library(foreign)
#Doc du lieu tu bo nho ngoai
data = read.csv("D://Datasets/Data-Analysis/salary.csv")
attach(data) #chuyen du lieu vao bo nho
#data
#Linear Regression (Y~X)
#fit = lm(salnow~salbeg)
fit = lm(salnow~salbeg, data = data)
fit
##
## Call:
## lm(formula = salnow ~ salbeg, data = data)
##
## Coefficients:
## (Intercept) salbeg
## 771.282 1.909
summary(fit)
##
## Call:
## lm(formula = salnow ~ salbeg, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14169.7 -1612.2 -461.7 1033.7 19717.1
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 771.28230 355.47194 2.17 0.0305 *
## salbeg 1.90945 0.04741 40.28 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3246 on 472 degrees of freedom
## Multiple R-squared: 0.7746, Adjusted R-squared: 0.7741
## F-statistic: 1622 on 1 and 472 DF, p-value: < 2.2e-16
a <- data.frame(salbeg = 300)
a
result <- predict(fit,a)
print(result)
## 1
## 1344.117
cov(salnow,salbeg)# ????
## [1] 18925532
cor(salnow,salbeg) # calculate correlation between salnow and salnbeg
## [1] 0.8801175
b = data.frame(salbeg=400)
predict(fit,b)
## 1
## 1535.062
range(salbeg)
## [1] 3600 31992
mad(salbeg)
## [1] 1494.461
# Plot the chart.
#plot(y,x,col = "blue",main = "Height & Weight Regression", abline(lm(x~y)),cex = 1.5,pch = 16,xlab = "Weight in Kg",ylab = "Height in cm")
plot(salbeg,salnow,col = "red",main = "Height & Weight Regression", cex = 1.1,pch = 16,xlab = "SalBegin",ylab = "SalNow")
abline(fit,lwd =3, col = "green")
arrows(5000,50000,16000, predict(fit, data.frame(salbeg=16000)))
text(10000,50000,"Line of the best fit", pos=3) # Text align to the right of the point of (10000,50000)
#png(file = "linearregression.png")
#scatter.smooth(x= salbeg, y = salnow, main = "salnow ~ salbeg", col = "red") # scatterplot
# Other useful functions
coefficients(fit) # model coefficients
## (Intercept) salbeg
## 771.28230 1.90945
confint(fit, level=0.95) # CIs for model parameters
## 2.5 % 97.5 %
## (Intercept) 72.77899 1469.78562
## salbeg 1.81629 2.00261
fitted(fit) # predicted values
## 1 2 3 4 5 6 7 8
## 13946.485 11082.311 10394.909 12800.816 12227.981 13946.485 12800.816 14519.320
## 9 10 11 12 13 14 15 16
## 12227.981 11082.311 15664.990 13373.651 15092.155 15664.990 16352.392 11655.146
## 17 18 19 20 21 22 23 24
## 12800.816 21966.174 12227.981 12227.981 15664.990 11884.280 12227.981 13373.651
## 25 26 27 28 29 30 31 32
## 12227.981 13831.918 13373.651 12227.981 15664.990 12227.981 12800.816 11540.579
## 33 34 35 36 37 38 39 40
## 13373.651 15664.990 12800.816 16237.825 11655.146 12227.981 13373.651 11082.311
## 41 42 43 44 45 46 47 48
## 12227.981 25196.963 14519.320 12800.816 11655.146 11655.146 13029.950 12227.981
## 49 50 51 52 53 54 55 56
## 12227.981 11655.146 12227.981 16810.660 10509.476 13946.485 11655.146 13373.651
## 57 58 59 60 61 62 63 64
## 13946.485 12800.816 11082.311 16993.967 12686.249 16237.825 11082.311 12800.816
## 65 66 67 68 69 70 71 72
## 11082.311 12227.981 12227.981 13373.651 15092.155 11540.579 12800.816 13373.651
## 73 74 75 76 77 78 79 80
## 12227.981 13946.485 9592.940 10509.476 9936.641 10853.177 10853.177 9936.641
## 81 82 83 84 85 86 87 88
## 9936.641 15092.155 14519.320 13373.651 11082.311 15664.990 11311.445 11082.311
## 89 90 91 92 93 94 95 96
## 9344.712 11655.146 13373.651 15092.155 16031.605 8218.136 8561.837 8561.837
## 97 98 99 100 101 102 103 104
## 8218.136 13373.651 9936.641 12457.115 10738.610 10509.476 11655.146 8561.837
## 105 106 107 108 109 110 111 112
## 9134.672 11655.146 10165.775 11082.311 8561.837 8561.837 8561.837 9134.672
## 113 114 115 116 117 118 119 120
## 11082.311 14519.320 11082.311 9363.806 11082.311 11769.713 11311.445 11540.579
## 121 122 123 124 125 126 127 128
## 9936.641 11082.311 9363.806 8561.837 10509.476 8561.837 8905.538 11082.311
## 129 130 131 132 133 134 135 136
## 9592.940 11082.311 12800.816 8218.136 10624.043 8561.837 9592.940 10509.476
## 137 138 139 140 141 142 143 144
## 11426.012 8561.837 11884.280 9936.641 11082.311 8447.270 8218.136 10280.342
## 145 146 147 148 149 150 151 152
## 12227.981 10853.177 8790.971 11655.146 12800.816 14519.320 8561.837 9936.641
## 153 154 155 156 157 158 159 160
## 8561.837 9936.641 11655.146 9134.672 9134.672 8218.136 8561.837 8561.837
## 161 162 163 164 165 166 167 168
## 11082.311 11082.311 14129.793 10509.476 13029.950 13373.651 10509.476 13373.651
## 169 170 171 172 173 174 175 176
## 12227.981 14519.320 12227.981 11655.146 12227.981 12227.981 12227.981 15664.990
## 177 178 179 180 181 182 183 184
## 12227.981 12227.981 12227.981 9592.940 12800.816 10738.610 12800.816 13373.651
## 185 186 187 188 189 190 191 192
## 11082.311 14519.320 18529.165 12227.981 16466.959 14519.320 11082.311 11082.311
## 193 194 195 196 197 198 199 200
## 12227.981 12800.816 12800.816 9936.641 11655.146 8561.837 8561.837 11082.311
## 201 202 203 204 205 206 207 208
## 9249.239 11655.146 12800.816 12227.981 10509.476 9936.641 13602.784 8218.136
## 209 210 211 212 213 214 215 216
## 8561.837 10509.476 11655.146 7645.301 8561.837 11082.311 8561.837 10509.476
## 217 218 219 220 221 222 223 224
## 9936.641 12227.981 9134.672 7645.301 9134.672 11426.012 7645.301 8561.837
## 225 226 227 228 229 230 231 232
## 9592.940 8561.837 10738.610 13373.651 12800.816 11998.847 13373.651 11655.146
## 233 234 235 236 237 238 239 240
## 12227.981 12227.981 12800.816 12800.816 12227.981 12800.816 12227.981 13373.651
## 241 242 243 244 245 246 247 248
## 12800.816 12800.816 13373.651 13373.651 14519.320 11655.146 12800.816 11655.146
## 249 250 251 252 253 254 255 256
## 13373.651 12800.816 12800.816 12227.981 12800.816 12800.816 13373.651 12227.981
## 257 258 259 260 261 262 263 264
## 12800.816 11655.146 12800.816 12800.816 13373.651 12800.816 9363.806 9363.806
## 265 266 267 268 269 270 271 272
## 9936.641 11082.311 10280.342 13946.485 9363.806 9936.641 10280.342 9363.806
## 273 274 275 276 277 278 279 280
## 10509.476 8790.971 9363.806 13373.651 13373.651 10280.342 9363.806 9592.940
## 281 282 283 284 285 286 287 288
## 9363.806 9363.806 11082.311 15092.155 9134.672 9592.940 9363.806 9363.806
## 289 290 291 292 293 294 295 296
## 9478.373 10967.744 9363.806 9592.940 15664.990 9936.641 10509.476 11426.012
## 297 298 299 300 301 302 303 304
## 15664.990 8790.971 9363.806 14519.320 9134.672 12227.981 9363.806 10280.342
## 305 306 307 308 309 310 311 312
## 9134.672 9363.806 9592.940 10509.476 9363.806 9134.672 13946.485 14519.320
## 313 314 315 316 317 318 319 320
## 9134.672 9936.641 9249.239 12800.816 10051.208 10509.476 12457.115 9363.806
## 321 322 323 324 325 326 327 328
## 11655.146 11082.311 11082.311 14519.320 9936.641 8790.971 9134.672 11082.311
## 329 330 331 332 333 334 335 336
## 9363.806 12227.981 13373.651 10509.476 9134.672 11082.311 13373.651 14519.320
## 337 338 339 340 341 342 343 344
## 11082.311 11426.012 9363.806 9363.806 11426.012 9936.641 9363.806 9936.641
## 345 346 347 348 349 350 351 352
## 11769.713 12227.981 12227.981 12800.816 12800.816 9478.373 12227.981 12227.981
## 353 354 355 356 357 358 359 360
## 12227.981 11655.146 8218.136 9363.806 10738.610 9936.641 9363.806 9134.672
## 361 362 363 364 365 366 367 368
## 9363.806 9134.672 9249.239 12800.816 11540.579 12800.816 12227.981 12800.816
## 369 370 371 372 373 374 375 376
## 12800.816 12227.981 12800.816 12800.816 12800.816 12800.816 11082.311 12227.981
## 377 378 379 380 381 382 383 384
## 12227.981 12800.816 12227.981 12800.816 12800.816 12800.816 7645.301 12227.981
## 385 386 387 388 389 390 391 392
## 12800.816 12800.816 12227.981 12227.981 12227.981 12227.981 16810.660 17383.495
## 393 394 395 396 397 398 399 400
## 25586.491 20820.504 26548.854 21782.867 17383.495 25219.877 21759.954 25976.019
## 401 402 403 404 405 406 407 408
## 21759.954 16810.660 21759.954 18895.779 23684.679 17383.495 24257.514 17956.330
## 409 410 411 412 413 414 415 416
## 17566.802 20820.504 16993.967 25196.963 22722.316 17177.274 17383.495 18529.165
## 417 418 419 420 421 422 423 424
## 15664.990 20820.504 16810.660 21759.954 23295.151 23684.679 24830.349 15092.155
## 425 426 427 428 429 430 431 432
## 14129.793 12800.816 15664.990 13946.485 16031.605 15664.990 22722.316 46598.076
## 433 434 435 436 437 438 439 440
## 20247.670 33995.708 21393.339 25976.019 21759.954 27488.303 27488.303 25586.491
## 441 442 443 444 445 446 447 448
## 20247.670 18895.779 25976.019 37043.189 23684.679 29413.028 21759.954 28450.666
## 449 450 451 452 453 454 455 456
## 25586.491 27511.216 24639.404 28840.193 27488.303 31314.840 16993.967 21782.867
## 457 458 459 460 461 462 463 464
## 27534.130 19865.780 22722.316 19858.142 23684.679 26548.854 34453.976 25586.491
## 465 466 467 468 469 470 471 472
## 33239.565 25586.491 14519.320 27488.303 33216.652 35141.377 61858.398 40869.727
## 473 474
## 35141.377 27488.303
residuals(fit) # residuals
## 1 2 3 4 5
## 2133.514566 3017.689160 2025.091063 2919.184404 -3347.980677
## 6 7 8 9 10
## -3566.485434 -4280.815596 -3059.320352 3312.019323 -162.310840
## 11 12 13 14 15
## -3928.990190 666.349485 987.844729 475.009810 -1352.392092
## 16 17 18 19 20
## -255.145759 -740.815596 -8118.174296 2892.019323 4092.019323
## 21 22 23 24 25
## -1264.990190 -3124.279726 72.019323 2466.349485 -587.980677
## 26 27 28 29 30
## -3451.918450 -1613.650515 1992.019323 5395.009810 5832.019323
## 31 32 33 34 35
## -200.815596 -1880.578775 -1073.650515 4555.009810 -3020.815596
## 36 37 38 39 40
## -2257.825108 824.854241 -2087.980677 2766.349485 -1062.310840
## 41 42 43 44 45
## -1907.980677 1553.036763 -719.320352 -2300.815596 44.854241
## 46 47 48 49 50
## 6744.854241 -2529.949564 -3407.980677 -1847.980677 -1635.145759
## 51 52 53 54 55
## 132.019323 1189.339973 170.524079 -3026.485434 5264.854241
## 56 57 58 59 60
## -1313.650515 -3026.485434 -3200.815596 -342.310840 956.032799
## 61 62 63 64 65
## -2186.248612 202.174892 1577.689160 759.184404 1757.689160
## 66 67 68 69 70
## -1487.980677 732.019323 906.349485 -692.155271 1839.421225
## 71 72 73 74 75
## -2000.815596 -1253.650515 132.019323 -3026.485434 -1072.940051
## 76 77 78 79 80
## -1569.475921 -1356.641002 -2093.176872 -2813.176872 -936.641002
## 81 82 83 84 85
## -1116.641002 -1292.155271 7080.679648 -1373.650515 2237.689160
## 86 87 88 89 90
## -2104.990190 -1711.444807 -2142.310840 1755.288414 -2655.145759
## 91 92 93 94 95
## -1973.650515 -5012.155271 -1631.604538 541.863754 -2261.837198
## 96 97 98 99 100
## -1601.837198 -1738.136246 -1733.650515 -156.641002 -3097.114645
## 101 102 103 104 105
## -2878.609889 -849.475921 1004.854241 378.162802 465.327884
## 106 107 108 109 110
## -1395.145759 -985.774970 -1542.310840 -1481.837198 -1721.837198
## 111 112 113 114 115
## -2201.837198 1245.327884 -2442.310840 1800.679648 797.689160
## 116 117 118 119 120
## 3176.193916 -2682.310840 -1689.712742 -2431.444807 -1460.578775
## 121 122 123 124 125
## -696.641002 -2442.310840 -1383.806084 -2081.837198 -1749.475921
## 126 127 128 129 130
## -1841.837198 574.461851 857.689160 907.059949 -1662.310840
## 131 132 133 134 135
## -3020.815596 541.863754 55.957095 -581.837198 -1192.940051
## 136 137 138 139 140
## 650.524079 -26.011791 -2081.837198 2035.720274 -1596.641002
## 141 142 143 144 145
## -1482.310840 1392.729786 -958.136246 -1580.341954 3312.019323
## 146 147 148 149 150
## -1073.176872 -1290.971165 -3375.145759 2259.184404 5880.679648
## 151 152 153 154 155
## -641.837198 -1596.641002 -1961.837198 3623.358998 -1395.145759
## 156 157 158 159 160
## 585.327884 1365.327884 -1558.136246 -1781.837198 -1661.837198
## 161 162 163 164 165
## -402.310840 557.689160 -809.792608 -2649.475921 -2529.949564
## 166 167 168 169 170
## -2153.650515 -1809.475921 -1133.650515 -3227.980677 -3719.320352
## 171 172 173 174 175
## -1607.980677 -435.145759 1872.019323 -47.980677 -1127.980677
## 176 177 178 179 180
## 415.009810 -647.980677 -3287.980677 -1547.980677 1507.059949
## 181 182 183 184 185
## -2300.815596 -658.609889 -3200.815596 1986.349485 1517.689160
## 186 187 188 189 190
## -3179.320352 -949.164783 -3287.980677 3133.040924 -239.320352
## 191 192 193 194 195
## -402.310840 -1602.310840 2172.019323 -2240.815596 -20.815596
## 196 197 198 199 200
## -36.641002 -1035.145759 -1601.837198 18.162802 -762.310840
## 201 202 203 204 205
## 350.760900 -1755.145759 -1940.815596 -2507.980677 -909.475921
## 206 207 208 209 210
## 1163.358998 437.215518 -358.136246 -2021.837198 -489.475921
## 211 212 213 214 215
## -1875.145759 -865.301328 -1781.837198 -642.310840 -1721.837198
## 216 217 218 219 220
## 50.524079 -696.641002 -287.980677 -974.672116 814.698672
## 221 222 223 224 225
## 885.327884 -3566.011791 34.698672 2418.162802 -172.940051
## 226 227 228 229 230
## -1181.837198 -2398.609889 -4373.650515 -1040.815596 -1018.846710
## 231 232 233 234 235
## 546.349485 1364.854241 -1187.980677 -887.980677 -680.815596
## 236 237 238 239 240
## 19199.184404 -1607.980677 -320.815596 -1007.980677 -2273.650515
## 241 242 243 244 245
## 615.184404 -140.815596 186.349485 -113.650515 -2999.320352
## 246 247 248 249 250
## -2355.145759 3159.184404 2804.854241 1746.349485 -692.815596
## 251 252 253 254 255
## 4563.184404 4572.019323 -1820.815596 -860.815596 186.349485
## 256 257 258 259 260
## -1427.980677 -2660.815596 1004.854241 2859.184404 -860.815596
## 261 262 263 264 265
## -2513.650515 759.184404 -1503.806084 -663.806084 1043.358998
## 266 267 268 269 270
## -1422.310840 -500.341954 333.514566 -423.806084 -1296.641002
## 271 272 273 274 275
## 879.658046 -1203.806084 -1929.475921 1769.028835 -303.806084
## 276 277 278 279 280
## -4493.650515 -1613.650515 1359.658046 1556.193916 67.059949
## 281 282 283 284 285
## -3.806084 -303.806084 -1722.310840 -2492.155271 585.327884
## 286 287 288 289 290
## 2107.059949 -1023.806084 2036.193916 1561.626933 3252.256144
## 291 292 293 294 295
## -1323.806084 847.059949 -4564.990190 263.358998 -1509.475921
## 296 297 298 299 300
## -2246.011791 -2524.990190 389.028835 -843.806084 -1319.320352
## 301 302 303 304 305
## 105.327884 -563.980677 -3.806084 1959.658046 -134.672116
## 306 307 308 309 310
## -1203.806084 1087.059949 1130.524079 596.193916 -1274.672116
## 311 312 313 314 315
## -146.485434 120.679648 -314.672116 263.358998 3290.760900
## 316 317 318 319 320
## -3500.815596 3748.792014 770.524079 -697.114645 236.193916
## 321 322 323 324 325
## 104.854241 -1242.310840 -522.310840 300.679648 -156.641002
## 326 327 328 329 330
## 2609.028835 765.327884 1937.689160 -243.806084 1092.019323
## 331 332 333 334 335
## 2046.349485 -969.475921 -1874.672116 -2742.310840 -1253.650515
## 336 337 338 339 340
## -1499.320352 77.689160 93.988209 -243.806084 -1083.806084
## 341 342 343 344 345
## -1346.011791 -1476.641002 -123.806084 1403.358998 -1569.712742
## 346 347 348 349 350
## -1607.980677 -1247.980677 -20.815596 -2120.815596 721.626933
## 351 352 353 354 355
## 312.019323 132.019323 -1067.980677 -555.145759 781.863754
## 356 357 358 359 360
## -843.806084 -118.609889 -36.641002 -183.806084 -314.672116
## 361 362 363 364 365
## -1143.806084 645.327884 -1569.239100 -500.815596 759.421225
## 366 367 368 369 370
## -500.815596 72.019323 -800.815596 -560.815596 552.019323
## 371 372 373 374 375
## -1400.815596 -20.815596 -800.815596 1299.184404 1217.689160
## 376 377 378 379 380
## 1272.019323 72.019323 999.184404 72.019323 -680.815596
## 381 382 383 384 385
## -980.815596 -320.815596 4654.698672 72.019323 -800.815596
## 386 387 388 389 390
## 1299.184404 -2507.980677 -227.980677 72.019323 72.019323
## 391 392 393 394 395
## -730.660027 1816.505054 1663.509018 1179.495542 -4348.853645
## 396 397 398 399 400
## 5717.132878 10616.505054 2030.123366 9540.046275 3423.981273
## 401 402 403 404 405
## 2390.046275 4439.339973 190.046275 5104.220869 7565.320948
## 406 407 408 409 410
## 6116.505054 1742.486030 6293.670135 1933.197880 8679.495542
## 411 412 413 414 415
## 1406.032799 803.036763 6277.683612 922.725625 16116.505054
## 416 417 418 419 420
## -279.164783 1795.009810 -3900.504458 5789.339973 5740.046275
## 421 422 423 424 425
## 13204.848693 8815.320948 5169.651111 6657.844729 3070.207392
## 426 427 428 429 430
## 2319.184404 -1900.990190 4803.514566 6268.395462 1735.009810
## 431 432 433 434 435
## 8677.683612 -5198.075801 1712.330461 -5645.707589 1406.660623
## 436 437 438 439 440
## -6956.018727 -1259.953725 -5488.302912 -488.302912 -3586.490982
## 441 442 443 444 445
## -4227.669539 -3415.779131 -1476.018727 -10643.189356 65.320948
## 446 447 448 449 450
## -3413.028239 -909.953725 -7870.665576 -5586.490982 11288.783691
## 451 452 453 454 455
## 11610.596084 -4090.193320 -2488.302912 5485.159831 1906.032799
## 456 457 458 459 460
## 19717.132878 465.870294 2754.220406 2027.683612 -3238.141795
## 461 462 463 464 465
## -984.679052 -2788.853645 5546.024476 -1586.490982 -3239.565496
## 466 467 468 469 470
## 1163.509018 8730.679648 -988.302912 -5516.652099 -641.377426
## 471 472 473 474
## -7858.398035 -14169.726613 9108.622574 5511.697088
anova(fit) # anova table
vcov(fit) # covariance matrix for model parameters
## (Intercept) salbeg
## (Intercept) 126360.30089 -15.298672783
## salbeg -15.29867 0.002247678
#influence(fit) # regression diagnostics
# diagnostic plots
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page
plot(fit)
