Rregression
Mohlatlego Nakeng
01/07/2020
#Libraries
library("readxl")## Warning: package 'readxl' was built under R version 4.0.2library(ggplot2)
library(dplyr)## Warning: package 'dplyr' was built under R version 4.0.2##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniondata = read_excel("Prov_total.xlsx")
data## # A tibble: 95 x 5
## Date GP WC KZN EC
## <dttm> <dbl> <dbl> <dbl> <dbl>
## 1 2020-03-20 00:00:00 109 56 24 0
## 2 2020-03-21 00:00:00 125 74 27 1
## 3 2020-03-22 00:00:00 132 88 36 2
## 4 2020-03-23 00:00:00 207 100 60 2
## 5 2020-03-24 00:00:00 302 113 80 2
## 6 2020-03-25 00:00:00 319 183 91 2
## 7 2020-03-26 00:00:00 409 229 134 5
## 8 2020-03-27 00:00:00 471 250 145 8
## 9 2020-03-28 00:00:00 533 271 156 10
## 10 2020-03-29 00:00:00 584 310 167 12
## # ... with 85 more rowsp = ggplot() +
geom_line(data=data, aes(x = Date, y = GP), color = "blue") +
geom_line(data=data, aes(x = Date, y = WC), color = "red") +
geom_line(data=data, aes(x = Date, y = KZN), color = "green") +
geom_line(data=data, aes(x = Date, y = EC), color = "yellow") +
xlab('Dates') +
ylab('Comfirmed cases')
print(p)
#Linear programming
#Gauteng
duration.freq = table(data$GP)
duration.cumfreq = cumsum(duration.freq)
duration.cumrelfreq = duration.cumfreq / nrow(data)
duration.cumrelfreq## 109 125 132 207 302 319 409
## 0.01052632 0.02105263 0.03157895 0.04210526 0.05263158 0.06315789 0.07368421
## 471 533 584 618 633 645 663
## 0.08421053 0.09473684 0.10526316 0.11578947 0.12631579 0.13684211 0.14736842
## 672 693 704 713 748 782 795
## 0.15789474 0.16842105 0.17894737 0.18947368 0.20000000 0.21052632 0.22105263
## 801 813 865 890 909 930 969
## 0.23157895 0.24210526 0.25263158 0.26315789 0.27368421 0.28421053 0.29473684
## 1018 1101 1148 1170 1199 1224 1252
## 0.30526316 0.31578947 0.32631579 0.33684211 0.34736842 0.35789474 0.36842105
## 1281 1304 1331 1353 1377 1408 1446
## 0.37894737 0.38947368 0.40000000 0.41052632 0.42105263 0.43157895 0.44210526
## 1507 1598 1624 1661 1697 1720 1804
## 0.45263158 0.46315789 0.47368421 0.48421053 0.49473684 0.50526316 0.51578947
## 1851 1910 1952 1971 2014 2074 2135
## 0.52631579 0.53684211 0.54736842 0.55789474 0.56842105 0.57894737 0.58947368
## 2210 2262 2329 2343 2361 2400 2453
## 0.60000000 0.61052632 0.62105263 0.63157895 0.64210526 0.65263158 0.66315789
## 2521 2633 2773 2993 3043 3167 3329
## 0.67368421 0.68421053 0.69473684 0.70526316 0.71578947 0.72631579 0.73684211
## 3583 3773 4003 4231 4276 4567 4845
## 0.74736842 0.75789474 0.76842105 0.77894737 0.78947368 0.80000000 0.81052632
## 5215 5626 5946 6258 6546 7195 7953
## 0.82105263 0.83157895 0.84210526 0.85263158 0.86315789 0.87368421 0.88421053
## 8781 9897 11164 12193 13023 14620 15898
## 0.89473684 0.90526316 0.91578947 0.92631579 0.93684211 0.94736842 0.95789474
## 17261 18978 20822 22341
## 0.96842105 0.97894737 0.98947368 1.00000000Regre = lm(data$GP~duration.cumrelfreq, data = data)
summary(Regre)##
## Call:
## lm(formula = data$GP ~ duration.cumrelfreq, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3102.8 -2255.6 -703.2 1424.5 12724.3
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2672.8 638.5 -4.186 6.44e-05 ***
## duration.cumrelfreq 12289.5 1097.3 11.200 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3087 on 93 degrees of freedom
## Multiple R-squared: 0.5742, Adjusted R-squared: 0.5697
## F-statistic: 125.4 on 1 and 93 DF, p-value: < 2.2e-16duration.freq1 = table(data$WC)
duration.cumfreq1 = cumsum(duration.freq1)
duration.cumrelfreq1 = duration.cumfreq1 / nrow(data)
duration.cumrelfreq1## 56 74 88 100 113 183 229
## 0.01052632 0.02105263 0.03157895 0.04210526 0.05263158 0.06315789 0.07368421
## 250 271 310 324 325 326 353
## 0.08421053 0.09473684 0.10526316 0.11578947 0.12631579 0.13684211 0.14736842
## 374 433 454 462 479 495 515
## 0.15789474 0.16842105 0.17894737 0.18947368 0.20000000 0.21052632 0.22105263
## 541 546 587 617 643 657 675
## 0.23157895 0.24210526 0.25263158 0.26315789 0.27368421 0.28421053 0.29473684
## 717 836 868 940 1010 1079 1279
## 0.30526316 0.31578947 0.32631579 0.33684211 0.34736842 0.35789474 0.36842105
## 1413 1514 1608 1737 1870 2135 2342
## 0.37894737 0.38947368 0.40000000 0.41052632 0.42105263 0.43157895 0.44210526
## 2507 2700 3044 3362 3609 3760 3994
## 0.45263158 0.46315789 0.47368421 0.48421053 0.49473684 0.50526316 0.51578947
## 4497 4809 5168 5621 6105 6713 7235
## 0.52631579 0.53684211 0.54736842 0.55789474 0.56842105 0.57894737 0.58947368
## 7798 8404 9294 10035 10639 11262 12153
## 0.60000000 0.61052632 0.62105263 0.63157895 0.64210526 0.65263158 0.66315789
## 12888 13826 14740 15396 15829 16893 17754
## 0.67368421 0.68421053 0.69473684 0.70526316 0.71578947 0.72631579 0.73684211
## 18906 20160 21382 22567 23583 24657 27006
## 0.74736842 0.75789474 0.76842105 0.77894737 0.78947368 0.80000000 0.81052632
## 28807 30379 31824 33568 34819 36021 37422
## 0.82105263 0.83157895 0.84210526 0.85263158 0.86315789 0.87368421 0.88421053
## 38926 40605 42539 44143 45357 46555 47522
## 0.89473684 0.90526316 0.91578947 0.92631579 0.93684211 0.94736842 0.95789474
## 48706 50173 51441 52554
## 0.96842105 0.97894737 0.98947368 1.00000000Regre2 = lm(data$WC~duration.cumrelfreq1, data = data)
summary(Regre2)##
## Call:
## lm(formula = data$WC ~ duration.cumrelfreq1, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9224 -6801 -1742 6114 16596
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11841 1571 -7.538 3.09e-11 ***
## duration.cumrelfreq1 47799 2699 17.708 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7595 on 93 degrees of freedom
## Multiple R-squared: 0.7713, Adjusted R-squared: 0.7688
## F-statistic: 313.6 on 1 and 93 DF, p-value: < 2.2e-16duration.freq2 = table(data$KZN)
duration.cumfreq2 = cumsum(duration.freq2)
duration.cumrelfreq2 = duration.cumfreq2 / nrow(data)
duration.cumrelfreq2## 24 27 36 60 80 91 134
## 0.01052632 0.02105263 0.03157895 0.04210526 0.05263158 0.06315789 0.07368421
## 145 156 167 171 179 186 206
## 0.08421053 0.09473684 0.10526316 0.11578947 0.12631579 0.13684211 0.14736842
## 215 232 246 257 306 354 387
## 0.15789474 0.16842105 0.17894737 0.18947368 0.20000000 0.21052632 0.22105263
## 412 418 443 465 489 519 539
## 0.23157895 0.24210526 0.25263158 0.26315789 0.27368421 0.28421053 0.29473684
## 591 604 617 639 671 758 807
## 0.30526316 0.31578947 0.32631579 0.33684211 0.34736842 0.35789474 0.36842105
## 841 847 863 902 919 956 980
## 0.37894737 0.38947368 0.40000000 0.41052632 0.42105263 0.43157895 0.44210526
## 1006 1051 1076 1106 1142 1189 1204
## 0.45263158 0.46315789 0.47368421 0.48421053 0.49473684 0.50526316 0.51578947
## 1253 1308 1353 1372 1394 1413 1444
## 0.52631579 0.53684211 0.54736842 0.55789474 0.56842105 0.57894737 0.58947368
## 1482 1498 1543 1567 1616 1650 1693
## 0.60000000 0.61052632 0.62105263 0.63157895 0.64210526 0.65263158 0.66315789
## 1735 1777 1815 1882 1927 2186 2349
## 0.67368421 0.68421053 0.69473684 0.70526316 0.71578947 0.72631579 0.73684211
## 2428 2476 2545 2565 2637 2707 2869
## 0.74736842 0.75789474 0.76842105 0.77894737 0.78947368 0.80000000 0.81052632
## 2936 3016 3108 3175 3255 3347 3472
## 0.82105263 0.83157895 0.84210526 0.85263158 0.86315789 0.87368421 0.88421053
## 3573 3763 3874 3959 4048 4238 4360
## 0.89473684 0.90526316 0.91578947 0.92631579 0.93684211 0.94736842 0.95789474
## 4538 4806 5030 5278
## 0.96842105 0.97894737 0.98947368 1.00000000Regre3 = lm(data$KZN~duration.cumrelfreq2, data = data)
summary(Regre3)##
## Call:
## lm(formula = data$KZN ~ duration.cumrelfreq2, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -581.11 -345.86 -86.95 248.10 1530.98
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -678.38 92.66 -7.321 8.64e-11 ***
## duration.cumrelfreq2 4425.40 159.24 27.791 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 448 on 93 degrees of freedom
## Multiple R-squared: 0.8925, Adjusted R-squared: 0.8914
## F-statistic: 772.4 on 1 and 93 DF, p-value: < 2.2e-16duration.freq4 = table(data$EC)
duration.cumfreq4 = cumsum(duration.freq4)
duration.cumrelfreq4 = duration.cumfreq4 / nrow(data)
duration.cumrelfreq4## 0 1 2 5 8 10 12
## 0.01052632 0.02105263 0.06315789 0.07368421 0.08421053 0.09473684 0.12631579
## 15 17 21 25 31 32 39
## 0.13684211 0.14736842 0.15789474 0.16842105 0.17894737 0.18947368 0.20000000
## 45 61 68 69 88 104 174
## 0.21052632 0.22105263 0.23157895 0.24210526 0.25263158 0.26315789 0.27368421
## 199 220 246 270 293 310 345
## 0.28421053 0.29473684 0.30526316 0.31578947 0.32631579 0.33684211 0.34736842
## 377 417 480 488 535 588 616
## 0.35789474 0.36842105 0.37894737 0.38947368 0.40000000 0.41052632 0.42105263
## 630 647 691 732 774 814 838
## 0.43157895 0.44210526 0.45263158 0.46315789 0.47368421 0.48421053 0.49473684
## 849 929 989 1078 1218 1356 1504
## 0.50526316 0.51578947 0.52631579 0.53684211 0.54736842 0.55789474 0.56842105
## 1534 1569 1662 1812 1936 2052 2135
## 0.57894737 0.58947368 0.60000000 0.61052632 0.62105263 0.63157895 0.64210526
## 2215 2324 2459 2569 2690 2748 2864
## 0.65263158 0.66315789 0.67368421 0.68421053 0.69473684 0.70526316 0.71578947
## 3047 3306 3583 3759 3927 4111 4324
## 0.72631579 0.73684211 0.74736842 0.75789474 0.76842105 0.77894737 0.78947368
## 4526 4936 5240 5629 5974 6341 6760
## 0.80000000 0.81052632 0.82105263 0.83157895 0.84210526 0.85263158 0.86315789
## 7154 7868 8615 9250 10027 10597 11039
## 0.87368421 0.88421053 0.89473684 0.90526316 0.91578947 0.92631579 0.93684211
## 11919 12639 13506 14721 15751 16895
## 0.94736842 0.95789474 0.96842105 0.97894737 0.98947368 1.00000000#Regre4 = lm(data$EC~duration.cumrelfreq4, data = data)
#summary(Regre4)beta <- coef(Regre)[2]
beta## duration.cumrelfreq
## 12289.5alpha <- exp(coef(Regre)[1])theta <- min(data$GP) * 0.5#model <- nls(y ~ alpha * exp(beta * x) + theta , data =data$GP, start = start)