testing

learning

R

set.seed(1)
library(tidyverse)
k=20
x=1:k
y=12*x+27
yd=y+runif(k,-20,20)
yd

 [1]  29.62035  45.88496  65.91413  91.32831  75.06728 114.93559 128.78701
 [8] 129.43191 140.16456 129.47145 147.23898 158.06227 190.48091 190.36415
[15] 217.79366 218.90797 239.70474 262.67624 250.20141 278.09781

plot(x,y)
lines(x,yd)

d=data.frame(x,yd)
d

x	yd
1	29.62035
2	45.88496
3	65.91413
4	91.32831
5	75.06728
6	114.93559
7	128.78701
8	129.43191
9	140.16456
10	129.47145
11	147.23898
12	158.06227
13	190.48091
14	190.36415
15	217.79366
16	218.90797
17	239.70474
18	262.67624
19	250.20141
20	278.09781

write.csv(d,"test.csv")
mylm=lm(yd~x,d)
mylm

Call:
lm(formula = yd ~ x, data = d)

Coefficients:
(Intercept)            x  
      25.81        12.32  

summary(mylm)

Call:
lm(formula = yd ~ x, data = d)

Residuals:
    Min      1Q  Median      3Q     Max 
-19.573  -8.823   3.289   6.145  16.713 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  25.8081     5.3851   4.792 0.000146 ***
x            12.3237     0.4495  27.414 3.93e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 11.59 on 18 degrees of freedom
Multiple R-squared:  0.9766,    Adjusted R-squared:  0.9753 
F-statistic: 751.5 on 1 and 18 DF,  p-value: 3.93e-16

Julia

using CSV,DataFrames,GLM,PrettyTables
d=CSV.File("test.csv")|>DataFrame

20×3 DataFrame
 Row │ Column1  x      yd
     │ Int64    Int64  Float64
─────┼──────────────────────────
   1 │       1      1   29.6203
   2 │       2      2   45.885
   3 │       3      3   65.9141
   4 │       4      4   91.3283
   5 │       5      5   75.0673
   6 │       6      6  114.936
   7 │       7      7  128.787
   8 │       8      8  129.432
  ⋮  │    ⋮       ⋮       ⋮
  14 │      14     14  190.364
  15 │      15     15  217.794
  16 │      16     16  218.908
  17 │      17     17  239.705
  18 │      18     18  262.676
  19 │      19     19  250.201
  20 │      20     20  278.098
                  5 rows omitted

pretty_table(d)

┌─────────┬───────┬─────────┐
│ Column1 │     x │      yd │
│   Int64 │ Int64 │ Float64 │
├─────────┼───────┼─────────┤
│       1 │     1 │ 29.6203 │
│       2 │     2 │  45.885 │
│       3 │     3 │ 65.9141 │
│       4 │     4 │ 91.3283 │
│       5 │     5 │ 75.0673 │
│       6 │     6 │ 114.936 │
│       7 │     7 │ 128.787 │
│       8 │     8 │ 129.432 │
│       9 │     9 │ 140.165 │
│      10 │    10 │ 129.471 │
│      11 │    11 │ 147.239 │
│      12 │    12 │ 158.062 │
│      13 │    13 │ 190.481 │
│      14 │    14 │ 190.364 │
│      15 │    15 │ 217.794 │
│      16 │    16 │ 218.908 │
│      17 │    17 │ 239.705 │
│      18 │    18 │ 262.676 │
│      19 │    19 │ 250.201 │
│      20 │    20 │ 278.098 │
└─────────┴───────┴─────────┘

ols = lm(@formula(yd ~ x), d)

StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}}}, Matrix{Float64}}

yd ~ 1 + x

Coefficients:
───────────────────────────────────────────────────────────────────────
               Coef.  Std. Error      t  Pr(>|t|)  Lower 95%  Upper 95%
───────────────────────────────────────────────────────────────────────
(Intercept)  25.8081    5.38511    4.79    0.0001    14.4944    37.1218
x            12.3237    0.449541  27.41    <1e-15    11.3792    13.2681
───────────────────────────────────────────────────────────────────────

# Print summary of the model
println(summary(ols))

StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, CholeskyPivoted{Float64, Matrix{Float64}, Vector{Int64}}}}, Matrix{Float64}}