This is Statistics' assignments by using R studio.

## ----setup, include=FALSE------------------------------------------------ knitr::opts_chunk$set(echo = TRUE) knitr::opts_chunk$set(fig.width=6, fig.height=4) ## ------------------------------------------------------------------------ hdi <- read.table('HDI.txt', sep = '\t', header = TRUE) ## ------------------------------------------------------------------------ imod0 <- lm(HDI ~ GDP.Per.Capita, data = hdi) ## ------------------------------------------------------------------------ summary(imod0) ## ------------------------------------------------------------------------ par(mfrow = c(1, 2)) hist(hdi$HDI, xlab = "HDI", main = "") qqnorm(hdi$HDI) qqline(hdi$HDI) ## ------------------------------------------------------------------------ par(mfrow = c(1, 2)) hist(hdi$HDI^2, xlab = expression(HDI^2), main = "") qqnorm(hdi$HDI^2) qqline(hdi$HDI^2) ## ------------------------------------------------------------------------ imod1 <- lm(HDI^2 ~ GDP.Per.Capita, data = hdi) ## ------------------------------------------------------------------------ par(mfrow = c(1,2)) plot(hdi$GDP.Per.Capita, hdi$HDI^2, xlab = 'GDPPC', ylab = expression(HDI^2)) plot(imod1$fitted.values, imod1$residuals, xlab = 'Fitted Value', ylab = 'Residual') abline(0,0) par(mfrow = c(1,1)) ## ------------------------------------------------------------------------ par(mfrow = c(1, 2)) plot(sqrt(hdi$GDP.Per.Capita), hdi$HDI^2, xlab = expression(sqrt(GDPPC)), ylab = expression(HDI^2)) plot(log10(hdi$GDP.Per.Capita), hdi$HDI^2, xlab = expression(Log[10](GDPPC)), ylab = expression(HDI^2)) ## ------------------------------------------------------------------------ par(mfrow = c(1, 2)) plot(-1/sqrt(hdi$GDP.Per.Capita), hdi$HDI^2, xlab = expression(-1/sqrt(GDPPC)), ylab = expression(HDI^2)) plot(-1/hdi$GDP.Per.Capita, hdi$HDI^2, xlab = expression(-1/GDPPC), ylab = expression(HDI^2)) ## ------------------------------------------------------------------------ imod2 <- lm(HDI^2 ~ log10(GDP.Per.Capita), data = hdi) ## ------------------------------------------------------------------------ plot(imod2$fitted.values, imod2$residuals, xlab = "Fitted Value", ylab = "Residual") abline(a = 0, b = 0) ## ------------------------------------------------------------------------ idx <- which.min(imod2$residuals) hdi[idx, ] ## ------------------------------------------------------------------------ hdi.new <- hdi[-idx, ] ## ------------------------------------------------------------------------ imod3 <- lm(HDI^2 ~ log10(GDP.Per.Capita), data = hdi.new) ## ------------------------------------------------------------------------ plot(log10(hdi$GDP.Per.Capita), hdi$HDI^2, xlab = expression(Log[10](GDPPC)), ylab = expression(HDI^2)) abline(imod2, col = 'blue') abline(imod3, col = 'red') ## ------------------------------------------------------------------------ summary(imod2) summary(imod3) ## ------------------------------------------------------------------------ pred.data <- data.frame(GDP.Per.Capita = 4000) ## ------------------------------------------------------------------------ result.pred <- predict(imod2, newdata = pred.data, interval = 'prediction', level = 0.9) result.pred ## ------------------------------------------------------------------------ sqrt(result.pred)