Question

1. The data set UN11 in the alr4 package contains several variables, including ppgdp, per capita gross domestic product in US dollars, and fertility, number of children per woman, from the year 2009-2011. The data are for 199 localities, and we will study the regression of ppgdp on fertility. (a) Draw the scatterplot of ppgdp against fertility and describe the relationship between these two variables. Is the trend linear? (b) Replace both variables by their natural logarithms and draw another scatterplot. Does the simple linear regression model seem plausible for a summary of this graph? (c) Without using the R function Im), find the least-squares estimates regressing log(ppgdp) on log(fertility) and add the line in the plot in (a).

Answer 1

a) R-code:

b)

> fertility-log (UN11Sfertility) > ppgdp-1 og (UNL1Sppgdp) yonx-1m(ppgdp fertility) > plot (fertility,ppgdp,main-"Scatter Plot" >abline (yonx) summary(yonx) 1m(formula-ppgdpfertility) Residuals: -2. 81279 -0.77154 -0.04034 0. 67183 3. 02858 Coefficients: Min 1Q Median 3Q Max (Intercept) 10.7801 fertility 2 Estimate std. Error t value Pr(ltI) 0.1742 61.88 <2e-16 0.1717-14.79<2e-16 -2. 5392 signif. codes 0.001 0.01 '*' 0.05.' 0.1''1 Residual standard error: 1.075 on 197 degrees of freedom Multiple R-squared F-statistic: 218.6 on 1 and 197 DF, p-value: < 2.2e-16 : 0.526, Adjusted R-squared 0. 5236

c)