##------------------- Telcom ----------------##
library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.1.2
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.6 v dplyr 1.0.8
## v tidyr 1.2.0 v stringr 1.4.0
## v readr 2.1.2 v forcats 0.5.1
## Warning: package 'ggplot2' was built under R version 4.1.2
## Warning: package 'tibble' was built under R version 4.1.2
## Warning: package 'tidyr' was built under R version 4.1.2
## Warning: package 'readr' was built under R version 4.1.2
## Warning: package 'purrr' was built under R version 4.1.2
## Warning: package 'dplyr' was built under R version 4.1.2
## Warning: package 'stringr' was built under R version 4.1.2
## Warning: package 'forcats' was built under R version 4.1.2
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
library(readxl)
## Warning: package 'readxl' was built under R version 4.1.2
library(psych)
## Warning: package 'psych' was built under R version 4.1.2
##
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
telcom = read_excel("C:\\Users\\user\\Downloads\\activity1_data.xlsx")
telcom
## # A tibble: 71 x 8
## MONTH PCOMP TEL GLO PHP PHIVTA PHMS TBILL
## <dttm> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2022-12-03 00:00:00 1442. 970 860 55505 238316 514214 0.0625
## 2 2022-11-03 00:00:00 1314. 755 720 55725 170921 470740 0.0644
## 3 2022-10-03 00:00:00 1399. 765 790 55330 167573 452675 0.0566
## 4 2022-09-03 00:00:00 1297. 640 695 54880 140652 445781 0.0533
## 5 2022-08-03 00:00:00 1193. 535 620 55025 162076 443137 0.0523
## 6 2022-07-03 00:00:00 1240. 530 665 54730 166045 440885 0.0524
## 7 2022-06-03 00:00:00 1223. 565 605 53480 130874 445392 0.0558
## 8 2022-05-03 00:00:00 1074. 432. 610 53225 109803 447526 0.0657
## 9 2022-04-03 00:00:00 1068. 380 550 52533 123576 442370 0.0735
## 10 2022-03-03 00:00:00 1040. 315 565 53525 157036 444956 0.0617
## # ... with 61 more rows
# Convert the TBILL into double
final_data <- telcom %>%
select(TEL,PCOMP, GLO, PHP, PHIVTA, PHMS, `TBILL`) %>%
mutate(`TBILL` =gsub('.{1}$', '', `TBILL`)) %>%
mutate(`TBILL` = as.double(`TBILL`))
head(final_data)
## # A tibble: 6 x 7
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 970 1442. 860 55505 238316 514214 0.062
## 2 755 1314. 720 55725 170921 470740 0.064
## 3 765 1399. 790 55330 167573 452675 0.056
## 4 640 1297. 695 54880 140652 445781 0.053
## 5 535 1193. 620 55025 162076 443137 0.052
## 6 530 1240. 665 54730 166045 440885 0.052
final_data
## # A tibble: 71 x 7
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 970 1442. 860 55505 238316 514214 0.062
## 2 755 1314. 720 55725 170921 470740 0.064
## 3 765 1399. 790 55330 167573 452675 0.056
## 4 640 1297. 695 54880 140652 445781 0.053
## 5 535 1193. 620 55025 162076 443137 0.052
## 6 530 1240. 665 54730 166045 440885 0.052
## 7 565 1223. 605 53480 130874 445392 0.055
## 8 432. 1074. 610 53225 109803 447526 0.065
## 9 380 1068. 550 52533 123576 442370 0.073
## 10 315 1040. 565 53525 157036 444956 0.061
## # ... with 61 more rows
#--------------- a. Run multiple linear regression ----------------#
## scatter plot matrix
plot(final_data, col="navy", main="Scatter plot Matrix")
#--------------- b. Create Different Models ----------------#
##--------- Model 1 Positive Correlation (Y = TEL and X = PCOMP & PHIVTA) -------##
model1 <-lm(final_data$TEL~final_data$PCOMP+final_data$PHIVTA)
model1
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PCOMP + final_data$PHIVTA)
##
## Coefficients:
## (Intercept) final_data$PCOMP final_data$PHIVTA
## -3.025e+02 5.439e-01 1.057e-03
## Coefficient Values
model1[["coefficients"]][["(Intercept)"]]
## [1] -302.5038
model1[["coefficients"]][["final_data$PCOMP"]]
## [1] 0.5438577
model1[["coefficients"]][["final_data$PHIVTA"]]
## [1] 0.001057461
## Regression Equation
## y(hat) = -3.025e+02 + 5.439e-01 * X1 + 1.057e-03 * X2
#--------------- C. Find the R squared of each model and interpret.----------#
summary(model1)
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PCOMP + final_data$PHIVTA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -196.98 -112.12 2.18 79.82 362.34
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.025e+02 1.069e+02 -2.830 0.00611 **
## final_data$PCOMP 5.439e-01 4.122e-02 13.194 < 2e-16 ***
## final_data$PHIVTA 1.058e-03 7.371e-04 1.435 0.15597
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 123.6 on 68 degrees of freedom
## Multiple R-squared: 0.7924, Adjusted R-squared: 0.7863
## F-statistic: 129.8 on 2 and 68 DF, p-value: < 2.2e-16
## The r squared is 0.7924. This means that there is 79.24 percent of variation
## in the response variable which is TEL when PCOMP and PHIVTA are considered.
## Fitted
fittedval= -302.5038 + 0.5438577 * (final_data$PCOMP) + 0.001057461 * (final_data$PHIVTA)
fittedval
## [1] 733.9501 592.7968 635.5931 551.8421 517.6150 547.6943 500.9195
## [8] 397.5432 409.0837 428.9882 423.8373 458.0107 453.4175 420.7347
## [15] 426.9819 456.7812 471.2487 489.0260 495.9848 585.8622 605.3287
## [22] 645.2510 624.4657 602.4151 508.5843 436.5145 354.5317 511.6771
## [29] 603.0830 627.7302 614.3033 617.0844 634.8704 680.9117 731.4036
## [36] 791.7747 692.0997 627.2544 553.1555 613.3396 701.8151 643.9216
## [43] 700.9654 670.4407 761.6733 814.3964 780.3461 979.0609 1087.7535
## [50] 981.5077 989.6841 1013.7851 1059.7396 1152.9732 1227.9839 1192.5665
## [57] 1218.9210 1005.1567 952.0758 960.9797 997.8167 983.6923 836.1979
## [64] 557.6608 525.3416 757.7121 825.6104 961.3527 1070.1802 1113.4693
## [71] 1114.0370
new_data<-cbind(final_data,fittedval)
new_data
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL fittedval
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 733.9501
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 592.7968
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 635.5931
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 551.8421
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 517.6150
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 547.6943
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 500.9195
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 397.5432
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 409.0837
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 428.9882
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 423.8373
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 458.0107
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 453.4175
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 420.7347
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 426.9819
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 456.7812
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 471.2487
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 489.0260
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 495.9848
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 585.8622
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 605.3287
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 645.2510
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 624.4657
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 602.4151
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 508.5843
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 436.5145
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 354.5317
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 511.6771
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 603.0830
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 627.7302
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 614.3033
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 617.0844
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 634.8704
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 680.9117
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 731.4036
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 791.7747
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 692.0997
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 627.2544
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 553.1555
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 613.3396
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 701.8151
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 643.9216
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 700.9654
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 670.4407
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 761.6733
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 814.3964
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 780.3461
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 979.0609
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 1087.7535
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 981.5077
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 989.6841
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 1013.7851
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 1059.7396
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 1152.9732
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 1227.9839
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 1192.5665
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 1218.9210
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 1005.1567
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 952.0758
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 960.9797
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 997.8167
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 983.6923
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 836.1979
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 557.6608
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 525.3416
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 757.7121
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 825.6104
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 961.3527
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 1070.1802
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1113.4693
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 1114.0370
## Residual
resid1 <- final_data$TEL - fittedval
resid1
## [1] 236.049894 162.203192 129.406896 88.157938 17.384971 -17.694280
## [7] 64.080454 34.956836 -29.083726 -113.988181 -131.337322 -163.010700
## [13] -183.417508 -130.734702 -196.981906 -176.781162 -186.248656 -174.026043
## [19] -125.984819 -148.362153 -145.328687 -110.250990 -119.465741 -92.415104
## [25] -91.084255 -9.014450 25.468301 -31.677070 -118.082986 47.269798
## [31] 110.696691 32.915569 55.129558 34.088278 63.596358 123.225300
## [37] 172.900255 177.745612 221.844467 196.660432 63.184927 26.078413
## [43] 74.034594 94.559345 -21.673310 85.603599 109.653908 -29.060903
## [49] -62.753535 -141.507661 -154.684060 -128.785138 -119.739612 -42.973238
## [55] -67.983880 -77.566468 11.078997 14.843333 -47.075808 -60.979707
## [61] 2.183337 46.307708 128.802076 362.339207 199.658417 167.287907
## [67] 124.389573 38.647338 4.819770 -58.469329 -39.037005
resid_model1 <- cbind(final_data,new_data,resid1)
resid_model1
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL TEL PCOMP GLO PHP
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 970.0 1442.37 860.0 55505
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 755.0 1313.87 720.0 55725
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 765.0 1399.07 790.0 55330
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 640.0 1297.42 695.0 54880
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 535.0 1192.83 620.0 55025
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 530.0 1240.42 665.0 54730
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 565.0 1222.80 605.0 53480
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 432.5 1073.69 610.0 53225
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 380.0 1068.13 550.0 52533
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 315.0 1039.67 565.0 53525
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 292.5 1019.33 525.0 54510
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 295.0 1056.69 530.0 53875
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 270.0 1018.41 447.5 53280
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 290.0 1047.22 435.0 53540
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 230.0 1048.53 410.0 53125
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 280.0 1129.34 465.0 52410
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 285.0 1103.36 485.0 51840
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 315.0 1123.24 510.0 51250
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 370.0 1156.35 520.0 50420
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 437.5 1315.00 670.0 50250
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 460.0 1346.09 645.0 50830
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 535.0 1403.62 640.0 51020
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 505.0 1406.22 636.0 51225
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 510.0 1361.94 596.0 51235
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 417.5 1168.08 544.0 51750
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 427.5 1128.47 456.0 52000
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 380.0 993.35 432.0 51950
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 480.0 1265.44 500.0 51365
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 485.0 1362.89 520.0 50930
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 675.0 1410.07 532.0 53540
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 725.0 1402.29 556.0 52405
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 650.0 1402.29 548.0 50500
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 690.0 1378.84 554.0 51400
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 715.0 1446.40 528.0 49500
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 795.0 1613.49 580.0 48275
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 915.0 1687.00 580.0 48275
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 865.0 1494.50 560.0 50010
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 805.0 1404.83 520.0 49600
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 775.0 1287.85 472.0 51550
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 810.0 1434.49 640.0 46165
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 765.0 1537.52 676.0 45135
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 670.0 1417.17 600.0 44835
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 775.0 1533.99 620.0 43250
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 765.0 1478.76 560.0 42645
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 740.0 1598.73 600.0 41300
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 900.0 1681.72 500.0 41140
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 890.0 1641.94 440.0 40140
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 950.0 1989.43 420.0 40573
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 1025.0 2142.97 440.0 40410
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 840.0 1979.42 430.0 40945
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 835.0 2036.05 470.0 40250
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 885.0 2096.20 440.0 40930
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 940.0 2173.82 450.0 39665
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 1110.0 2342.81 490.0 38495
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 1160.0 2486.86 480.0 38065
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 1115.0 2419.83 490.0 38000
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 1230.0 2443.70 396.0 38007
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 1020.0 2028.21 248.0 38775
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 905.0 1965.05 252.0 39070
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 900.0 1954.15 256.0 38550
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 1000.0 1968.78 244.0 39150
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 1030.0 1975.36 268.0 39380
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 965.0 1755.04 196.0 40390
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 920.0 1259.64 170.0 43950
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 725.0 1192.25 172.0 43875
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 925.0 1607.61 232.0 42030
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 950.0 1760.13 236.0 41800
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 1000.0 2011.45 204.0 38825
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 1075.0 2181.32 200.0 40190
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1055.0 2238.42 184.0 37975
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 1075.0 2266.30 124.0 39840
## PHIVTA PHMS TBILL fittedval resid1
## 1 238316 514214 0.062 733.9501 236.049894
## 2 170921 470740 0.064 592.7968 162.203192
## 3 167573 452675 0.056 635.5931 129.406896
## 4 140652 445781 0.053 551.8421 88.157938
## 5 162076 443137 0.052 517.6150 17.384971
## 6 166045 440885 0.052 547.6943 -17.694280
## 7 130874 445392 0.055 500.9195 64.080454
## 8 109803 447526 0.065 397.5432 34.956836
## 9 123576 442370 0.073 409.0837 -29.083726
## 10 157036 444956 0.061 428.9882 -113.988181
## 11 162626 442370 0.056 423.8373 -131.337322
## 12 175728 444956 0.051 458.0107 -163.010700
## 13 191072 470056 0.052 453.4175 -183.417508
## 14 145348 434771 0.052 420.7347 -130.734702
## 15 150582 420590 0.052 426.9819 -196.981906
## 16 137201 411308 0.047 456.7812 -176.781162
## 17 164244 404530 0.047 471.2487 -186.248656
## 18 170831 404147 0.047 489.0260 -174.026043
## 19 160383 405491 0.046 495.9848 -125.984819
## 20 163782 405438 0.046 585.8622 -148.362153
## 21 166201 403614 0.046 605.3287 -145.328687
## 22 174366 389816 0.063 645.2510 -110.250990
## 23 153373 373088 0.071 624.4657 -119.465741
## 24 155294 364867 0.078 602.4151 -92.415104
## 25 166265 387989 0.088 508.5843 -91.084255
## 26 118483 353080 0.095 436.5145 -9.014450
## 27 110448 350421 0.097 354.5317 25.468301
## 28 119117 353183 0.095 511.6771 -31.677070
## 29 155437 360712 0.095 603.0830 -118.082986
## 30 154480 369211 0.088 627.7302 47.269798
## 31 145784 377970 0.087 614.3033 110.696691
## 32 148414 379962 0.090 617.0844 32.915569
## 33 177294 389215 0.090 634.8704 55.129558
## 34 186087 367264 0.090 680.9117 34.088278
## 35 147900 361013 0.106 731.4036 63.596358
## 36 167184 382023 0.120 791.7747 123.225300
## 37 171929 386981 0.130 692.0997 172.900255
## 38 156725 358852 0.150 627.2544 177.745612
## 39 146816 339811 0.090 553.1555 221.844467
## 40 128312 342487 0.090 613.3396 196.660432
## 41 158991 341249 0.080 701.8151 63.184927
## 42 166140 339541 0.080 643.9216 26.078413
## 43 160003 341264 0.080 700.9654 74.034594
## 44 159542 342222 0.080 670.4407 94.559345
## 45 184116 347534 0.080 761.6733 -21.673310
## 46 191292 337505 0.080 814.3964 85.603599
## 47 179551 326894 0.080 780.3461 109.653908
## 48 188752 343054 0.080 979.0609 -29.060903
## 49 212572 394127 0.080 1087.7535 -62.753535
## 50 196214 334674 0.080 981.5077 -141.507661
## 51 174821 313796 0.080 989.6841 -154.684060
## 52 166677 307055 0.080 1013.7851 -128.785138
## 53 170214 297737 0.080 1059.7396 -119.739612
## 54 171469 298875 0.084 1152.9732 -42.973238
## 55 168318 293971 0.092 1227.9839 -67.983880
## 56 169299 305896 0.099 1192.5665 -77.566468
## 57 181945 290772 0.100 1218.9210 11.078997
## 58 193485 285161 0.121 1005.1567 14.843333
## 59 175772 285161 0.127 952.0758 -47.075808
## 60 189798 262399 0.132 960.9797 -60.979707
## 61 217109 281514 0.134 997.8167 2.183337
## 62 200368 253719 0.134 983.6923 46.307708
## 63 174200 243915 0.135 836.1979 128.802076
## 64 165585 238422 0.138 557.6608 362.339207
## 65 169681 235853 0.140 525.3416 199.658417
## 66 175803 241070 0.146 757.7121 167.287907
## 67 161570 251214 0.100 825.6104 124.389573
## 68 160681 255527 0.143 961.3527 38.647338
## 69 176230 247455 0.150 1070.1802 4.819770
## 70 187800 241935 0.160 1113.4693 -58.469329
## 71 173998 243119 0.177 1114.0370 -39.037005
sum(resid1)
## [1] -0.006847618
## The residual is -0.006847618.
##--------- Model 2 Positive Correlation (Y = TEL and X = PCOMP & TBILL) -------##
model2 <- lm(final_data$TEL~final_data$PCOMP+final_data$TBILL)
model2
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PCOMP + final_data$TBILL)
##
## Coefficients:
## (Intercept) final_data$PCOMP final_data$TBILL
## -225.5783 0.4812 2200.0279
## Coefficient Values
model2[["coefficients"]][["(Intercept)"]]
## [1] -225.5783
model2[["coefficients"]][["final_data$PCOMP"]]
## [1] 0.4811881
model2[["coefficients"]][["final_data$TBILL"]]
## [1] 2200.028
## Regression Equation
## y(hat) = -225.5783 + 0.4811881 * X1 + 2200.028 * X2
#--------------- C. Find the R squared of each model and interpret.----------#
summary(model2)
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PCOMP + final_data$TBILL)
##
## Residuals:
## Min 1Q Median 3Q Max
## -179.34 -94.14 2.81 66.84 365.13
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -225.57834 51.85112 -4.351 4.67e-05 ***
## final_data$PCOMP 0.48119 0.03732 12.894 < 2e-16 ***
## final_data$TBILL 2200.02791 473.81446 4.643 1.62e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 109.3 on 68 degrees of freedom
## Multiple R-squared: 0.8376, Adjusted R-squared: 0.8328
## F-statistic: 175.3 on 2 and 68 DF, p-value: < 2.2e-16
## The r squared is 0.8376. This means that there is 83.76 percent of variation
## in the response variable which is TEL when PCOMP and TBILL are considered.
## Fitted
fittedval= -225.5783 + 0.4811881 * (final_data$PCOMP) + 2200.028 * (final_data$TBILL)
fittedval
## [1] 604.8747 547.4421 570.8391 515.3262 462.7988 485.6985 483.8200
## [8] 434.0704 448.9952 408.9002 388.1127 395.0898 378.8699 392.7330
## [15] 393.3633 421.2480 408.7467 418.3127 432.0448 508.3853 523.3455
## [22] 588.4287 607.2800 601.3732 530.0904 526.4307 465.8126 592.3390
## [29] 639.2308 646.5331 640.5894 647.1895 635.9056 668.4147 784.0169
## [36] 850.1894 779.5610 780.4134 592.1223 662.6837 690.2603 632.3493
## [43] 688.5617 661.9857 719.7138 759.6476 740.5059 907.7140 981.5956
## [50] 902.8973 930.1470 959.0904 996.4403 1086.5563 1173.4717 1156.6179
## [57] 1170.3039 1016.5756 999.3839 1005.1391 1016.5790 1019.7452 915.9298
## [64] 684.1493 656.1221 869.1886 841.3781 1056.9115 1154.0511 1203.5272
## [71] 1254.3432
new_data<-cbind(final_data,fittedval)
new_data
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL fittedval
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 604.8747
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 547.4421
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 570.8391
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 515.3262
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 462.7988
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 485.6985
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 483.8200
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 434.0704
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 448.9952
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 408.9002
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 388.1127
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 395.0898
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 378.8699
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 392.7330
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 393.3633
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 421.2480
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 408.7467
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 418.3127
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 432.0448
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 508.3853
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 523.3455
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 588.4287
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 607.2800
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 601.3732
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 530.0904
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 526.4307
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 465.8126
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 592.3390
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 639.2308
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 646.5331
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 640.5894
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 647.1895
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 635.9056
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 668.4147
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 784.0169
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 850.1894
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 779.5610
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 780.4134
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 592.1223
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 662.6837
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 690.2603
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 632.3493
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 688.5617
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 661.9857
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 719.7138
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 759.6476
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 740.5059
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 907.7140
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 981.5956
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 902.8973
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 930.1470
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 959.0904
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 996.4403
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 1086.5563
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 1173.4717
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 1156.6179
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 1170.3039
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 1016.5756
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 999.3839
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 1005.1391
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 1016.5790
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 1019.7452
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 915.9298
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 684.1493
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 656.1221
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 869.1886
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 841.3781
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 1056.9115
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 1154.0511
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1203.5272
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 1254.3432
## Residual
resid1 <- final_data$TEL - fittedval
resid1
## [1] 365.125284 207.557899 194.160897 124.673751 72.201243 44.301501
## [7] 81.179951 -1.570371 -68.995189 -93.900240 -95.612734 -100.089781
## [13] -108.869929 -102.732958 -163.363314 -141.247985 -123.746718 -103.312737
## [19] -62.044847 -70.885339 -63.345478 -53.428705 -102.280018 -91.373205
## [25] -112.590360 -98.930695 -85.812615 -112.339029 -154.230810 28.466932
## [31] 84.410603 2.810519 54.094380 46.585312 10.983145 64.810615
## [37] 85.439045 24.586621 182.877685 147.316262 74.739732 37.650720
## [43] 86.438326 103.014345 20.286209 140.352408 149.494071 42.286018
## [49] 43.404397 -62.897289 -95.146971 -74.090435 -56.440256 23.443655
## [55] -13.471714 -41.617872 59.696140 3.424396 -94.383932 -105.139122
## [61] -16.578960 10.254823 49.070157 235.850658 68.877868 55.811411
## [67] 108.621890 -56.911508 -79.051126 -148.527247 -179.343247
resid_model1 <- cbind(final_data,new_data,resid1)
resid_model1
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL TEL PCOMP GLO PHP
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 970.0 1442.37 860.0 55505
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 755.0 1313.87 720.0 55725
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 765.0 1399.07 790.0 55330
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 640.0 1297.42 695.0 54880
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 535.0 1192.83 620.0 55025
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 530.0 1240.42 665.0 54730
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 565.0 1222.80 605.0 53480
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 432.5 1073.69 610.0 53225
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 380.0 1068.13 550.0 52533
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 315.0 1039.67 565.0 53525
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 292.5 1019.33 525.0 54510
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 295.0 1056.69 530.0 53875
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 270.0 1018.41 447.5 53280
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 290.0 1047.22 435.0 53540
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 230.0 1048.53 410.0 53125
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 280.0 1129.34 465.0 52410
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 285.0 1103.36 485.0 51840
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 315.0 1123.24 510.0 51250
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 370.0 1156.35 520.0 50420
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 437.5 1315.00 670.0 50250
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 460.0 1346.09 645.0 50830
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 535.0 1403.62 640.0 51020
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 505.0 1406.22 636.0 51225
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 510.0 1361.94 596.0 51235
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 417.5 1168.08 544.0 51750
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 427.5 1128.47 456.0 52000
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 380.0 993.35 432.0 51950
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 480.0 1265.44 500.0 51365
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 485.0 1362.89 520.0 50930
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 675.0 1410.07 532.0 53540
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 725.0 1402.29 556.0 52405
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 650.0 1402.29 548.0 50500
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 690.0 1378.84 554.0 51400
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 715.0 1446.40 528.0 49500
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 795.0 1613.49 580.0 48275
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 915.0 1687.00 580.0 48275
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 865.0 1494.50 560.0 50010
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 805.0 1404.83 520.0 49600
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 775.0 1287.85 472.0 51550
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 810.0 1434.49 640.0 46165
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 765.0 1537.52 676.0 45135
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 670.0 1417.17 600.0 44835
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 775.0 1533.99 620.0 43250
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 765.0 1478.76 560.0 42645
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 740.0 1598.73 600.0 41300
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 900.0 1681.72 500.0 41140
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 890.0 1641.94 440.0 40140
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 950.0 1989.43 420.0 40573
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 1025.0 2142.97 440.0 40410
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 840.0 1979.42 430.0 40945
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 835.0 2036.05 470.0 40250
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 885.0 2096.20 440.0 40930
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 940.0 2173.82 450.0 39665
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 1110.0 2342.81 490.0 38495
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 1160.0 2486.86 480.0 38065
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 1115.0 2419.83 490.0 38000
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 1230.0 2443.70 396.0 38007
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 1020.0 2028.21 248.0 38775
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 905.0 1965.05 252.0 39070
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 900.0 1954.15 256.0 38550
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 1000.0 1968.78 244.0 39150
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 1030.0 1975.36 268.0 39380
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 965.0 1755.04 196.0 40390
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 920.0 1259.64 170.0 43950
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 725.0 1192.25 172.0 43875
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 925.0 1607.61 232.0 42030
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 950.0 1760.13 236.0 41800
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 1000.0 2011.45 204.0 38825
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 1075.0 2181.32 200.0 40190
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1055.0 2238.42 184.0 37975
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 1075.0 2266.30 124.0 39840
## PHIVTA PHMS TBILL fittedval resid1
## 1 238316 514214 0.062 604.8747 365.125284
## 2 170921 470740 0.064 547.4421 207.557899
## 3 167573 452675 0.056 570.8391 194.160897
## 4 140652 445781 0.053 515.3262 124.673751
## 5 162076 443137 0.052 462.7988 72.201243
## 6 166045 440885 0.052 485.6985 44.301501
## 7 130874 445392 0.055 483.8200 81.179951
## 8 109803 447526 0.065 434.0704 -1.570371
## 9 123576 442370 0.073 448.9952 -68.995189
## 10 157036 444956 0.061 408.9002 -93.900240
## 11 162626 442370 0.056 388.1127 -95.612734
## 12 175728 444956 0.051 395.0898 -100.089781
## 13 191072 470056 0.052 378.8699 -108.869929
## 14 145348 434771 0.052 392.7330 -102.732958
## 15 150582 420590 0.052 393.3633 -163.363314
## 16 137201 411308 0.047 421.2480 -141.247985
## 17 164244 404530 0.047 408.7467 -123.746718
## 18 170831 404147 0.047 418.3127 -103.312737
## 19 160383 405491 0.046 432.0448 -62.044847
## 20 163782 405438 0.046 508.3853 -70.885339
## 21 166201 403614 0.046 523.3455 -63.345478
## 22 174366 389816 0.063 588.4287 -53.428705
## 23 153373 373088 0.071 607.2800 -102.280018
## 24 155294 364867 0.078 601.3732 -91.373205
## 25 166265 387989 0.088 530.0904 -112.590360
## 26 118483 353080 0.095 526.4307 -98.930695
## 27 110448 350421 0.097 465.8126 -85.812615
## 28 119117 353183 0.095 592.3390 -112.339029
## 29 155437 360712 0.095 639.2308 -154.230810
## 30 154480 369211 0.088 646.5331 28.466932
## 31 145784 377970 0.087 640.5894 84.410603
## 32 148414 379962 0.090 647.1895 2.810519
## 33 177294 389215 0.090 635.9056 54.094380
## 34 186087 367264 0.090 668.4147 46.585312
## 35 147900 361013 0.106 784.0169 10.983145
## 36 167184 382023 0.120 850.1894 64.810615
## 37 171929 386981 0.130 779.5610 85.439045
## 38 156725 358852 0.150 780.4134 24.586621
## 39 146816 339811 0.090 592.1223 182.877685
## 40 128312 342487 0.090 662.6837 147.316262
## 41 158991 341249 0.080 690.2603 74.739732
## 42 166140 339541 0.080 632.3493 37.650720
## 43 160003 341264 0.080 688.5617 86.438326
## 44 159542 342222 0.080 661.9857 103.014345
## 45 184116 347534 0.080 719.7138 20.286209
## 46 191292 337505 0.080 759.6476 140.352408
## 47 179551 326894 0.080 740.5059 149.494071
## 48 188752 343054 0.080 907.7140 42.286018
## 49 212572 394127 0.080 981.5956 43.404397
## 50 196214 334674 0.080 902.8973 -62.897289
## 51 174821 313796 0.080 930.1470 -95.146971
## 52 166677 307055 0.080 959.0904 -74.090435
## 53 170214 297737 0.080 996.4403 -56.440256
## 54 171469 298875 0.084 1086.5563 23.443655
## 55 168318 293971 0.092 1173.4717 -13.471714
## 56 169299 305896 0.099 1156.6179 -41.617872
## 57 181945 290772 0.100 1170.3039 59.696140
## 58 193485 285161 0.121 1016.5756 3.424396
## 59 175772 285161 0.127 999.3839 -94.383932
## 60 189798 262399 0.132 1005.1391 -105.139122
## 61 217109 281514 0.134 1016.5790 -16.578960
## 62 200368 253719 0.134 1019.7452 10.254823
## 63 174200 243915 0.135 915.9298 49.070157
## 64 165585 238422 0.138 684.1493 235.850658
## 65 169681 235853 0.140 656.1221 68.877868
## 66 175803 241070 0.146 869.1886 55.811411
## 67 161570 251214 0.100 841.3781 108.621890
## 68 160681 255527 0.143 1056.9115 -56.911508
## 69 176230 247455 0.150 1154.0511 -79.051126
## 70 187800 241935 0.160 1203.5272 -148.527247
## 71 173998 243119 0.177 1254.3432 -179.343247
sum(resid1)
## [1] -0.003864812
## The residual is -0.003864812
##--------- Model 3 Positive Correlation (Y = TEL and X = PHIVTA & TBILL) -------##
model3 <- lm(final_data$TEL~final_data$PHIVTA+final_data$TBILL)
model3
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PHIVTA + final_data$TBILL)
##
## Coefficients:
## (Intercept) final_data$PHIVTA final_data$TBILL
## -4.553e+02 4.499e-03 4.782e+03
## Coefficient Values
model3[["coefficients"]][["(Intercept)"]]
## [1] -455.3205
model3[["coefficients"]][["final_data$PHIVTA"]]
## [1] 0.004499324
model3[["coefficients"]][["final_data$TBILL"]]
## [1] 4781.846
## Regression Equation
## y(hat) = -455.3205 + 0.004499324 * X1 + 4781.846 * X2
#--------------- C. Find the R squared of each model and interpret.----------#
summary(model3)
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PHIVTA + final_data$TBILL)
##
## Residuals:
## Min 1Q Median 3Q Max
## -383.03 -106.56 -10.43 121.81 418.07
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.553e+02 1.533e+02 -2.971 0.0041 **
## final_data$PHIVTA 4.499e-03 9.234e-04 4.873 6.91e-06 ***
## final_data$TBILL 4.782e+03 6.556e+02 7.293 4.19e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 174.7 on 68 degrees of freedom
## Multiple R-squared: 0.5853, Adjusted R-squared: 0.5731
## F-statistic: 47.98 on 2 and 68 DF, p-value: 1.008e-13
## The r squared is 0.5853. This means that there is 58.53 percent of variation
## in the response variable which is TEL when PHIVTA and TBILL are considered.
## Fitted
fittedval= -455.3205 + 0.004499324 * (final_data$PHIVTA) + 4781.846 * (final_data$TBILL)
fittedval
## [1] 913.4149 619.7466 566.4281 430.9563 522.5679 540.4257 396.5256
## [8] 349.5388 449.7627 542.9279 544.1699 579.2109 653.0303 447.3032
## [15] 470.8527 386.7380 508.4132 538.0503 486.2595 501.5527 512.4366
## [22] 630.4649 574.2654 616.3815 713.5621 532.0483 505.4599 534.9008
## [29] 698.3163 660.5375 616.6296 642.8083 772.7488 812.3113 717.0052
## [36] 870.7160 939.8838 967.1130 635.6184 552.3629 642.5792 674.7449
## [43] 647.1325 645.0583 755.6247 787.9119 735.0853 776.4836 883.6575
## [50] 810.0575 713.8035 677.1610 693.0751 717.8492 741.9265 779.8133
## [57] 841.4936 993.8346 942.8291 1029.8459 1162.2906 1086.9674 974.0110
## [64] 949.5948 977.5877 1033.8237 749.8199 951.4394 1054.8723 1154.7479
## [71] 1173.9396
new_data<-cbind(final_data,fittedval)
new_data
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL fittedval
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 913.4149
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 619.7466
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 566.4281
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 430.9563
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 522.5679
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 540.4257
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 396.5256
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 349.5388
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 449.7627
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 542.9279
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 544.1699
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 579.2109
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 653.0303
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 447.3032
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 470.8527
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 386.7380
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 508.4132
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 538.0503
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 486.2595
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 501.5527
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 512.4366
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 630.4649
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 574.2654
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 616.3815
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 713.5621
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 532.0483
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 505.4599
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 534.9008
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 698.3163
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 660.5375
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 616.6296
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 642.8083
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 772.7488
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 812.3113
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 717.0052
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 870.7160
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 939.8838
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 967.1130
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 635.6184
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 552.3629
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 642.5792
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 674.7449
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 647.1325
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 645.0583
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 755.6247
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 787.9119
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 735.0853
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 776.4836
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 883.6575
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 810.0575
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 713.8035
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 677.1610
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 693.0751
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 717.8492
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 741.9265
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 779.8133
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 841.4936
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 993.8346
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 942.8291
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 1029.8459
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 1162.2906
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 1086.9674
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 974.0110
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 949.5948
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 977.5877
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 1033.8237
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 749.8199
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 951.4394
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 1054.8723
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1154.7479
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 1173.9396
## Residual
resid1 <- final_data$TEL - fittedval
resid1
## [1] 56.585150 135.253399 198.571903 209.043743 12.432071 -10.425746
## [7] 168.474441 82.961237 -69.762721 -227.927950 -251.669941 -284.210854
## [13] -383.030327 -157.303237 -240.852699 -106.738014 -223.413233 -223.050280
## [19] -116.259497 -64.052699 -52.436564 -95.464927 -69.265386 -106.381509
## [25] -296.062053 -104.548275 -125.459899 -54.900847 -213.316295 14.462480
## [31] 108.370448 7.191688 -82.748789 -97.311345 77.994804 44.283996
## [37] -74.883756 -162.112954 139.381608 257.637099 122.420798 -4.744869
## [43] 127.867482 119.941670 -15.624718 112.088133 154.914696 173.516416
## [49] 141.342519 29.942461 121.196499 207.838994 246.924885 392.150849
## [55] 418.073451 335.186692 388.506395 26.165430 -37.829120 -129.845869
## [61] -162.290598 -56.967415 -9.010951 -29.594813 -252.587736 -108.823673
## [67] 200.180121 48.560642 20.127731 -99.747907 -98.939619
resid_model1 <- cbind(final_data,new_data,resid1)
resid_model1
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL TEL PCOMP GLO PHP
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 970.0 1442.37 860.0 55505
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 755.0 1313.87 720.0 55725
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 765.0 1399.07 790.0 55330
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 640.0 1297.42 695.0 54880
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 535.0 1192.83 620.0 55025
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 530.0 1240.42 665.0 54730
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 565.0 1222.80 605.0 53480
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 432.5 1073.69 610.0 53225
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 380.0 1068.13 550.0 52533
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 315.0 1039.67 565.0 53525
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 292.5 1019.33 525.0 54510
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 295.0 1056.69 530.0 53875
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 270.0 1018.41 447.5 53280
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 290.0 1047.22 435.0 53540
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 230.0 1048.53 410.0 53125
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 280.0 1129.34 465.0 52410
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 285.0 1103.36 485.0 51840
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 315.0 1123.24 510.0 51250
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 370.0 1156.35 520.0 50420
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 437.5 1315.00 670.0 50250
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 460.0 1346.09 645.0 50830
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 535.0 1403.62 640.0 51020
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 505.0 1406.22 636.0 51225
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 510.0 1361.94 596.0 51235
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 417.5 1168.08 544.0 51750
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 427.5 1128.47 456.0 52000
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 380.0 993.35 432.0 51950
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 480.0 1265.44 500.0 51365
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 485.0 1362.89 520.0 50930
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 675.0 1410.07 532.0 53540
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 725.0 1402.29 556.0 52405
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 650.0 1402.29 548.0 50500
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 690.0 1378.84 554.0 51400
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 715.0 1446.40 528.0 49500
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 795.0 1613.49 580.0 48275
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 915.0 1687.00 580.0 48275
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 865.0 1494.50 560.0 50010
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 805.0 1404.83 520.0 49600
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 775.0 1287.85 472.0 51550
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 810.0 1434.49 640.0 46165
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 765.0 1537.52 676.0 45135
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 670.0 1417.17 600.0 44835
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 775.0 1533.99 620.0 43250
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 765.0 1478.76 560.0 42645
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 740.0 1598.73 600.0 41300
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 900.0 1681.72 500.0 41140
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 890.0 1641.94 440.0 40140
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 950.0 1989.43 420.0 40573
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 1025.0 2142.97 440.0 40410
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 840.0 1979.42 430.0 40945
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 835.0 2036.05 470.0 40250
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 885.0 2096.20 440.0 40930
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 940.0 2173.82 450.0 39665
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 1110.0 2342.81 490.0 38495
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 1160.0 2486.86 480.0 38065
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 1115.0 2419.83 490.0 38000
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 1230.0 2443.70 396.0 38007
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 1020.0 2028.21 248.0 38775
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 905.0 1965.05 252.0 39070
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 900.0 1954.15 256.0 38550
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 1000.0 1968.78 244.0 39150
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 1030.0 1975.36 268.0 39380
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 965.0 1755.04 196.0 40390
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 920.0 1259.64 170.0 43950
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 725.0 1192.25 172.0 43875
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 925.0 1607.61 232.0 42030
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 950.0 1760.13 236.0 41800
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 1000.0 2011.45 204.0 38825
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 1075.0 2181.32 200.0 40190
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1055.0 2238.42 184.0 37975
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 1075.0 2266.30 124.0 39840
## PHIVTA PHMS TBILL fittedval resid1
## 1 238316 514214 0.062 913.4149 56.585150
## 2 170921 470740 0.064 619.7466 135.253399
## 3 167573 452675 0.056 566.4281 198.571903
## 4 140652 445781 0.053 430.9563 209.043743
## 5 162076 443137 0.052 522.5679 12.432071
## 6 166045 440885 0.052 540.4257 -10.425746
## 7 130874 445392 0.055 396.5256 168.474441
## 8 109803 447526 0.065 349.5388 82.961237
## 9 123576 442370 0.073 449.7627 -69.762721
## 10 157036 444956 0.061 542.9279 -227.927950
## 11 162626 442370 0.056 544.1699 -251.669941
## 12 175728 444956 0.051 579.2109 -284.210854
## 13 191072 470056 0.052 653.0303 -383.030327
## 14 145348 434771 0.052 447.3032 -157.303237
## 15 150582 420590 0.052 470.8527 -240.852699
## 16 137201 411308 0.047 386.7380 -106.738014
## 17 164244 404530 0.047 508.4132 -223.413233
## 18 170831 404147 0.047 538.0503 -223.050280
## 19 160383 405491 0.046 486.2595 -116.259497
## 20 163782 405438 0.046 501.5527 -64.052699
## 21 166201 403614 0.046 512.4366 -52.436564
## 22 174366 389816 0.063 630.4649 -95.464927
## 23 153373 373088 0.071 574.2654 -69.265386
## 24 155294 364867 0.078 616.3815 -106.381509
## 25 166265 387989 0.088 713.5621 -296.062053
## 26 118483 353080 0.095 532.0483 -104.548275
## 27 110448 350421 0.097 505.4599 -125.459899
## 28 119117 353183 0.095 534.9008 -54.900847
## 29 155437 360712 0.095 698.3163 -213.316295
## 30 154480 369211 0.088 660.5375 14.462480
## 31 145784 377970 0.087 616.6296 108.370448
## 32 148414 379962 0.090 642.8083 7.191688
## 33 177294 389215 0.090 772.7488 -82.748789
## 34 186087 367264 0.090 812.3113 -97.311345
## 35 147900 361013 0.106 717.0052 77.994804
## 36 167184 382023 0.120 870.7160 44.283996
## 37 171929 386981 0.130 939.8838 -74.883756
## 38 156725 358852 0.150 967.1130 -162.112954
## 39 146816 339811 0.090 635.6184 139.381608
## 40 128312 342487 0.090 552.3629 257.637099
## 41 158991 341249 0.080 642.5792 122.420798
## 42 166140 339541 0.080 674.7449 -4.744869
## 43 160003 341264 0.080 647.1325 127.867482
## 44 159542 342222 0.080 645.0583 119.941670
## 45 184116 347534 0.080 755.6247 -15.624718
## 46 191292 337505 0.080 787.9119 112.088133
## 47 179551 326894 0.080 735.0853 154.914696
## 48 188752 343054 0.080 776.4836 173.516416
## 49 212572 394127 0.080 883.6575 141.342519
## 50 196214 334674 0.080 810.0575 29.942461
## 51 174821 313796 0.080 713.8035 121.196499
## 52 166677 307055 0.080 677.1610 207.838994
## 53 170214 297737 0.080 693.0751 246.924885
## 54 171469 298875 0.084 717.8492 392.150849
## 55 168318 293971 0.092 741.9265 418.073451
## 56 169299 305896 0.099 779.8133 335.186692
## 57 181945 290772 0.100 841.4936 388.506395
## 58 193485 285161 0.121 993.8346 26.165430
## 59 175772 285161 0.127 942.8291 -37.829120
## 60 189798 262399 0.132 1029.8459 -129.845869
## 61 217109 281514 0.134 1162.2906 -162.290598
## 62 200368 253719 0.134 1086.9674 -56.967415
## 63 174200 243915 0.135 974.0110 -9.010951
## 64 165585 238422 0.138 949.5948 -29.594813
## 65 169681 235853 0.140 977.5877 -252.587736
## 66 175803 241070 0.146 1033.8237 -108.823673
## 67 161570 251214 0.100 749.8199 200.180121
## 68 160681 255527 0.143 951.4394 48.560642
## 69 176230 247455 0.150 1054.8723 20.127731
## 70 187800 241935 0.160 1154.7479 -99.747907
## 71 173998 243119 0.177 1173.9396 -98.939619
sum(resid1)
## [1] -0.007151976
## The residual is -0.007151976.
##--------- Model 4 Negative Correlation (Y = TEL and X = PHP & PHMS) -------##
model4 <- lm(final_data$TEL~final_data$PHP+final_data$PHMS)
model4
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PHP + final_data$PHMS)
##
## Coefficients:
## (Intercept) final_data$PHP final_data$PHMS
## 2.354e+03 -3.445e-02 -5.507e-05
## Coefficient Values
model4[["coefficients"]][["(Intercept)"]]
## [1] 2354.435
model4[["coefficients"]][["final_data$PHP"]]
## [1] -0.03445317
model4[["coefficients"]][["final_data$PHMS"]]
## [1] -5.507376e-05
## Regression Equation
## y(hat) = 2.354e+03 - 3.445e-02 * X1 -5.507e-05 * X2
#--------------- C. Find the R squared of each model and interpret.----------#
summary(model4)
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PHP + final_data$PHMS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -270.95 -115.67 -15.60 95.61 556.21
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.354e+03 1.614e+02 14.590 < 2e-16 ***
## final_data$PHP -3.445e-02 6.188e-03 -5.568 4.75e-07 ***
## final_data$PHMS -5.507e-05 5.449e-04 -0.101 0.92
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 163.4 on 68 degrees of freedom
## Multiple R-squared: 0.6375, Adjusted R-squared: 0.6268
## F-statistic: 59.79 on 2 and 68 DF, p-value: 1.041e-15
## The r squared is 0.6375. This means that there is 63.75 percent of variation
## in the response variable which is TEL when PHP and PHMS are considered.
## Fitted
fittedval= 2354.435 - 0.03445317 * (final_data$PHP) - 5.507376e-05 * (final_data$PHMS)
fittedval
## [1] 413.7921 408.6067 423.2106 439.0942 434.2441 444.5318 487.3501
## [8] 496.0181 520.1436 485.8237 452.0297 473.7651 492.8824 485.8678
## [15] 500.9469 526.0921 546.1037 566.4521 594.9743 600.8342 580.9518
## [22] 575.1656 569.0240 569.1322 550.1154 543.4247 545.2938 565.2968
## [29] 579.8693 489.4784 528.1004 593.6240 562.1065 628.7765 671.3259
## [36] 670.1688 610.1195 625.7944 559.6594 745.0424 780.5973 791.0273
## [43] 845.5407 866.3321 912.3791 918.4439 953.4815 937.6733 940.4763
## [50] 925.3182 950.4130 927.3561 971.4525 1011.7001 1026.7850 1028.3677
## [57] 1028.9595 1002.8084 992.6448 1011.8140 990.0894 983.6959 949.4381
## [64] 827.0874 829.8129 893.0916 900.4572 1002.7178 956.1338 1032.7516
## [71] 968.4312
new_data<-cbind(final_data,fittedval)
new_data
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL fittedval
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 413.7921
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 408.6067
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 423.2106
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 439.0942
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 434.2441
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 444.5318
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 487.3501
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 496.0181
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 520.1436
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 485.8237
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 452.0297
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 473.7651
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 492.8824
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 485.8678
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 500.9469
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 526.0921
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 546.1037
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 566.4521
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 594.9743
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 600.8342
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 580.9518
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 575.1656
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 569.0240
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 569.1322
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 550.1154
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 543.4247
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 545.2938
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 565.2968
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 579.8693
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 489.4784
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 528.1004
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 593.6240
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 562.1065
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 628.7765
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 671.3259
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 670.1688
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 610.1195
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 625.7944
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 559.6594
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 745.0424
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 780.5973
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 791.0273
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 845.5407
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 866.3321
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 912.3791
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 918.4439
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 953.4815
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 937.6733
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 940.4763
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 925.3182
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 950.4130
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 927.3561
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 971.4525
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 1011.7001
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 1026.7850
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 1028.3677
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 1028.9595
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 1002.8084
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 992.6448
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 1011.8140
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 990.0894
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 983.6959
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 949.4381
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 827.0874
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 829.8129
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 893.0916
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 900.4572
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 1002.7178
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 956.1338
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1032.7516
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 968.4312
## Residual
resid1 <- final_data$TEL - fittedval
resid1
## [1] 556.207899 346.393320 341.789410 200.905805 100.755900 85.468189
## [7] 77.649944 -63.518087 -140.143641 -170.823676 -159.529724 -178.765066
## [13] -222.882351 -195.867804 -270.946871 -246.092082 -261.103679 -251.452143
## [19] -224.974255 -163.334212 -120.951828 -40.165634 -64.024008 -59.132237
## [25] -132.615439 -115.924717 -165.293816 -85.296807 -94.869286 185.521560
## [31] 196.899603 56.376021 127.893471 86.223524 123.674125 244.831225
## [37] 254.880530 179.205561 215.340583 64.957640 -15.597307 -121.027324
## [43] -70.540706 -101.332113 -172.379075 -18.443917 -63.481474 12.326740
## [49] 84.523656 -85.318199 -115.412982 -42.356079 -31.452516 98.299949
## [55] 133.215004 86.632303 201.040540 17.191555 -87.644760 -111.813997
## [61] 9.910640 46.304094 15.561852 92.912618 -104.812855 31.908366
## [67] 49.542806 -2.717842 118.866180 22.248401 106.568770
resid_model1 <- cbind(final_data,new_data,resid1)
resid_model1
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL TEL PCOMP GLO PHP
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 970.0 1442.37 860.0 55505
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 755.0 1313.87 720.0 55725
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 765.0 1399.07 790.0 55330
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 640.0 1297.42 695.0 54880
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 535.0 1192.83 620.0 55025
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 530.0 1240.42 665.0 54730
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 565.0 1222.80 605.0 53480
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 432.5 1073.69 610.0 53225
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 380.0 1068.13 550.0 52533
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 315.0 1039.67 565.0 53525
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 292.5 1019.33 525.0 54510
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 295.0 1056.69 530.0 53875
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 270.0 1018.41 447.5 53280
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 290.0 1047.22 435.0 53540
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 230.0 1048.53 410.0 53125
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 280.0 1129.34 465.0 52410
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 285.0 1103.36 485.0 51840
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 315.0 1123.24 510.0 51250
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 370.0 1156.35 520.0 50420
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 437.5 1315.00 670.0 50250
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 460.0 1346.09 645.0 50830
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 535.0 1403.62 640.0 51020
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 505.0 1406.22 636.0 51225
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 510.0 1361.94 596.0 51235
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 417.5 1168.08 544.0 51750
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 427.5 1128.47 456.0 52000
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 380.0 993.35 432.0 51950
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 480.0 1265.44 500.0 51365
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 485.0 1362.89 520.0 50930
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 675.0 1410.07 532.0 53540
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 725.0 1402.29 556.0 52405
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 650.0 1402.29 548.0 50500
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 690.0 1378.84 554.0 51400
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 715.0 1446.40 528.0 49500
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 795.0 1613.49 580.0 48275
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 915.0 1687.00 580.0 48275
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 865.0 1494.50 560.0 50010
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 805.0 1404.83 520.0 49600
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 775.0 1287.85 472.0 51550
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 810.0 1434.49 640.0 46165
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 765.0 1537.52 676.0 45135
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 670.0 1417.17 600.0 44835
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 775.0 1533.99 620.0 43250
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 765.0 1478.76 560.0 42645
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 740.0 1598.73 600.0 41300
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 900.0 1681.72 500.0 41140
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 890.0 1641.94 440.0 40140
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 950.0 1989.43 420.0 40573
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 1025.0 2142.97 440.0 40410
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 840.0 1979.42 430.0 40945
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 835.0 2036.05 470.0 40250
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 885.0 2096.20 440.0 40930
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 940.0 2173.82 450.0 39665
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 1110.0 2342.81 490.0 38495
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 1160.0 2486.86 480.0 38065
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 1115.0 2419.83 490.0 38000
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 1230.0 2443.70 396.0 38007
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 1020.0 2028.21 248.0 38775
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 905.0 1965.05 252.0 39070
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 900.0 1954.15 256.0 38550
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 1000.0 1968.78 244.0 39150
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 1030.0 1975.36 268.0 39380
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 965.0 1755.04 196.0 40390
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 920.0 1259.64 170.0 43950
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 725.0 1192.25 172.0 43875
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 925.0 1607.61 232.0 42030
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 950.0 1760.13 236.0 41800
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 1000.0 2011.45 204.0 38825
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 1075.0 2181.32 200.0 40190
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1055.0 2238.42 184.0 37975
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 1075.0 2266.30 124.0 39840
## PHIVTA PHMS TBILL fittedval resid1
## 1 238316 514214 0.062 413.7921 556.207899
## 2 170921 470740 0.064 408.6067 346.393320
## 3 167573 452675 0.056 423.2106 341.789410
## 4 140652 445781 0.053 439.0942 200.905805
## 5 162076 443137 0.052 434.2441 100.755900
## 6 166045 440885 0.052 444.5318 85.468189
## 7 130874 445392 0.055 487.3501 77.649944
## 8 109803 447526 0.065 496.0181 -63.518087
## 9 123576 442370 0.073 520.1436 -140.143641
## 10 157036 444956 0.061 485.8237 -170.823676
## 11 162626 442370 0.056 452.0297 -159.529724
## 12 175728 444956 0.051 473.7651 -178.765066
## 13 191072 470056 0.052 492.8824 -222.882351
## 14 145348 434771 0.052 485.8678 -195.867804
## 15 150582 420590 0.052 500.9469 -270.946871
## 16 137201 411308 0.047 526.0921 -246.092082
## 17 164244 404530 0.047 546.1037 -261.103679
## 18 170831 404147 0.047 566.4521 -251.452143
## 19 160383 405491 0.046 594.9743 -224.974255
## 20 163782 405438 0.046 600.8342 -163.334212
## 21 166201 403614 0.046 580.9518 -120.951828
## 22 174366 389816 0.063 575.1656 -40.165634
## 23 153373 373088 0.071 569.0240 -64.024008
## 24 155294 364867 0.078 569.1322 -59.132237
## 25 166265 387989 0.088 550.1154 -132.615439
## 26 118483 353080 0.095 543.4247 -115.924717
## 27 110448 350421 0.097 545.2938 -165.293816
## 28 119117 353183 0.095 565.2968 -85.296807
## 29 155437 360712 0.095 579.8693 -94.869286
## 30 154480 369211 0.088 489.4784 185.521560
## 31 145784 377970 0.087 528.1004 196.899603
## 32 148414 379962 0.090 593.6240 56.376021
## 33 177294 389215 0.090 562.1065 127.893471
## 34 186087 367264 0.090 628.7765 86.223524
## 35 147900 361013 0.106 671.3259 123.674125
## 36 167184 382023 0.120 670.1688 244.831225
## 37 171929 386981 0.130 610.1195 254.880530
## 38 156725 358852 0.150 625.7944 179.205561
## 39 146816 339811 0.090 559.6594 215.340583
## 40 128312 342487 0.090 745.0424 64.957640
## 41 158991 341249 0.080 780.5973 -15.597307
## 42 166140 339541 0.080 791.0273 -121.027324
## 43 160003 341264 0.080 845.5407 -70.540706
## 44 159542 342222 0.080 866.3321 -101.332113
## 45 184116 347534 0.080 912.3791 -172.379075
## 46 191292 337505 0.080 918.4439 -18.443917
## 47 179551 326894 0.080 953.4815 -63.481474
## 48 188752 343054 0.080 937.6733 12.326740
## 49 212572 394127 0.080 940.4763 84.523656
## 50 196214 334674 0.080 925.3182 -85.318199
## 51 174821 313796 0.080 950.4130 -115.412982
## 52 166677 307055 0.080 927.3561 -42.356079
## 53 170214 297737 0.080 971.4525 -31.452516
## 54 171469 298875 0.084 1011.7001 98.299949
## 55 168318 293971 0.092 1026.7850 133.215004
## 56 169299 305896 0.099 1028.3677 86.632303
## 57 181945 290772 0.100 1028.9595 201.040540
## 58 193485 285161 0.121 1002.8084 17.191555
## 59 175772 285161 0.127 992.6448 -87.644760
## 60 189798 262399 0.132 1011.8140 -111.813997
## 61 217109 281514 0.134 990.0894 9.910640
## 62 200368 253719 0.134 983.6959 46.304094
## 63 174200 243915 0.135 949.4381 15.561852
## 64 165585 238422 0.138 827.0874 92.912618
## 65 169681 235853 0.140 829.8129 -104.812855
## 66 175803 241070 0.146 893.0916 31.908366
## 67 161570 251214 0.100 900.4572 49.542806
## 68 160681 255527 0.143 1002.7178 -2.717842
## 69 176230 247455 0.150 956.1338 118.866180
## 70 187800 241935 0.160 1032.7516 22.248401
## 71 173998 243119 0.177 968.4312 106.568770
sum(resid1)
## [1] -0.01072414
## The residual is -0.01072414.
##--------- Model 5 (Y = TEL and X = PHMS & GLo) -------##
model5 <- lm(final_data$TEL~final_data$PHMS+final_data$GLO)
model5
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PHMS + final_data$GLO)
##
## Coefficients:
## (Intercept) final_data$PHMS final_data$GLO
## 1786.98288 -0.00396 0.70331
## Coefficient Values
model5[["coefficients"]][["(Intercept)"]]
## [1] 1786.983
model5[["coefficients"]][["final_data$PHMS"]]
## [1] -0.003960381
model5[["coefficients"]][["final_data$GLO"]]
## [1] 0.7033058
## Regression Equation
## y(hat) = 1786.98288 - 0.00396 * X1 + 0.70331 * X2
#--------------- C. Find the R squared of each model and interpret.----------#
summary(model5)
##
## Call:
## lm(formula = final_data$TEL ~ final_data$PHMS + final_data$GLO)
##
## Residuals:
## Min 1Q Median 3Q Max
## -323.01 -128.85 1.84 97.39 614.66
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.787e+03 1.232e+02 14.500 < 2e-16 ***
## final_data$PHMS -3.960e-03 5.367e-04 -7.378 2.94e-10 ***
## final_data$GLO 7.033e-01 2.320e-01 3.032 0.00344 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 185 on 68 degrees of freedom
## Multiple R-squared: 0.535, Adjusted R-squared: 0.5214
## F-statistic: 39.12 on 2 and 68 DF, p-value: 4.922e-12
## The r squared is 0.535. This means that there is 53.5 percent of variation
## in the response variable which is TEL when PHMS and GLO are considered.
## Fitted
fittedval= 1786.983 - 0.003960381 * (final_data$PHMS) + 0.7033058 * (final_data$GLO)
fittedval
## [1] 355.3426 429.0534 549.8291 510.3179 468.0412 508.6088 448.5610 443.6261
## [9] 421.8474 422.1555 404.2648 397.5398 240.1115 371.0622 409.6417 485.0838
## [17] 525.9934 545.0929 546.8032 652.5089 642.1500 693.2788 756.7149 761.1409
## [25] 632.9971 709.3591 703.0104 739.8967 724.1451 698.9255 681.1158 667.6003
## [33] 635.1747 703.8231 765.1513 681.9437 648.2420 731.5114 773.1623 880.7197
## [41] 910.9417 864.2548 871.4971 825.5047 832.5994 801.9875 801.8128 723.7469
## [49] 535.5445 763.9679 874.7850 880.3828 924.3187 947.9440 960.3326 920.1381
## [57] 913.9242 832.0566 834.8699 927.8293 843.6869 970.6450 958.8346 962.3030
## [65] 973.8839 995.4209 958.0600 918.4731 947.6281 958.2365 911.3491
new_data<-cbind(final_data,fittedval)
new_data
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL fittedval
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 355.3426
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 429.0534
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 549.8291
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 510.3179
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 468.0412
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 508.6088
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 448.5610
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 443.6261
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 421.8474
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 422.1555
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 404.2648
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 397.5398
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 240.1115
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 371.0622
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 409.6417
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 485.0838
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 525.9934
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 545.0929
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 546.8032
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 652.5089
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 642.1500
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 693.2788
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 756.7149
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 761.1409
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 632.9971
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 709.3591
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 703.0104
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 739.8967
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 724.1451
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 698.9255
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 681.1158
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 667.6003
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 635.1747
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 703.8231
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 765.1513
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 681.9437
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 648.2420
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 731.5114
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 773.1623
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 880.7197
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 910.9417
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 864.2548
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 871.4971
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 825.5047
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 832.5994
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 801.9875
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 801.8128
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 723.7469
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 535.5445
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 763.9679
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 874.7850
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 880.3828
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 924.3187
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 947.9440
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 960.3326
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 920.1381
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 913.9242
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 832.0566
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 834.8699
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 927.8293
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 843.6869
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 970.6450
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 958.8346
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 962.3030
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 973.8839
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 995.4209
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 958.0600
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 918.4731
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 947.6281
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 958.2365
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 911.3491
## Residual
resid1 <- final_data$TEL - fittedval
resid1
## [1] 614.657368 325.946576 215.170887 129.682072 66.958759 21.391220
## [7] 116.439005 -11.126071 -41.847447 -107.155489 -111.764802 -102.539786
## [13] 29.888506 -81.062215 -179.641733 -205.083809 -240.993387 -230.092858
## [19] -176.803164 -215.008934 -182.150024 -158.278832 -251.714862 -251.140922
## [25] -215.497091 -281.859121 -323.010435 -259.896657 -239.145065 -23.925456
## [31] 43.884182 -17.600293 54.825278 11.176905 29.848662 233.056267
## [37] 216.757952 73.488627 1.837690 -70.719704 -145.941665 -194.254755
## [43] -96.497134 -60.504741 -92.599430 98.012489 88.187235 226.253108
## [49] 489.455530 76.032057 -39.785010 4.617236 15.681348 162.056029
## [55] 199.667379 194.861864 316.075807 187.943368 70.130145 -27.829271
## [61] 156.313082 59.354953 6.165395 -42.303027 -248.883858 -70.420898
## [67] -8.060016 81.526893 127.371920 96.763510 163.650949
resid_model1 <- cbind(final_data,new_data,resid1)
resid_model1
## TEL PCOMP GLO PHP PHIVTA PHMS TBILL TEL PCOMP GLO PHP
## 1 970.0 1442.37 860.0 55505 238316 514214 0.062 970.0 1442.37 860.0 55505
## 2 755.0 1313.87 720.0 55725 170921 470740 0.064 755.0 1313.87 720.0 55725
## 3 765.0 1399.07 790.0 55330 167573 452675 0.056 765.0 1399.07 790.0 55330
## 4 640.0 1297.42 695.0 54880 140652 445781 0.053 640.0 1297.42 695.0 54880
## 5 535.0 1192.83 620.0 55025 162076 443137 0.052 535.0 1192.83 620.0 55025
## 6 530.0 1240.42 665.0 54730 166045 440885 0.052 530.0 1240.42 665.0 54730
## 7 565.0 1222.80 605.0 53480 130874 445392 0.055 565.0 1222.80 605.0 53480
## 8 432.5 1073.69 610.0 53225 109803 447526 0.065 432.5 1073.69 610.0 53225
## 9 380.0 1068.13 550.0 52533 123576 442370 0.073 380.0 1068.13 550.0 52533
## 10 315.0 1039.67 565.0 53525 157036 444956 0.061 315.0 1039.67 565.0 53525
## 11 292.5 1019.33 525.0 54510 162626 442370 0.056 292.5 1019.33 525.0 54510
## 12 295.0 1056.69 530.0 53875 175728 444956 0.051 295.0 1056.69 530.0 53875
## 13 270.0 1018.41 447.5 53280 191072 470056 0.052 270.0 1018.41 447.5 53280
## 14 290.0 1047.22 435.0 53540 145348 434771 0.052 290.0 1047.22 435.0 53540
## 15 230.0 1048.53 410.0 53125 150582 420590 0.052 230.0 1048.53 410.0 53125
## 16 280.0 1129.34 465.0 52410 137201 411308 0.047 280.0 1129.34 465.0 52410
## 17 285.0 1103.36 485.0 51840 164244 404530 0.047 285.0 1103.36 485.0 51840
## 18 315.0 1123.24 510.0 51250 170831 404147 0.047 315.0 1123.24 510.0 51250
## 19 370.0 1156.35 520.0 50420 160383 405491 0.046 370.0 1156.35 520.0 50420
## 20 437.5 1315.00 670.0 50250 163782 405438 0.046 437.5 1315.00 670.0 50250
## 21 460.0 1346.09 645.0 50830 166201 403614 0.046 460.0 1346.09 645.0 50830
## 22 535.0 1403.62 640.0 51020 174366 389816 0.063 535.0 1403.62 640.0 51020
## 23 505.0 1406.22 636.0 51225 153373 373088 0.071 505.0 1406.22 636.0 51225
## 24 510.0 1361.94 596.0 51235 155294 364867 0.078 510.0 1361.94 596.0 51235
## 25 417.5 1168.08 544.0 51750 166265 387989 0.088 417.5 1168.08 544.0 51750
## 26 427.5 1128.47 456.0 52000 118483 353080 0.095 427.5 1128.47 456.0 52000
## 27 380.0 993.35 432.0 51950 110448 350421 0.097 380.0 993.35 432.0 51950
## 28 480.0 1265.44 500.0 51365 119117 353183 0.095 480.0 1265.44 500.0 51365
## 29 485.0 1362.89 520.0 50930 155437 360712 0.095 485.0 1362.89 520.0 50930
## 30 675.0 1410.07 532.0 53540 154480 369211 0.088 675.0 1410.07 532.0 53540
## 31 725.0 1402.29 556.0 52405 145784 377970 0.087 725.0 1402.29 556.0 52405
## 32 650.0 1402.29 548.0 50500 148414 379962 0.090 650.0 1402.29 548.0 50500
## 33 690.0 1378.84 554.0 51400 177294 389215 0.090 690.0 1378.84 554.0 51400
## 34 715.0 1446.40 528.0 49500 186087 367264 0.090 715.0 1446.40 528.0 49500
## 35 795.0 1613.49 580.0 48275 147900 361013 0.106 795.0 1613.49 580.0 48275
## 36 915.0 1687.00 580.0 48275 167184 382023 0.120 915.0 1687.00 580.0 48275
## 37 865.0 1494.50 560.0 50010 171929 386981 0.130 865.0 1494.50 560.0 50010
## 38 805.0 1404.83 520.0 49600 156725 358852 0.150 805.0 1404.83 520.0 49600
## 39 775.0 1287.85 472.0 51550 146816 339811 0.090 775.0 1287.85 472.0 51550
## 40 810.0 1434.49 640.0 46165 128312 342487 0.090 810.0 1434.49 640.0 46165
## 41 765.0 1537.52 676.0 45135 158991 341249 0.080 765.0 1537.52 676.0 45135
## 42 670.0 1417.17 600.0 44835 166140 339541 0.080 670.0 1417.17 600.0 44835
## 43 775.0 1533.99 620.0 43250 160003 341264 0.080 775.0 1533.99 620.0 43250
## 44 765.0 1478.76 560.0 42645 159542 342222 0.080 765.0 1478.76 560.0 42645
## 45 740.0 1598.73 600.0 41300 184116 347534 0.080 740.0 1598.73 600.0 41300
## 46 900.0 1681.72 500.0 41140 191292 337505 0.080 900.0 1681.72 500.0 41140
## 47 890.0 1641.94 440.0 40140 179551 326894 0.080 890.0 1641.94 440.0 40140
## 48 950.0 1989.43 420.0 40573 188752 343054 0.080 950.0 1989.43 420.0 40573
## 49 1025.0 2142.97 440.0 40410 212572 394127 0.080 1025.0 2142.97 440.0 40410
## 50 840.0 1979.42 430.0 40945 196214 334674 0.080 840.0 1979.42 430.0 40945
## 51 835.0 2036.05 470.0 40250 174821 313796 0.080 835.0 2036.05 470.0 40250
## 52 885.0 2096.20 440.0 40930 166677 307055 0.080 885.0 2096.20 440.0 40930
## 53 940.0 2173.82 450.0 39665 170214 297737 0.080 940.0 2173.82 450.0 39665
## 54 1110.0 2342.81 490.0 38495 171469 298875 0.084 1110.0 2342.81 490.0 38495
## 55 1160.0 2486.86 480.0 38065 168318 293971 0.092 1160.0 2486.86 480.0 38065
## 56 1115.0 2419.83 490.0 38000 169299 305896 0.099 1115.0 2419.83 490.0 38000
## 57 1230.0 2443.70 396.0 38007 181945 290772 0.100 1230.0 2443.70 396.0 38007
## 58 1020.0 2028.21 248.0 38775 193485 285161 0.121 1020.0 2028.21 248.0 38775
## 59 905.0 1965.05 252.0 39070 175772 285161 0.127 905.0 1965.05 252.0 39070
## 60 900.0 1954.15 256.0 38550 189798 262399 0.132 900.0 1954.15 256.0 38550
## 61 1000.0 1968.78 244.0 39150 217109 281514 0.134 1000.0 1968.78 244.0 39150
## 62 1030.0 1975.36 268.0 39380 200368 253719 0.134 1030.0 1975.36 268.0 39380
## 63 965.0 1755.04 196.0 40390 174200 243915 0.135 965.0 1755.04 196.0 40390
## 64 920.0 1259.64 170.0 43950 165585 238422 0.138 920.0 1259.64 170.0 43950
## 65 725.0 1192.25 172.0 43875 169681 235853 0.140 725.0 1192.25 172.0 43875
## 66 925.0 1607.61 232.0 42030 175803 241070 0.146 925.0 1607.61 232.0 42030
## 67 950.0 1760.13 236.0 41800 161570 251214 0.100 950.0 1760.13 236.0 41800
## 68 1000.0 2011.45 204.0 38825 160681 255527 0.143 1000.0 2011.45 204.0 38825
## 69 1075.0 2181.32 200.0 40190 176230 247455 0.150 1075.0 2181.32 200.0 40190
## 70 1055.0 2238.42 184.0 37975 187800 241935 0.160 1055.0 2238.42 184.0 37975
## 71 1075.0 2266.30 124.0 39840 173998 243119 0.177 1075.0 2266.30 124.0 39840
## PHIVTA PHMS TBILL fittedval resid1
## 1 238316 514214 0.062 355.3426 614.657368
## 2 170921 470740 0.064 429.0534 325.946576
## 3 167573 452675 0.056 549.8291 215.170887
## 4 140652 445781 0.053 510.3179 129.682072
## 5 162076 443137 0.052 468.0412 66.958759
## 6 166045 440885 0.052 508.6088 21.391220
## 7 130874 445392 0.055 448.5610 116.439005
## 8 109803 447526 0.065 443.6261 -11.126071
## 9 123576 442370 0.073 421.8474 -41.847447
## 10 157036 444956 0.061 422.1555 -107.155489
## 11 162626 442370 0.056 404.2648 -111.764802
## 12 175728 444956 0.051 397.5398 -102.539786
## 13 191072 470056 0.052 240.1115 29.888506
## 14 145348 434771 0.052 371.0622 -81.062215
## 15 150582 420590 0.052 409.6417 -179.641733
## 16 137201 411308 0.047 485.0838 -205.083809
## 17 164244 404530 0.047 525.9934 -240.993387
## 18 170831 404147 0.047 545.0929 -230.092858
## 19 160383 405491 0.046 546.8032 -176.803164
## 20 163782 405438 0.046 652.5089 -215.008934
## 21 166201 403614 0.046 642.1500 -182.150024
## 22 174366 389816 0.063 693.2788 -158.278832
## 23 153373 373088 0.071 756.7149 -251.714862
## 24 155294 364867 0.078 761.1409 -251.140922
## 25 166265 387989 0.088 632.9971 -215.497091
## 26 118483 353080 0.095 709.3591 -281.859121
## 27 110448 350421 0.097 703.0104 -323.010435
## 28 119117 353183 0.095 739.8967 -259.896657
## 29 155437 360712 0.095 724.1451 -239.145065
## 30 154480 369211 0.088 698.9255 -23.925456
## 31 145784 377970 0.087 681.1158 43.884182
## 32 148414 379962 0.090 667.6003 -17.600293
## 33 177294 389215 0.090 635.1747 54.825278
## 34 186087 367264 0.090 703.8231 11.176905
## 35 147900 361013 0.106 765.1513 29.848662
## 36 167184 382023 0.120 681.9437 233.056267
## 37 171929 386981 0.130 648.2420 216.757952
## 38 156725 358852 0.150 731.5114 73.488627
## 39 146816 339811 0.090 773.1623 1.837690
## 40 128312 342487 0.090 880.7197 -70.719704
## 41 158991 341249 0.080 910.9417 -145.941665
## 42 166140 339541 0.080 864.2548 -194.254755
## 43 160003 341264 0.080 871.4971 -96.497134
## 44 159542 342222 0.080 825.5047 -60.504741
## 45 184116 347534 0.080 832.5994 -92.599430
## 46 191292 337505 0.080 801.9875 98.012489
## 47 179551 326894 0.080 801.8128 88.187235
## 48 188752 343054 0.080 723.7469 226.253108
## 49 212572 394127 0.080 535.5445 489.455530
## 50 196214 334674 0.080 763.9679 76.032057
## 51 174821 313796 0.080 874.7850 -39.785010
## 52 166677 307055 0.080 880.3828 4.617236
## 53 170214 297737 0.080 924.3187 15.681348
## 54 171469 298875 0.084 947.9440 162.056029
## 55 168318 293971 0.092 960.3326 199.667379
## 56 169299 305896 0.099 920.1381 194.861864
## 57 181945 290772 0.100 913.9242 316.075807
## 58 193485 285161 0.121 832.0566 187.943368
## 59 175772 285161 0.127 834.8699 70.130145
## 60 189798 262399 0.132 927.8293 -27.829271
## 61 217109 281514 0.134 843.6869 156.313082
## 62 200368 253719 0.134 970.6450 59.354953
## 63 174200 243915 0.135 958.8346 6.165395
## 64 165585 238422 0.138 962.3030 -42.303027
## 65 169681 235853 0.140 973.8839 -248.883858
## 66 175803 241070 0.146 995.4209 -70.420898
## 67 161570 251214 0.100 958.0600 -8.060016
## 68 160681 255527 0.143 918.4731 81.526893
## 69 176230 247455 0.150 947.6281 127.371920
## 70 187800 241935 0.160 958.2365 96.763510
## 71 173998 243119 0.177 911.3491 163.650949
sum(resid1)
## [1] -0.007712218
## The residual is -0.007712218.
#------------ d. What is your final model? Why, discuss. -----------#
## Of all the model I created, my final model will be the model 1
## Which includes the TEL as the response variable and "The Philippine
# Composite Index (PCOMP) and "Philippine Visitor Travel Arrivals (PHIVTA)"
## as the predictor variable. Based on the correlation matrix, both of the
## independent variables are positively correlated with the dependents variable.
## This means that when the PCOMP and PHIVTA are increasing the TEL is also
## increasing. This model can be used to predict the value of the y.