Given the data set as the table below, which are the monthly supply of electricity (millions of kWh), water (L), and chocolate-based production in country XYZ over the period of January 1958 to December 1990. Answer all the questions with complete calculation and coding in R:

Write the suitable model for the :

a. Time series regression model

b. ARIMA or SARIMA model.

Time Chocolate Water Electricity 1958 Jan 1451 96.3 1497 1958 Feb 2037 84.4 1463 1958 Mar 2477 91.2 1648 1958 Apr 2785 81.9 1595 1958 May 2994 80.5 1777 1958 Jun 2681 70.4 1824 1958 Jul 3098 74.8 1994 1958 Aug 2708 75.9 1835 1958 Sep 2517 86.3 1787 1958 Oct 2445 98.7 1699 1958 Nov 2087 100.9 1633 1958 Dec 1801 113.8 1645 1959 Jan 1216 89.8 1597 1959 Feb 2173 84.4 1577 1959 Mar 2286 87.2 1709 1959 Apr 3121 85.6 1756 1959 May 3458 72 1936 1959 Jun 3511 69.2 2052 1959 Jul 3524 77.5 2105 1959 Aug 2767 78.1 2016 1959 Sep 2744 94.3 1914 1959 Oct 2603 97.7 1925 1959 Nov 2527 100.2 1824 1959 Dec 1846 116.4 1765 1960 Jan 1066 97.1 1721 1960 Feb 2327 93 1752 1960 Mar 3066 96 1914 1960 Apr 3048 80.5 1857 1960 May 3806 76.1 2159 1960 Jun 4042 69.9 2195 1960 Jul 3583 73.6 2287 1960 Aug 3438 92.6 2276 1960 Sep 2957 94.2 2096 1960 Oct 2885 93.5 2055 1960 Nov 2744 108.5 2004 1960 Dec 1837 109.4 1924 1961 Jan 1961 Feb 1961 Mar 1961 Apr 1961 May 1961 Jun 1961 Jul 1961 Aug 1961 Sep 1961 Oct 1961 Nov 1961 Dec 1962 Jan 1962 Feb 1962 Mar 1962 Apr 1962 May 1962 Jun 1962 Jul 1962 Aug 1962 Sep 1962 Oct 1962 Nov 1962 Dec 1963 Jan 1963 Feb 1963 Mar 1963 Apr 1963 May 1963 Jun 1963 Jul 1963 Aug 1963 Sep 1963 Oct 1963 Nov 1963 Dec 1447 2504 3248 3098 4318 3561 3316 3379 2717 2354 2445 1542 1606 2590 3588 3202 4704 4005 3810 3488 2781 2944 2817 1960 1937 2903 3357 3552 4581 3905 4581 4037 3345 3175 2808 2050 105.1 92.5 97.1 81.4 79.1 72.1 78.7 87.1 91.4 109.9 116.3 113 100 84.8 94.3 87.1 90.3 72.4 84.9 92.7 92.2 114.9 112.5 118.3 106 91.2 96.6 96.3 88.2 70.2 86.5 88.2 102.8 119.1 119.2 125.1 1851 1839 2019 1937 2270 2251 2382 2364 2129 2110 2072 1980 1995 1932 2171 2162 2489 2424 2641 2630 2324 2412 2284 2186 2184 2144 2379 2383 2717 2774 3051 2891 2613 2600 2493 2410 1964 Jan 1964 Feb 1964 Mar 1964 Apr 1964 May 1964 Jun 1964 Jul 1964 Aug 1964 Sep 1964 Oct 1964 Nov 1964 Dec 1965 Jan 1965 Feb 1965 Mar 1965 Apr 1965 May 1965 Jun 1965 Jul 1965 Aug 1965 Sep 1965 Oct 1965 Nov 1965 Dec 1966 Jan 1966 Feb 1966 Mar 1966 Apr 1966 May 1966 Jun 1966 Jul 1966 Aug 1966 Sep 1966 Oct 1966 Nov 1966 Dec 1719 3143 3756 4776 4540 4309 4563 3506 3665 3361 3094 2440 1633 2935 4159 4159 4894 4921 4577 4155 3851 3429 3370 2726 1674 3257 4731 4481 5443 5566 5044 4781 4014 3561 3801 2685 106.1 102.1 105.2 101 84.3 87.5 92.7 94.4 113 113.9 122.9 132.7 106.9 96.6 127.3 98.2 100.2 89.4 95.3 104.2 106.4 116.2 135.9 134 104.6 107.1 123.5 98.8 98.6 90.6 89.1 105.2 114 122.1 138 142.2 2390 2463 2616 2734 2970 3125 3342 3207 2964 2919 2764 2732 2622 2698 2950 2895 3200 3408 3679 3473 3154 3107 3052 2918 2786 2739 3125 3033 3486 3661 3927 3851 3456 3390 3280 3166 1967 Jan 1967 Feb 1967 Mar 1967 Apr 1967 May 1967 Jun 1967 Jul 1967 Aug 1967 Sep 1967 Oct 1967 Nov 1967 Dec 1968 Jan 1968 Feb 1968 Mar 1968 Apr 1968 May 1968 Jun 1968 Jul 1968 Aug 1968 Sep 1968 Oct 1968 Nov 1968 Dec 1969 Jan 1969 Feb 1969 Mar 1969 Apr 1969 May 1969 Jun 1969 Jul 1969 Aug 1969 Sep 1969 Oct 1969 Nov 1969 Dec 1805 3756 4227 4595 5702 4681 4395 4459 4191 3742 3279 2468 1742 3366 3633 3701 4926 4522 5275 4717 4114 3851 3493 2654 2168 3561 4305 4413 5307 5361 4948 4472 3846 3715 3343 2939 116.4 112.6 123.8 103.6 113.9 98.6 95 116 113.9 127.5 131.4 145.9 131.5 131 130.5 118.9 114.3 85.7 104.6 105.1 117.3 142.5 140 159.8 131.2 125.4 126.5 119.4 113.5 98.7 114.5 113.8 133.1 143.4 137.3 165.2 3080 3069 3340 3310 3798 3883 4191 4213 3766 3628 3520 3322 3250 3287 3552 3440 4153 4265 4655 4492 4051 3967 3807 3639 3647 3560 3929 3858 4485 4697 4977 4675 4596 4491 4127 4144 1970 Jan 1970 Feb 1970 Mar 1970 Apr 1970 May 1970 Jun 1970 Jul 1970 Aug 1970 Sep 1970 Oct 1970 Nov 1970 Dec 1971 Jan 1971 Feb 1971 Mar 1971 Apr 1971 May 1971 Jun 1971 Jul 1971 Aug 1971 Sep 1971 Oct 1971 Nov 1971 Dec 1972 Jan 1972 Feb 1972 Mar 1972 Apr 1972 May 1972 Jun 1972 Jul 1972 Aug 1972 Sep 1972 Oct 1972 Nov 1972 Dec 1615 3497 3915 4858 4962 4504 4767 4291 4091 4164 3915 3130 1696 3887 4749 4781 5089 5484 5072 4611 4117 3910 4252 3624 1678 3851 5021 4581 6195 5338 4909 4640 3706 4113 3879 3411 126.9 124 135.7 130 109.4 117.8 120.3 121 132.3 142.9 147.4 175.9 132.6 123.7 153.3 134 119.6 116.2 118.6 130.7 129.3 144.4 163.2 179.4 128.1 138.4 152.7 120 140.5 116.2 121.4 127.8 143.6 157.6 166.2 182.3 4014 3994 4320 4400 5002 5091 5471 5193 4997 4737 4546 4498 4350 4206 4743 4582 5191 5457 5891 5618 5158 5030 4800 4654 4453 4440 4945 4788 5425 5706 6061 5846 5242 5408 5114 5042 1973 Jan 1973 Feb 1973 Mar 1973 Apr 1973 May 1973 Jun 1973 Jul 1973 Aug 1973 Sep 1973 Oct 1973 Nov 1973 Dec 1974 Jan 1974 Feb 1974 Mar 1974 Apr 1974 May 1974 Jun 1974 Jul 1974 Aug 1974 Sep 1974 Oct 1974 Nov 1974 Dec 1975 Jan 1975 Feb 1975 Mar 1975 Apr 1975 May 1975 Jun 1975 Jul 1975 Aug 1975 Sep 1975 Oct 1975 Nov 1975 Dec 2043 3736 4490 3715 5623 4671 5591 5461 4795 4846 4843 3278 2411 4278 4639 4559 6404 4851 6480 6394 5752 4718 4659 3842 2873 5556 5389 6135 6707 5220 6249 5281 4192 4867 3752 3492 153.1 147.6 157.7 137.2 151.5 98.7 145.8 151.7 129.4 174.1 197 193.9 164.1 142.8 157.9 159.2 162.2 123.1 130 150.1 169.4 179.7 182.1 194.3 161.4 169.4 168.8 158.1 158.5 135.3 149.3 143.4 142.2 188.4 166.2 199.2 5008 4657 5359 5193 5891 5980 6390 6366 5756 5640 5429 5398 5413 5141 5695 5554 6369 6592 7107 6917 6353 6205 5830 5646 5379 5489 5824 5907 6482 6795 7028 6776 6274 6362 5940 5958 1976 Jan 1976 Feb 1976 Mar 1976 Apr 1976 May 1976 Jun 1976 Jul 1976 Aug 1976 Sep 1976 Oct 1976 Nov 1976 Dec 1977 Jan 1977 Feb 1977 Mar 1977 Apr 1977 May 1977 Jun 1977 Jul 1977 Aug 1977 Sep 1977 Oct 1977 Nov 1977 Dec 1978 Jan 1978 Feb 1978 Mar 1978 Apr 1978 May 1978 Jun 1978 Jul 1978 Aug 1978 Sep 1978 Oct 1978 Nov 1978 Dec 1979 4584 5139 5044 5501 5044 5035 5167 4650 5298 4373 3941 2334 4381 5665 4393 5232 5876 5900 5704 4718 4650 4446 3061 2155 4274 4695 4362 4889 5370 5072 4985 3978 4139 3995 3025 182.7 145.2 182.1 158.7 141.6 132.6 139.6 147 166.6 157 180.4 210.2 159.8 157.8 168.2 158.4 152 142.2 137.2 152.6 166.8 165.6 198.6 201.5 170.7 164.4 179.7 157 168 139.3 138.6 153.4 138.9 172.1 198.4 217.8 5769 5887 6367 6165 6868 7201 7601 7581 7090 6841 6408 6435 6176 6138 6717 6470 7312 7763 8171 7788 7311 6679 6704 6724 6552 6427 7105 6869 7683 8082 8555 8386 7553 7398 7112 6886 1979 Jan 1979 Feb 1979 Mar 1979 Apr 1979 May 1979 Jun 1979 Jul 1979 Aug 1979 Sep 1979 Oct 1979 Nov 1979 Dec 1980 Jan 1980 Feb 1980 Mar 1980 Apr 1980 May 1980 Jun 1980 Jul 1980 Aug 1980 Sep 1980 Oct 1980 Nov 1980 Dec 1981 Jan 1981 Feb 1981 Mar 1981 Apr 1981 May 1981 Jun 1981 Jul 1981 Aug 1981 Sep 1981 Oct 1981 Nov 1981 Dec 1949 4357 4638 3994 6174 5656 4411 5504 4463 4458 4528 2830 1843 5042 5348 5257 6699 5388 6001 5966 4845 4507 4214 3460 1833 4978 6464 5820 6447 6191 6628 5452 5295 5080 5564 3965 173.7 153.8 175.6 147.1 160.3 135.2 148.8 151 148.2 182.2 189.2 183.1 170 158.4 176.1 156.2 153.2 117.9 149.8 156.6 166.7 156.8 158.6 210.8 203.6 175.2 168.7 155.9 147.3 137 141.1 167.4 160.2 191.9 174.4 208.2 7077 6820 7426 7143 8261 8240 8977 8991 8026 7911 7510 7381 7366 7414 7824 7524 8279 8707 9486 8973 8231 8206 7927 7999 7834 7521 8284 7999 8940 9381 10078 9796 8471 8572 8150 8168 1982 Jan 1982 Feb 1982 Mar 1982 Apr 1982 May 1982 Jun 1982 Jul 1982 Aug 1982 Sep 1982 Oct 1982 Nov 1982 Dec 1983 Jan 1983 Feb 1983 Mar 1983 Apr 1983 May 1983 Jun 1983 Jul 1983 Aug 1983 Sep 1983 Oct 1983 Nov 1983 Dec 1984 Jan 1984 Feb 1984 Mar 1984 Apr 1984 May 1984 Jun 1984 Jul 1984 Aug 1984 Sep 1984 Oct 1984 Nov 1984 Dec 2062 5099 6162 5529 6416 6382 5624 5785 4644 5331 5143 4596 2180 5786 5840 5666 6360 6219 6082 5653 5726 5049 5859 4091 2167 6480 7375 6583 7251 6730 6428 5228 4716 6101 5753 4000 159.4 161.1 172.1 158.4 114.6 159.6 159.7 159.4 160.7 165.5 205 205.2 141.6 148.1 184.9 132.5 137.3 135.5 121.7 166.1 146.8 162.8 186.8 185.5 151.5 158.1 143 151.2 147.6 130.7 137.5 146.1 133.6 167.9 181.9 202 8166 7903 8606 8071 9178 9873 10476 9296 8818 8697 8381 8293 7942 8001 8744 8397 9115 9773 10358 9849 9083 9143 8800 8741 8492 8795 9354 8796 10072 10174 11326 10744 9806 9740 9373 9244 10923 10790 1985 Jan 1985 Feb 1985 Mar 1985 Apr 1985 May 1985 Jun 1985 Jul 1985 Aug 1985 Sep 1985 Oct 1985 Nov 1985 Dec 1986 Jan 1986 Feb 1986 Mar 1986 Apr 1986 May 1986 Jun 1986 Jul 1986 Aug 1986 Sep 1986 Oct 1986 Nov 1986 Dec 1987 Jan 1987 Feb 1987 Mar 1987 Apr 1987 May 1987 Jun 1987 Jul 1987 Aug 1987 Sep 1987 Oct 1987 Nov 1987 Dec 2691 5898 6526 5840 6650 5717 7236 6523 5729 6004 5950 4690 3687 7791 7153 6434 7850 6809 8379 6914 6919 7265 6994 5503 3782 7502 8119 7292 6886 7049 7977 8519 6680 7994 7047 5782 166.5 151.3 146.2 148.3 144.7 123.6 151.6 133.9 137.4 181.6 182 190 161.2 155.5 141.9 164.6 136.2 126.8 152.5 126.6 150.1 186.3 147.5 200.4 177.2 127.4 177.1 154.4 135.2 126.4 147.3 140.6 152.3 151.2 172.2 215.3 9407 8827 9880 9364 10580 10899 11687 11280 10208 10212 9725 9721 9846 9407 10265 9970 10801 11246 12167 11578 10645 10613 10104 10348 10263 9973 10803 10409 11458 11845 12559 12070 11221 11338 10761 11012 1988 Jan 1988 Feb 1988 Mar 1988 Apr 1988 May 1988 Jun 1988 Jul 1988 Aug 1988 Sep 1988 Oct 1988 Nov 1988 Dec 1989 Jan 1989 Feb 1989 Mar 1989 Apr 1989 May 1989 Jun 1989 Jul 1989 Aug 1989 Sep 1989 Oct 1989 Nov 1989 Dec 1990 Jan 1990 Feb 1990 Mar 1990 Apr 1990 May 1990 Jun 1990 Jul 1990 Aug 1990 Sep 1990 Oct 1990 Nov 1990 Dec 3771 7906 8970 6077 7919 7340 7791 7368 8255 7816 7476 6696 4484 8274 8866 8572 9176 8645 8265 9558 7037 9101 8180 7072 3832 7253 8667 7658 8859 7291 7529 8715 8450 9085 8350 7080 154.1 159.3 160.4 151.9 148.4 139.6 148.2 153.5 145.1 183.7 210.5 203.3 153.3 144.3 169.6 143.7 160 135.5 141.7 159.9 145.6 11427 10788 11772 12104 12634 12772 11764 11956 11646 11750 11485 11198 12265 11704 12419 13259 13945 13839 12387 12546 12038 11977 12336 11793 12877 11923 13306 13988 14002 14338 12867 12761 12449 12658 183.4 198.1 186.7 171.9 150.5 163 153.6 152.8 135.4 148.3 148.3 133.5 193.8 208.4 197