fertility rate

Run the R code (in next page) and then based on R output to answer the following questions.

(a) Ata=0.05 level do we accept or reject the null hypothesis b₁=0?So, does the contraceptive use affect the fertility rate? Justify your answer.

(b) Interpret the estimate of b_1.

(c) Findand interpret it.

(d) Find a 95% confidence interval of the mean fertility rate when the contraceptive prevalence was 50%.

(e) Find the proportion of sample variability in fertrate explained by the linear relationship with contprev.

(f) Check the model assumptions using residual plots, and state whether you feel comfortable trusting the results of the regression. Justify your answer clearly.

R code

my.datafile

cat(file=my.datafile, "

Mauritius762.2

Thailand692.3

Colombia662.9

CostaRica713.5

SriLanka632.7

Turkey623.4

Peru603.5

Mexico554.0

Jamaica552.9

Indonesia503.1

Tunisia514.3

ElSalvador484.5

Morocco424.0

Zimbabwe465.4

Egypt404.5

Bangladesh405.5

Botswana354.8

Kenya286.5

Guatemala245.5

Cameroon165.8

Ghana146.0

Pakistan135.0

Senegal136.5

Sudan104.8

Yemen97.0

Nigeria75.7

", sep=" ")

options(scipen=999) # suppressing scientific notation

fertdata

attach(fertdata)

fert.reg=lm(fertrate~contprev)

summary(fert.reg)

x.value

predict(fert.reg, x.value, interval="confidence", level=0.95)

par(mfrow=c(1,2))

plot(fitted(fert.reg), resid(fert.reg)); abline(h=0)

qqnorm(resid(fert.reg))

qqline(resid(fert.reg))

Output:

R . Global Environment . fertdata It1 ) (Intercept)