x <- 1:30
n <- length(x)

b0 <- 90
b1 <- 1.2

set.seed(2)
e <- rnorm(n, mean = 0, sd = 5)

y <- b0 + b1 * x + e

ybar <- mean(y)

d <- data.frame(x, y)
d

##     x         y
## 1   1  86.71543
## 2   2  93.32425
## 3   3 101.53923
## 4   4  89.14812
## 5   5  95.59874
## 6   6  97.86210
## 7   7 101.93977
## 8   8  98.40151
## 9   9 110.72237
## 10 10 101.30606
## 11 11 105.28825
## 12 12 109.30876
## 13 13 103.63652
## 14 14 101.60166
## 15 15 116.91114
## 16 16  97.64465
## 17 17 114.79302
## 18 18 111.77903
## 19 19 117.86414
## 20 20 116.16133
## 21 21 125.65410
## 22 22 110.40037
## 23 23 125.54819
## 24 24 128.57326
## 25 25 120.02469
## 26 26 108.94147
## 27 27 124.78619
## 28 28 120.61721
## 29 29 128.76102
## 30 30 127.44818

COL <- c(rgb(255,   0,   0,  255, max = 255),
         rgb(  0,   0, 255,  255, max = 255),
         rgb(  0, 155,   0,  255, max = 255))

matplot(x, y, pch = 1, col = COL[1])
grid()

fit <- lm(y ~ x, data = d)
summary(fit)

## 
## Call:
## lm(formula = y ~ x, data = d)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.5989  -2.8452   0.0335   3.6787   9.2076 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  90.8526     2.2356  40.638  < 2e-16 ***
## x             1.2188     0.1259   9.678 1.97e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.97 on 28 degrees of freedom
## Multiple R-squared:  0.7699, Adjusted R-squared:  0.7616 
## F-statistic: 93.66 on 1 and 28 DF,  p-value: 1.972e-10

matplot(x, y, pch = 1, col = COL[1], main = '回帰分析')
grid()
matlines(x, fit$fitted, col = COL[2])

library(latex2exp)
legend('topleft', lty = c(NA, 1), pch = c(1, NA), col = COL, 
       legend = c('Data', TeX('$\\hat{y}_i = b_0 + b_1 x_i $')))

library(plotly)

plot_ly() |>
  add_trace(x = x, y = y,          mode = 'markers', name = 'Data') |>
  add_trace(x = x, y = fit$fitted, mode = 'lines',   name = '$\\hat{y}_i = b_0 + b_1 x_i $') |>
  layout(font  = list(size = 11, color = 'red', family = 'UD Digi Kyokasho NK-R'),
         title = '回帰分析',
         xaxis = list(title = 'x'),
         yaxis = list(title = 'y')) |>
  config(mathjax = 'cdn')