x <- 1:30
n <- length(x)
b0 <- 20
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 16.71543
## 2   2 23.32425
## 3   3 31.53923
## 4   4 19.14812
## 5   5 25.59874
## 6   6 27.86210
## 7   7 31.93977
## 8   8 28.40151
## 9   9 40.72237
## 10 10 31.30606
## 11 11 35.28825
## 12 12 39.30876
## 13 13 33.63652
## 14 14 31.60166
## 15 15 46.91114
## 16 16 27.64465
## 17 17 44.79302
## 18 18 41.77903
## 19 19 47.86414
## 20 20 46.16133
## 21 21 55.65410
## 22 22 40.40037
## 23 23 55.54819
## 24 24 58.57326
## 25 25 50.02469
## 26 26 38.94147
## 27 27 54.78619
## 28 28 50.61721
## 29 29 58.76102
## 30 30 57.44818

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)  20.8526     2.2356   9.327 4.38e-10 ***
## 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 = '回帰係数')
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)

##  要求されたパッケージ ggplot2 をロード中です

## 
##  次のパッケージを付け加えます: 'plotly'

##  以下のオブジェクトは 'package:ggplot2' からマスクされています:
## 
##     last_plot

##  以下のオブジェクトは 'package:latex2exp' からマスクされています:
## 
##     TeX

##  以下のオブジェクトは 'package:stats' からマスクされています:
## 
##     filter

##  以下のオブジェクトは 'package:graphics' からマスクされています:
## 
##     layout

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 = 'blue', family = 'UD Digi Kyokasho NK-R'),
         title = '回帰係数',
         xaxis = list(title = 'x'),
         yaxis = list(title = 'y')) |>
  config(mathjax = 'cdn')

## No trace type specified:
##   Based on info supplied, a 'scatter' trace seems appropriate.
##   Read more about this trace type -> https://plotly.com/r/reference/#scatter

## No trace type specified:
##   Based on info supplied, a 'scatter' trace seems appropriate.
##   Read more about this trace type -> https://plotly.com/r/reference/#scatter

import numpy as np
import pandas as pd

b0 = 20
b1 = 1.2 

np.random.seed(3)
e = np.random.normal(loc = 0, scale = 5, size = 30).reshape(-1,1)

x = np.arange(1, 31, 1).reshape(-1,1)
y = b0 + b1*x + e

from sklearn.linear_model import LinearRegression

model_lr = LinearRegression()
model_lr.fit(x, y)

LinearRegression()

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import matplotlib.pyplot as plt

# ラベル
plt.title('回帰係数',font='MS Gothic')
plt.xlabel('x',font='MS Gothic')
plt.ylabel('y',font='MS Gothic')

plt.grid(linestyle = '--', color = (0.9, 0.9, 0.9, 0.25))
plt.plot(x, y, 'o', label = 'Data points')
plt.plot(x, model_lr.predict(x), linestyle = 'solid', 
         label = '$\hat{y}_i = b_0 + b_1 x_i$')

plt.legend(loc = 'lower right')

plt.show()