d <- read.csv('https://stats.dip.jp/01_ds/data/car_mileage.csv')
rownames(d) <- paste0('No.', 1:nrow(d))
colnames(d) <- c('km', 'ncy', 'cc', 'hp', 'kg', 'sec', 'yr', 'type', 'name')

library(DT)
datatable(d)

n <- nrow(d)
ii.tr <- sample(1:n, size = floor(0.8*n))
d.tr <- d[ ii.tr, ]
d.te <- d[-ii.tr, ]
fit <- lm(km ~ kg + cc, data = d.tr)
kmhat <- predict(fit, newdata = d.te)
RMSE <- sqrt(mean((d.te$km -kmhat)^2))
RMSE

## [1] 1.9033

get.accuracy <- function(yhat, y, digits = 2)
{
  d <- data.frame(MBE  = mean(yhat - y),
                  MAE  = mean(abs(yhat - y)),
                  MAPE = mean(abs((yhat - y) / y)) * 100,
                  RMSE = sqrt(mean((yhat - y)^2)))
  return(round(d, digits))
}

(a <- get.accuracy(d.te$km, kmhat))

##    MBE  MAE MAPE RMSE
## 1 0.03 1.44 14.4  1.9

fit <- lm(km ~ poly(kg, 2, raw = TRUE), data = d)

library(sjPlot)

## Learn more about sjPlot with 'browseVignettes("sjPlot")'.

tab_model(fit)

	km
Predictors	Estimates	CI	p
(Intercept)	26.47	23.96 – 28.97	<0.001
kg [1st degree]	-0.02	-0.02 – -0.01	<0.001
kg [2nd degree]	0.00	0.00 – 0.00	<0.001
Observations	392
R2 / R2 adjusted	0.715 / 0.714

kg.p <- seq(0, 3000, 100)


conf <- predict(fit, newdata = data.frame(kg = kg.p),
                interval = 'confidence')
# 予測区間
pred <- predict(fit, newdata = data.frame(kg = kg.p),
                interval = 'prediction')
COL <- c(rgb(255,   0,   0,  105, max = 255), # 赤
         rgb(  0,   0, 255,  105, max = 255), # 青
         rgb(  0, 155,   0,  105, max = 255), # 緑
         rgb(140, 140, 140,  105, max = 255), # 暗灰
         rgb(180, 180, 180,  105, max = 255))


matplot (x = d$kg, y = d$km,
         type = 'p', pch = 16, col = COL[1], ylim = c(0, 20),
         main = '２次多項式回帰モデルを使った燃費予測', 
         xlab = '車体重量［kg］', ylab = '燃費［km］')


gray.area <- function(x, lwr, upr, col)
{
  polygon(c(x, rev(x)), c(lwr, rev(upr)), col = col, border = NA)
}
gray.area(kg.p, conf[, 'lwr'], conf[, 'upr'], col = COL[4]) # 信頼区間
gray.area(kg.p, pred[, 'lwr'], pred[, 'upr'], col = COL[5]) # 予測区間


matlines(x = kg.p, y = conf[, 'fit'], col = COL[2], lwd = 3)


legend('topright',
       pch = c(16, NA, NA, NA), col = COL[-3],
       lty = c(NA, 1, NA, NA), lwd = c(NA, 3, NA, NA), 
       fill = c(NA, NA, COL[4], COL[5]), border = F,
       legend = c('燃費', '予測値', '95％信頼区間', '95％予測区'))