set.seed(123)
x <- rnorm(100, mean = 5, sd = 2)
y <- 2 * x + rnorm(100, mean = 0, sd = 1)
x
## [1] 3.8790487 4.5396450 8.1174166 5.1410168 5.2585755 8.4301300 5.9218324
## [8] 2.4698775 3.6262943 4.1086761 7.4481636 5.7196277 5.8015429 5.2213654
## [15] 3.8883177 8.5738263 5.9957010 1.0667657 6.4027118 4.0544172 2.8643526
## [22] 4.5640502 2.9479911 3.5422175 3.7499215 1.6266134 6.6755741 5.3067462
## [29] 2.7237261 7.5076298 5.8529284 4.4098570 6.7902513 6.7562670 6.6431622
## [36] 6.3772805 6.1078353 4.8761766 4.3880747 4.2390580 3.6105860 4.5841654
## [43] 2.4692073 9.3379119 7.4159240 2.7537828 4.1942303 4.0666893 6.5599302
## [50] 4.8332619 5.5066370 4.9429065 4.9142591 7.7372046 4.5484580 8.0329412
## [57] 1.9024944 6.1692275 5.2477085 5.4318831 5.7592790 3.9953531 4.3335852
## [64] 2.9628492 2.8564175 5.6070573 5.8964196 5.1060085 6.8445349 9.1001694
## [71] 4.0179377 0.3816622 7.0114770 3.5815985 3.6239828 7.0511427 4.4304540
## [78] 2.5585646 5.3626070 4.7222173 5.0115284 5.7705608 4.2586799 6.2887531
## [85] 4.5590269 5.6635639 7.1936780 5.8703630 4.3481368 7.2976152 6.9870077
## [92] 6.0967939 5.4774635 3.7441878 7.7213049 3.7994808 9.3746660 8.0652213
## [99] 4.5285993 2.9471582
y
## [1] 7.0476909 9.3361738 15.9881414 9.9344910 9.5655324 16.8152322
## [7] 11.0587604 3.2718131 6.8723621 9.1363487 14.3209802 12.0472196
## [13] 9.9852031 10.3871689 8.2960427 17.4488059 12.0970781 1.4928254
## [19] 11.9557193 7.0847056 5.8463518 8.1806257 5.4054248 6.8283429
## [25] 9.3437049 2.6012769 13.5865348 10.6914533 4.4855956 14.9439516
## [31] 13.1504077 9.2712181 13.6217356 13.0900371 11.2330771 13.8858982
## [37] 10.7550305 10.4923007 10.6852529 7.0342228 7.9229564 8.9061334
## [43] 3.3662704 17.1611562 13.2303118 4.9766591 6.9267051 8.8212954
## [49] 15.2199694 8.3794933 11.8010129 10.6548552 10.1607207 14.4660325
## [55] 8.9774635 15.7854871 4.3679783 11.9660162 11.4723904 10.4891854
## [61] 12.5712694 6.9415292 7.4070152 9.1667384 5.2959775 11.5123422
## [67] 12.4294088 9.7282363 14.2059319 18.5693033 7.8204948 0.8286175
## [73] 13.9888868 9.2916488 6.5066294 13.0062892 8.8986964 5.4276099
## [79] 11.1617374 8.9860692 8.9597306 12.8043068 8.1677095 11.7119933
## [85] 8.8817742 11.1299520 15.4972763 11.8254633 9.4503274 14.0959385
## [91] 14.1884607 11.8689019 11.0495105 6.5930123 14.1318083 9.5961750
## [97] 19.3500408 14.8791711 8.4460326 4.7088363
x <- cbind(1,x)
x
## x
## [1,] 1 3.8790487
## [2,] 1 4.5396450
## [3,] 1 8.1174166
## [4,] 1 5.1410168
## [5,] 1 5.2585755
## [6,] 1 8.4301300
## [7,] 1 5.9218324
## [8,] 1 2.4698775
## [9,] 1 3.6262943
## [10,] 1 4.1086761
## [11,] 1 7.4481636
## [12,] 1 5.7196277
## [13,] 1 5.8015429
## [14,] 1 5.2213654
## [15,] 1 3.8883177
## [16,] 1 8.5738263
## [17,] 1 5.9957010
## [18,] 1 1.0667657
## [19,] 1 6.4027118
## [20,] 1 4.0544172
## [21,] 1 2.8643526
## [22,] 1 4.5640502
## [23,] 1 2.9479911
## [24,] 1 3.5422175
## [25,] 1 3.7499215
## [26,] 1 1.6266134
## [27,] 1 6.6755741
## [28,] 1 5.3067462
## [29,] 1 2.7237261
## [30,] 1 7.5076298
## [31,] 1 5.8529284
## [32,] 1 4.4098570
## [33,] 1 6.7902513
## [34,] 1 6.7562670
## [35,] 1 6.6431622
## [36,] 1 6.3772805
## [37,] 1 6.1078353
## [38,] 1 4.8761766
## [39,] 1 4.3880747
## [40,] 1 4.2390580
## [41,] 1 3.6105860
## [42,] 1 4.5841654
## [43,] 1 2.4692073
## [44,] 1 9.3379119
## [45,] 1 7.4159240
## [46,] 1 2.7537828
## [47,] 1 4.1942303
## [48,] 1 4.0666893
## [49,] 1 6.5599302
## [50,] 1 4.8332619
## [51,] 1 5.5066370
## [52,] 1 4.9429065
## [53,] 1 4.9142591
## [54,] 1 7.7372046
## [55,] 1 4.5484580
## [56,] 1 8.0329412
## [57,] 1 1.9024944
## [58,] 1 6.1692275
## [59,] 1 5.2477085
## [60,] 1 5.4318831
## [61,] 1 5.7592790
## [62,] 1 3.9953531
## [63,] 1 4.3335852
## [64,] 1 2.9628492
## [65,] 1 2.8564175
## [66,] 1 5.6070573
## [67,] 1 5.8964196
## [68,] 1 5.1060085
## [69,] 1 6.8445349
## [70,] 1 9.1001694
## [71,] 1 4.0179377
## [72,] 1 0.3816622
## [73,] 1 7.0114770
## [74,] 1 3.5815985
## [75,] 1 3.6239828
## [76,] 1 7.0511427
## [77,] 1 4.4304540
## [78,] 1 2.5585646
## [79,] 1 5.3626070
## [80,] 1 4.7222173
## [81,] 1 5.0115284
## [82,] 1 5.7705608
## [83,] 1 4.2586799
## [84,] 1 6.2887531
## [85,] 1 4.5590269
## [86,] 1 5.6635639
## [87,] 1 7.1936780
## [88,] 1 5.8703630
## [89,] 1 4.3481368
## [90,] 1 7.2976152
## [91,] 1 6.9870077
## [92,] 1 6.0967939
## [93,] 1 5.4774635
## [94,] 1 3.7441878
## [95,] 1 7.7213049
## [96,] 1 3.7994808
## [97,] 1 9.3746660
## [98,] 1 8.0652213
## [99,] 1 4.5285993
## [100,] 1 2.9471582
beta <- solve(t(x) %*% x) %*% t(x) %*% y
beta
## [,1]
## 0.02837598
## x 1.97376419
cat("Parameter Beta: \n")
## Parameter Beta:
print(beta)
## [,1]
## 0.02837598
## x 1.97376419