R version 4.2.3 (2023-03-15 ucrt) -- "Shortstop Beagle"
Copyright (C) 2023 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64 (64-bit)

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> x <- rnorm(30)
> y <- 2*x -3 + rnorm(30)
> plot(x,y)
> lm(y ~ 1 + x)

Call:
lm(formula = y ~ 1 + x)

Coefficients:
(Intercept)            x  
     -2.740        2.018  

> lm(y ~ x)

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
     -2.740        2.018  

> lm(y ~ 0 + x)

Call:
lm(formula = y ~ 0 + x)

Coefficients:
    x  
1.776  

> reg1 <- lm(y ~ x)
> reg1

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
     -2.740        2.018  

> reg1$coef
(Intercept)           x 
  -2.740491    2.017643 
> coef(reg1)
(Intercept)           x 
  -2.740491    2.017643 
> plot(x,y)
> abline(reg1$coef)
> reg1$fitted
         1          2          3          4 
-1.3251749 -5.2710408 -4.1121753 -2.9256397 
         5          6          7          8 
-3.1220225 -1.4063942 -3.1214447 -0.8905963 
         9         10         11         12 
-0.3847513 -3.4980010 -4.9577325 -0.8221440 
        13         14         15         16 
-1.2396261 -5.0137336 -0.6389268 -4.3856314 
        17         18         19         20 
 0.9284030 -2.7138658  0.6835133 -1.0005437 
        21         22         23         24 
-3.8661891 -4.4807969 -4.5218197 -2.8757003 
        25         26         27         28 
-1.2010849 -3.9056531 -2.3932222 -2.7626299 
        29         30 
-3.3076761 -3.9146694 
> points(x,reg1$fitted)
> reg1$resid # residuals, hibák
          1           2           3           4 
-0.89217623 -0.03358074 -0.77540866 -2.66060812 
          5           6           7           8 
-1.78066813 -0.95313011  0.74591976 -0.05831520 
          9          10          11          12 
-0.02874831  0.59897872 -0.14321249  0.79810465 
         13          14          15          16 
 0.62651230  0.71862230 -1.47590747  0.77194998 
         17          18          19          20 
 1.91300506  0.07123948 -0.93829340  0.32345718 
         21          22          23          24 
-1.15022009  0.24091508 -0.35073173  0.60653270 
         25          26          27          28 
-0.04143946  0.88568259  1.93911217  0.21633810 
         29          30 
-0.07939263  0.90546269 
> qqnorm(reg1$resid)
> qqline(reg1$resid)
> plot(x,reg1$resid)
> plot(reg1)
Waiting to confirm page change...
Waiting to confirm page change...
Waiting to confirm page change...
Waiting to confirm page change...
> plot(reg1$fitted,reg1$resid)
> z <- rnorm(30)
> reg2 <- lm(z ~ x)
> reg2

Call:
lm(formula = z ~ x)

Coefficients:
(Intercept)            x  
    -0.4814       0.2858  

> plot(x,z)
> abline(reg2$coef)
> summary(reg2)

Call:
lm(formula = z ~ x)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.5019 -0.7440 -0.1642  0.6126  2.2247 

Coefficients:
            Estimate Std. Error t value
(Intercept)  -0.4814     0.1911  -2.519
x             0.2858     0.2273   1.257
            Pr(>|t|)  
(Intercept)   0.0178 *
x             0.2191  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.044 on 28 degrees of freedom
Multiple R-squared:  0.05342,   Adjusted R-squared:  0.01962 
F-statistic:  1.58 on 1 and 28 DF,  p-value: 0.2191

> summary(reg2)

Call:
lm(formula = z ~ x)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.5019 -0.7440 -0.1642  0.6126  2.2247 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)  -0.4814     0.1911  -2.519   0.0178 *
x             0.2858     0.2273   1.257   0.2191  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.044 on 28 degrees of freedom
Multiple R-squared:  0.05342,   Adjusted R-squared:  0.01962 
F-statistic:  1.58 on 1 and 28 DF,  p-value: 0.2191

> x <- rnorm(30)
> y <- x^2 + x + rnorm(30)
> reg1 <- lm(y ~ x)
> plot(x,y)
> abline(reg1$coef)
> plot(x,reg1$resid)
> plot(reg1$fitted,reg1$resid)
> reg2 <- lm(y ~ x + I(x^2))
> reg2

Call:
lm(formula = y ~ x + I(x^2))

Coefficients:
(Intercept)            x       I(x^2)  
    -0.2127       1.1152       1.2286  

> lm(y ~ x + x^2)

Call:
lm(formula = y ~ x + x^2)

Coefficients:
(Intercept)            x  
     0.9939       1.7421  

> plot(x,reg2$fitted)
> plot(x,reg2$fitted,type="l")
> sort(x)
 [1] -1.99196706 -1.19096626 -1.03488407 -0.97235622
 [5] -0.92489372 -0.89405407 -0.76075144 -0.60460101
 [9] -0.52321368 -0.44841373 -0.42905162 -0.42612160
[13] -0.41182089 -0.17958619 -0.14116787 -0.09009809
[17] -0.07701307  0.04150317  0.08311077  0.39270177
[21]  0.39446773  0.62494769  0.66604958  1.06753858
[25]  1.30719221  1.43091471  1.56311862  1.86008696
[29]  1.86109455  2.02477961
> order(x)
 [1]  4 12  7 19 23  5  6 27 14 26 16 11 20 17 21 28  2 13
[19] 18  1 29 25 24  8 10 15 22  9 30  3
> x[order(x)]
 [1] -1.99196706 -1.19096626 -1.03488407 -0.97235622
 [5] -0.92489372 -0.89405407 -0.76075144 -0.60460101
 [9] -0.52321368 -0.44841373 -0.42905162 -0.42612160
[13] -0.41182089 -0.17958619 -0.14116787 -0.09009809
[17] -0.07701307  0.04150317  0.08311077  0.39270177
[21]  0.39446773  0.62494769  0.66604958  1.06753858
[25]  1.30719221  1.43091471  1.56311862  1.86008696
[29]  1.86109455  2.02477961
> plot(x[order(x)],reg2$fitted[order(x)])
> plot(x[order(x)],reg2$fitted[order(x)],type="l")
> f <- predict(reg2,z)
Error in model.frame.default(Terms, newdata, na.action = na.action, xlev = object$xlevels) : 
  'data' must be a data.frame, environment, or list
> as.data.frame(z)
              z
1  -0.273620304
2  -1.661995642
3  -0.195540208
4  -0.665910693
5  -0.095568583
6   1.932320254
7  -0.239102315
8   0.562627886
9   1.301974429
10 -0.789140420
11 -2.297389546
12 -1.572333937
13  1.882863371
14  0.757930935
15 -0.700446827
16  0.514363376
17 -0.709157578
18 -0.644175183
19 -0.462828189
20 -1.197562196
21 -0.802681619
22 -2.161587929
23  0.181550321
24 -0.979633275
25 -1.406971321
26 -1.207264397
27 -1.166046236
28 -0.211714512
29 -1.610263532
30  0.009099006
> f <- predict(reg2,as.data.frame(z))
> f
          1           2           3           4           5 
 0.41475173 -0.29126274  7.08222818  2.44072724 -0.22769813 
          6           7           8           9          10 
-0.35004578 -0.05101147  2.37800829  6.11250909  3.34447065 
         11          12          13          14          15 
-0.46480074  0.20174597 -0.16426091 -0.45983939  3.89864591 
         16          17          18          19          20 
-0.46498998 -0.37331865 -0.11148908 -0.13547466 -0.46357440 
         21          22          23          24          25 
-0.34561305  4.53237892 -0.19317380  1.07515304  0.96412432 
         26          27          28          29          30 
-0.46571021 -0.43783439 -0.30316902  0.41842901  6.11823918 
> plot(x,y)
> lines(z,f)
> z <- seq(-2.5,2.5,0.1)
> f <- predict(reg2,as.data.frame(z))
Warning message:
'newdata' had 51 rows but variables found have 30 rows 
> plot(x,y)
> lines(z,f)
Error in xy.coords(x, y) : 'x' and 'y' lengths differ
> f <- predict(reg2,as.data.frame(z))
Warning message:
'newdata' had 51 rows but variables found have 30 rows 
> lines(z,f)
Error in xy.coords(x, y) : 'x' and 'y' lengths differ
> z <- seq(-2.5,2.5,0.1)
> f <- predict(reg2,as.data.frame(z))
Warning message:
'newdata' had 51 rows but variables found have 30 rows 
> plot(x,y)
> lines(z,f)
Error in xy.coords(x, y) : 'x' and 'y' lengths differ
> plot(x,y)
> lines(z,f)
Error in xy.coords(x, y) : 'x' and 'y' lengths differ
> f <- predict(reg2,as.data.frame(z))
Warning message:
'newdata' had 51 rows but variables found have 30 rows 
> reg2

Call:
lm(formula = y ~ x + I(x^2))

Coefficients:
(Intercept)            x       I(x^2)  
    -0.2127       1.1152       1.2286  

> z <- seq(-2.5,2.5,0.2)
> f <- predict(reg2,as.data.frame(z))
Warning message:
'newdata' had 26 rows but variables found have 30 rows 
> ?predict
starting httpd help server ... done
> predict(reg2,as.data.frame(x))
          1           2           3           4           5 
 0.41475173 -0.29126274  7.08222818  2.44072724 -0.22769813 
          6           7           8           9          10 
-0.35004578 -0.05101147  2.37800829  6.11250909  3.34447065 
         11          12          13          14          15 
-0.46480074  0.20174597 -0.16426091 -0.45983939  3.89864591 
         16          17          18          19          20 
-0.46498998 -0.37331865 -0.11148908 -0.13547466 -0.46357440 
         21          22          23          24          25 
-0.34561305  4.53237892 -0.19317380  1.07515304  0.96412432 
         26          27          28          29          30 
-0.46571021 -0.43783439 -0.30316902  0.41842901  6.11823918 
> predict(reg2,new.data=as.data.frame(z))
          1           2           3           4           5 
 0.41475173 -0.29126274  7.08222818  2.44072724 -0.22769813 
          6           7           8           9          10 
-0.35004578 -0.05101147  2.37800829  6.11250909  3.34447065 
         11          12          13          14          15 
-0.46480074  0.20174597 -0.16426091 -0.45983939  3.89864591 
         16          17          18          19          20 
-0.46498998 -0.37331865 -0.11148908 -0.13547466 -0.46357440 
         21          22          23          24          25 
-0.34561305  4.53237892 -0.19317380  1.07515304  0.96412432 
         26          27          28          29          30 
-0.46571021 -0.43783439 -0.30316902  0.41842901  6.11823918 
> f <- predict(reg2,new.data=as.data.frame(z))
> plot(x,y)
> lines(z,f)
Error in xy.coords(x, y) : 'x' and 'y' lengths differ
> f <- predict(reg2,new.data=as.data.frame(z))
> lines(z,f)
Error in xy.coords(x, y) : 'x' and 'y' lengths differ
> predict(reg2,new.data=as.data.frame(z))
          1           2           3           4           5 
 0.41475173 -0.29126274  7.08222818  2.44072724 -0.22769813 
          6           7           8           9          10 
-0.35004578 -0.05101147  2.37800829  6.11250909  3.34447065 
         11          12          13          14          15 
-0.46480074  0.20174597 -0.16426091 -0.45983939  3.89864591 
         16          17          18          19          20 
-0.46498998 -0.37331865 -0.11148908 -0.13547466 -0.46357440 
         21          22          23          24          25 
-0.34561305  4.53237892 -0.19317380  1.07515304  0.96412432 
         26          27          28          29          30 
-0.46571021 -0.43783439 -0.30316902  0.41842901  6.11823918 
> length(z)
[1] 26
> z <- seq(-2.5,2.5,length=30)
> f <- predict(reg2,new.data=as.data.frame(z))
> plot(x,y)
> lines(z,f)
> f <- predict(reg2,newdata=as.data.frame(z))
> plot(x,y)
> lines(z,f)
> z <- seq(-2.5,2.5,0.1)
> f <- predict(reg2,newdata=data.frame(x=z))
> plot(x,y)
> lines(z,f)
> plot(x,reg2$resid)
> plot(x,reg1$resid)
> plot(x,reg2$resid)
> summary(reg2)

Call:
lm(formula = y ~ x + I(x^2))

Residuals:
     Min       1Q   Median       3Q      Max 
-1.47203 -0.63103  0.07065  0.41699  1.84062 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.2127     0.1875  -1.134    0.267    
x             1.1152     0.1541   7.235 8.81e-08 ***
I(x^2)        1.2286     0.1251   9.821 2.09e-10 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.774 on 27 degrees of freedom
Multiple R-squared:  0.9027,    Adjusted R-squared:  0.8955 
F-statistic: 125.3 on 2 and 27 DF,  p-value: 2.173e-14

> reg3 <- lm(y ~ 0+x+I(x^2) )
> reg3

Call:
lm(formula = y ~ 0 + x + I(x^2))

Coefficients:
     x  I(x^2)  
 1.154   1.136  

> plot(x,y)
> points(x,reg3$fitted,col="red")
> plot(x,reg3$resid)
> summary(reg3)

Call:
lm(formula = y ~ 0 + x + I(x^2))

Residuals:
     Min       1Q   Median       3Q      Max 
-1.62002 -0.74397 -0.08064  0.26340  1.80576 

Coefficients:
       Estimate Std. Error t value Pr(>|t|)    
x        1.1539     0.1511   7.636 2.56e-08 ***
I(x^2)   1.1356     0.0950  11.955 1.63e-12 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7779 on 28 degrees of freedom
Multiple R-squared:  0.917,     Adjusted R-squared:  0.9111 
F-statistic: 154.6 on 2 and 28 DF,  p-value: 7.385e-16

> reg1

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)            x  
     0.9939       1.7421  

> reg2

Call:
lm(formula = y ~ x + I(x^2))

Coefficients:
(Intercept)            x       I(x^2)  
    -0.2127       1.1152       1.2286  

> reg3

Call:
lm(formula = y ~ 0 + x + I(x^2))

Coefficients:
     x  I(x^2)  
 1.154   1.136  

> anova(reg1,reg2)
Analysis of Variance Table

Model 1: y ~ x
Model 2: y ~ x + I(x^2)
  Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
1     28 73.957                                  
2     27 16.175  1    57.783 96.454 2.088e-10 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> anova(reg2,reg3)
Analysis of Variance Table

Model 1: y ~ x + I(x^2)
Model 2: y ~ 0 + x + I(x^2)
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     27 16.175                           
2     28 16.945 -1  -0.77036 1.2859 0.2668
> a <- rnorm(30)
> b <- rnorm(30)
> c <- 2 *a -b + rnorm(30)
> reg4 <- lm(c ~ a + b)
> reg4

Call:
lm(formula = c ~ a + b)

Coefficients:
(Intercept)            a            b  
    0.06035      2.03639     -1.05219  

> plot(x,y)
> read.table("adat3B.txt")
                   V1                V2
1                   x                 y
2    -1.8128998382017  1.26669337503769
3   -1.78000617120415  1.71519363544058
4   -1.53761506639421  1.53039595994982
5   -1.38548593875021  2.72491049194419
6   -1.36370046436787  1.54231349922645
7   -1.06372281443328  2.88488442579417
8    -1.0034651523456   2.3685727509976
9  -0.576038711704314  3.84214062542247
10 -0.511751984246075  3.26162721906042
11 -0.501689574681222  3.91782015629168
12 -0.418183164671063  3.39803187033859
13 -0.263308608904481  4.39116859949933
14 -0.202671359293163  3.03084561916818
15 -0.171649440191686  2.88538221901632
16 -0.136144533753395  4.16882140549909
17 -0.122023028321564  4.56867890337556
18  0.111457922495902  4.56005239290003
19  0.187089855782688   4.3856096725553
20  0.211925454437733  3.72069757748924
21  0.496581580489874   2.7570106560698
22  0.624563951045275  3.28052419828612
23  0.677349402569234  3.57347895464101
24   0.69881484284997   4.3505365426658
25  0.712974446825683  2.68153536193289
26  0.754332346841693  3.09814415196959
27  0.923411292955279  3.06342903785826
28   1.06195071432739  2.80959437953245
29   1.30101988278329  2.54548965410528
30   1.42867687996477  2.06092751859977
31   1.75527362432331 0.941456016204296
> read.table("adat3B.txt",head=TRUE) -> adat
> head(adat)
          x        y
1 -1.812900 1.266693
2 -1.780006 1.715194
3 -1.537615 1.530396
4 -1.385486 2.724910
5 -1.363700 1.542313
6 -1.063723 2.884884
>