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## Installing package into '/cloud/lib/x86_64-pc-linux-gnu-library/4.3'
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## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
## Loading required package: zoo
##
##
## Attaching package: 'zoo'
##
##
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## chnimp bchlimp befile6 affile6 afdec6 befile12 affile12 afdec12 chempi
## 1 220.4620 9578.376 0 0 0 0 0 0 100.1
## 2 94.7980 11219.480 0 0 0 0 0 0 100.9
## 3 219.3575 9719.900 0 0 0 0 0 0 101.1
## 4 317.4215 12920.950 0 0 0 0 0 0 102.5
## 5 114.6390 9790.446 0 0 0 0 0 0 104.1
## gas rtwex spr sum fall lchnimp lgas lrtwex lchempi t feb mar
## 1 7830000128 86.74 0 0 0 5.395725 22.78123 4.462915 4.606170 1 1 0
## 2 8819999744 85.63 1 0 0 4.551748 22.90029 4.450036 4.614130 2 0 1
## 3 8449999872 85.42 1 0 0 5.390703 22.85743 4.447580 4.616110 3 0 0
## 4 9240000512 87.29 1 0 0 5.760231 22.94681 4.469236 4.629863 4 0 0
## 5 9150000128 86.60 0 1 0 4.741788 22.93702 4.461300 4.645352 5 0 0
## apr may jun jul aug sep oct nov dec percchn
## 1 0 0 0 0 0 0 0 0 0 2.3016636
## 2 0 0 0 0 0 0 0 0 0 0.8449411
## 3 1 0 0 0 0 0 0 0 0 2.2567875
## 4 0 1 0 0 0 0 0 0 0 2.4566422
## 5 0 0 1 0 0 0 0 0 0 1.1709272
## Loading required package: carData
##
## Attaching package: 'car'
##
## The following object is masked from 'package:dplyr':
##
## recode
##
## The following object is masked from 'package:purrr':
##
## some
(i) Add a linear time trend to equation (10.22)
## chnimp bchlimp befile6 affile6
## Min. : 39.68 Min. : 8302 Min. :0.0000 Min. :0.0000
## 1st Qu.: 317.88 1st Qu.:13765 1st Qu.:0.0000 1st Qu.:0.0000
## Median : 535.72 Median :17716 Median :0.0000 Median :0.0000
## Mean : 589.24 Mean :19157 Mean :0.0458 Mean :0.0458
## 3rd Qu.: 821.36 3rd Qu.:23646 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1794.52 Max. :45717 Max. :1.0000 Max. :1.0000
## afdec6 befile12 affile12 afdec12
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.0458 Mean :0.0916 Mean :0.0916 Mean :0.0916
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## chempi gas rtwex spr
## Min. :100.1 Min. :6.900e+09 Min. : 79.45 Min. :0.0000
## 1st Qu.:112.6 1st Qu.:8.210e+09 1st Qu.: 85.86 1st Qu.:0.0000
## Median :120.2 Median :8.520e+09 Median : 99.21 Median :0.0000
## Mean :122.8 Mean :8.519e+09 Mean :102.50 Mean :0.2519
## 3rd Qu.:131.8 3rd Qu.:8.860e+09 3rd Qu.:116.38 3rd Qu.:0.5000
## Max. :159.0 Max. :1.020e+10 Max. :146.45 Max. :1.0000
## sum fall lchnimp lgas
## Min. :0.0000 Min. :0.0000 Min. :3.681 Min. :22.65
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:5.762 1st Qu.:22.83
## Median :0.0000 Median :0.0000 Median :6.284 Median :22.87
## Mean :0.2519 Mean :0.2519 Mean :6.175 Mean :22.86
## 3rd Qu.:0.5000 3rd Qu.:0.5000 3rd Qu.:6.711 3rd Qu.:22.90
## Max. :1.0000 Max. :1.0000 Max. :7.492 Max. :23.05
## lrtwex lchempi t feb
## Min. :4.375 Min. :4.606 Min. : 1.0 Min. :0.00000
## 1st Qu.:4.453 1st Qu.:4.724 1st Qu.: 33.5 1st Qu.:0.00000
## Median :4.597 Median :4.789 Median : 66.0 Median :0.00000
## Mean :4.615 Mean :4.804 Mean : 66.0 Mean :0.08397
## 3rd Qu.:4.757 3rd Qu.:4.882 3rd Qu.: 98.5 3rd Qu.:0.00000
## Max. :4.987 Max. :5.069 Max. :131.0 Max. :1.00000
## mar apr may jun
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.08397 Mean :0.08397 Mean :0.08397 Mean :0.08397
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## jul aug sep oct
## Min. :0.00000 Min. :0.00000 Min. :0.00000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.00000
## Median :0.00000 Median :0.00000 Median :0.00000 Median :0.00000
## Mean :0.08397 Mean :0.08397 Mean :0.08397 Mean :0.08397
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.00000 Max. :1.00000 Max. :1.00000
## nov dec percchn
## Min. :0.00000 Min. :0.00000 Min. : 0.1726
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.: 1.8059
## Median :0.00000 Median :0.00000 Median : 2.7824
## Mean :0.08397 Mean :0.08397 Mean : 3.2726
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.: 4.2495
## Max. :1.00000 Max. :1.00000 Max. :10.2326
##
## Call:
## lm(formula = log(chnimp) ~ log(chempi) + log(gas) + log(rtwex) +
## befile6 + affile6 + afdec6 + t, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.94317 -0.31168 0.03172 0.36366 1.21218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.367308 20.782159 -0.114 0.90949
## log(chempi) -0.686233 1.239711 -0.554 0.58090
## log(gas) 0.465669 0.876178 0.531 0.59605
## log(rtwex) 0.078222 0.472440 0.166 0.86877
## befile6 0.090470 0.251289 0.360 0.71945
## affile6 0.097006 0.257313 0.377 0.70683
## afdec6 -0.351502 0.282542 -1.244 0.21584
## t 0.012706 0.003844 3.305 0.00124 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5748 on 123 degrees of freedom
## Multiple R-squared: 0.3616, Adjusted R-squared: 0.3252
## F-statistic: 9.951 on 7 and 123 DF, p-value: 8.358e-10
(ii) Test for joint significance of all variables except the time
trend
##
## Call:
## lm(formula = log(chnimp) ~ poly(log(chempi), 2) + log(gas) +
## log(rtwex) + befile6 + affile6 + afdec6, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.01477 -0.38667 0.02185 0.40410 1.48967
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.04449 21.65600 -0.094 0.9249
## poly(log(chempi), 2)1 4.02720 0.62067 6.489 1.91e-09 ***
## poly(log(chempi), 2)2 0.26912 0.69013 0.390 0.6972
## log(gas) 0.15165 0.91692 0.165 0.8689
## log(rtwex) 1.03473 0.42286 2.447 0.0158 *
## befile6 0.06699 0.26256 0.255 0.7990
## affile6 -0.02244 0.26643 -0.084 0.9330
## afdec6 -0.56317 0.28687 -1.963 0.0519 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5994 on 123 degrees of freedom
## Multiple R-squared: 0.3057, Adjusted R-squared: 0.2662
## F-statistic: 7.737 on 7 and 123 DF, p-value: 9.737e-08
## [1] 34 8
(iii) Add monthly dummy variables and test for seasonality
##
## Call:
## lm(formula = log(chnimp) ~ poly(log(chempi), 2) + log(gas) +
## log(rtwex) + befile6 + affile6 + afdec6 + feb + mar + apr +
## may + jun + jul + aug + sep + oct + nov + dec, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.95723 -0.35273 0.07999 0.41126 1.33548
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.89513 33.26642 1.019 0.3104
## poly(log(chempi), 2)1 4.22170 0.63826 6.614 1.33e-09 ***
## poly(log(chempi), 2)2 0.39128 0.69716 0.561 0.5757
## log(gas) -1.35522 1.39999 -0.968 0.3351
## log(rtwex) 0.73640 0.49047 1.501 0.1361
## befile6 0.15120 0.26840 0.563 0.5743
## affile6 0.02663 0.28065 0.095 0.9246
## afdec6 -0.51889 0.30290 -1.713 0.0895 .
## feb -0.42928 0.30607 -1.403 0.1635
## mar 0.05476 0.26565 0.206 0.8370
## apr -0.46008 0.26964 -1.706 0.0907 .
## may 0.02819 0.27022 0.104 0.9171
## jun -0.21630 0.27065 -0.799 0.4259
## jul -0.00404 0.27997 -0.014 0.9885
## aug -0.16338 0.27907 -0.585 0.5594
## sep -0.14124 0.26877 -0.526 0.6003
## oct 0.04562 0.26788 0.170 0.8651
## nov -0.25463 0.26405 -0.964 0.3370
## dec 0.12592 0.27253 0.462 0.6449
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.603 on 112 degrees of freedom
## Multiple R-squared: 0.3601, Adjusted R-squared: 0.2573
## F-statistic: 3.502 on 18 and 112 DF, p-value: 2.278e-05