Fit a predictive linear regression model to estimate weight of the fish from its length (length1, length2, length3), height and width using the data source fish xls provided to you Use only 70 of the data as training set (15 points) Report the coefficients values by using the standard Least Square Estimates What is the standard error of the estimated coefficients, R squared term, and the 95 confidence interval Is there any dependence between the length and weight of the fish Q2 Using the data source in Q1(only 70 of the data points as training set), fit the Ridge and Lasso Regression Models (15 points) Report the coefficients for both the models Report the attribute(s) least impacting the weight of the fish Justify your answer Q3 Using remaining 30 of the data in Q1 first , test the trained regression models in Q1 and Q2 and report their performance (model accuracy) using MSE (mean square error) and R squared metrics Which model is performing the best Explain your answer (20 points) fish xls file is below as text format Species Weight Length1 Length2 Length3 Height Width Bream 242 23 2 25 4 30 11 52 4 02 Bream 290 24 26 3 31 2 12 48 4 3056 Bream 340 23 9 26 5 31 1 12 3778 4 6961 Bream 363 26 3 29 33 5 12 73 4 4555 Bream 430 26 5 29 34 12 444 5 134 Bream 450 26 8 29 7 34 7 13 6024 4 9274 Bream 500 26 8 29 7 34 5 14 1795 5 2785 Bream 390 27 6 30 35 12 67 4 69 Bream 450 27 6 30 35 1 14 0049 4 8438 Bream 500 28 5 30 7 36 2 14 2266 4 9594 Bream 475 28 4 31 36 2 14 2628 5 1042 Bream 500 28 7 31 36 2 14 3714 4 8146 Bream 500 29 1 31 5 36 4 13 7592 4 368 Bream 340 29 5 32 37 3 13 9129 5 0728 Bream 600 29 4 32 37 2 14 9544 5 1708 Bream 600 29 4 32 37 2 15 438 5 58 Bream 700 30 4 33 38 3 14 8604 5 2854 Bream 700 30 4 33 38 5 14 938 5 1975 Bream 610 30 9 33 5 38 6 15 633 5 1338 Bream 650 31 33 5 38 7 14 4738 5 7276 Bream 575 31 3 34 39 5 15 1285 5 5695 Bream 685 31 4 34 39 2 15 9936 5 3704 Bream 620 31 5 34 5 39 7 15 5227 5 2801 Bream 680 31 8 35 40 6 15 4686 6 1306 Bream 700 31 9 35 40 5 16 2405 5 589 Bream 725 31 8 35 40 9 16 36 6 0532 Bream 720 32 35 40 6 16 3618 6 09 Bream 714 32 7 36 41 5 16 517 5 8515 Bream 850 32 8 36 41 6 16 8896 6 1984 Bream 1000 33 5 37 42 6 18 957 6 603 Bream 920 35 38 5 44 1 18 0369 6 3063 Bream 955 35 38 5 44 18 084 6 292 Bream 925 36 2 39 5 45 3 18 7542 6 7497 Bream 975 37 4 41 45 9 18 6354 6 7473 Bream 950 38 41 46 5 17 6235 6 3705 Roach 40 12 9 14 1 16 2 4 1472 2 268 Roach 69 16 5 18 2 20 3 5 2983 2 8217 Roach 78 17 5 18 8 21 2 5 5756 2 9044 Roach 87 18 2 19 8 22 2 5 6166 3 1746 Roach 120 18 6 20 22 2 6 216 3 5742 Roach 0 19 20 5 22 8 6 4752 3 3516 Roach 110 19 1 20 8 23 1 6 1677 3 3957 Roach 120 19 4 21 23 7 6 1146 3 2943 Roach 150 20 4 22 24 7 5 8045 3 7544 Roach 145 20 5 22 24 3 6 6339 3 5478 Roach 160 20 5 22 5 25 3 7 0334 3 8203 Roach 140 21 22 5 25 6 55 3 325 Roach 160 21 1 22 5 25 6 4 3 8 Roach 169 22 24 27 2 7 5344 3 8352 Roach 161 22 23 4 26 7 6 9153 3 6312 Roach 200 22 1 23 5 26 8 7 3968 4 1272 Roach 180 23 6 25 2 27 9 7 0866 3 906 Roach 290 24 26 29 2 8 8768 4 4968 Roach 272 25 27 30 6 8 568 4 7736 Roach 390 29 5 31 7 35 9 485 5 355 Whitefish 270 23 6 26 28 7 8 3804 4 2476 Whitefish 270 24 1 26 5 29 3 8 1454 4 2485 Whitefish 306 25 6 28 30 8 8 778 4 6816 Whitefish 540 28 5 31 34 10 744 6 562 Whitefish 800 33 7 36 4 39 6 11 7612 6 5736 Whitefish 1000 37 3 40 43 5 12 354 6 525 Parkki 55 13 5 14 7 16 5 6 8475 2 3265 Parkki 60 14 3 15 5 17 4 6 5772 2 3142 Parkki 90 16 3 17 7 19 8 7 4052 2 673 Parkki 120 17 5 19 21 3 8 3922 2 9181 Parkki 150 18 4 20 22 4 8 8928 3 2928 Parkki 140 19 20 7 23 2 8 5376 3 2944 Parkki 170 19 20 7 23 2 9 396 3 4104 Parkki 145 19 8 21 5 24 1 9 7364 3 1571 Parkki 200 21 2 23 25 8 10 3458 3 6636 Parkki 273 23 25 28 11 088 4 144 Parkki 300 24 26 29 11 368 4 234 Perch 5 9 7 5 8 4 8 8 2 112 1 408 Perch 32 12 5 13 7 14 7 3 528 1 9992 Perch 40 13 8 15 16 3 824 2 432 Perch 51 5 15 16 2 17 2 4 5924 2 6316 Perch 70 15 7 17 4 18 5 4 588 2 9415 Perch 100 16 2 18 19 2 5 2224 3 3216 Perch 78 16 8 18 7 19 4 5 1992 3 1234 Perch 80 17 2 19 20 2 5 6358 3 0502 Perch 85 17 8 19 6 20 8 5 1376 3 0368 Perch 85 18 2 20 21 5 082 2 772 Perch 110 19 21 22 5 5 6925 3 555 Perch 115 19 21 22 5 5 9175 3 3075 Perch 125 19 21 22 5 5 6925 3 6675 Perch 130 19 3 21 3 22 8 6 384 3 534 Perch 120 20 22 23 5 6 11 3 4075 Perch 120 20 22 23 5 5 64 3 525 Perch 130 20 22 23 5 6 11 3 525 Perch 135 20 22 23 5 5 875 3 525 Perch 110 20 22 23 5 5 5225 3 995 Perch 130 20 5 22 5 24 5 856 3 624 Perch 150 20 5 22 5 24 6 792 3 624 Perch 145 20 7 22 7 24 2 5 9532 3 63 Perch 150 21 23 24 5 5 2185 3 626 Perch 170 21 5 23 5 25 6 275 3 725 Perch 225 22 24 25 5 7 293 3 723 Perch 145 22 24 25 5 6 375 3 825 Perch 188 22 6 24 6 26 2 6 7334 4 1658 Perch 180 23 25 26 5 6 4395 3 6835 Perch 197 23 5 25 6 27 6 561 4 239 Perch 218 25 26 5 28 7 168 4 144 Perch 300 25 2 27 3 28 7 8 323 5 1373 Perch 260 25 4 27 5 28 9 7 1672 4 335 Perch 265 25 4 27 5 28 9 7 0516 4 335 Perch 250 25 4 27 5 28 9 7 2828 4 5662 Perch 250 25 9 28 29 4 7 8204 4 2042 Perch 300 26 9 28 7 30 1 7 5852 4 6354 Perch 320 27 8 30 31 6 7 6156 4 7716 Perch 514 30 5 32 8 34 10 03 6 018 Perch 556 32 34 5 36 5 10 2565 6 3875 Perch 840 32 5 35 37 3 11 4884 7 7957 Perch 685 34 36 5 39 10 881 6 864 Perch 700 34 36 38 3 10 6091 6 7408 Perch 700 34 5 37 39 4 10 835 6 2646 Perch 690 34 6 37 39 3 10 5717 6 3666 Perch 900 36 5 39 41 4 11 1366 7 4934 Perch 650 36 5 39 41 4 11 1366 6 003 Perch 820 36 6 39 41 3 12 4313 7 3514 Perch 850 36 9 40 42 3 11 9286 7 1064 Perch 900 37 40 42 5 11 73 7 225 Perch 1015 37 40 42 4 12 3808 7 4624 Perch 820 37 1 40 42 5 11 135 6 63 Perch 1100 39 42 44 6 12 8002 6 8684 Perch 1000 39 8 43 45 2 11 9328 7 2772 Perch 1100 40 1 43 45 5 12 5125 7 4165 Perch 1000 40 2 43 5 46 12 604 8 142 Perch 1000 41 1 44 46 6 12 4888 7 5958 Pike 200 30 32 3 34 8 5 568 3 3756 Pike 300 31 7 34 37 8 5 7078 4 158 Pike 300 32 7 35 38 8 5 9364 4 3844 Pike 300 34 8 37 3 39 8 6 2884 4 0198 Pike 430 35 5 38 40 5 7 29 4 5765 Pike 345 36 38 5 41 6 396 3 977 Pike 456 40 42 5 45 5 7 28 4 3225 Pike 510 40 42 5 45 5 6 825 4 459 Pike 540 40 1 43 45 8 7 786 5 1296 Pike 500 42 45 48 6 96 4 896 Pike 567 43 2 46 48 7 7 792 4 87 Pike 770 44 8 48 51 2 7 68 5 376 Pike 950 48 3 51 7 55 1 8 9262 6 1712 Pike 1250 52 56 59 7 10 6863 6 9849 Pike 1600 56 60 64 9 6 6 144 Pike 1550 56 60 64 9 6 6 144 Pike 1650 59 63 4 68 10 812 7 48 Smelt 6 7 9 3 9 8 10 8 1 7388 1 0476 Smelt 7 5 10 10 5 11 6 1 972 1 16 Smelt 7 10 1 10 6 11 6 1 7284 1 1484 Smelt 9 7 10 4 11 12 2 196 1 38 Smelt 9 8 10 7 11 2 12 4 2 0832 1 2772 Smelt 8 7 10 8 11 3 12 6 1 9782 1 2852 Smelt 10 11 3 11 8 13 1 2 2139 1 2838 Smelt 9 9 11 3 11 8 13 1 2 2139 1 1659 Smelt 9 8 11 4 12 13 2 2 2044 1 1484 Smelt 12 2 11 5 12 2 13 4 2 0904 1 3936 Smelt 13 4 11 7 12 4 13 5 2 43 1 269 Smelt 12 2 12 1 13 13 8 2 277 1 2558 Smelt 19 7 13 2 14 3 15 2 2 8728 2 0672 Smelt 19 9 13 8 15 16 2 2 9322 1 8792

Question: Fit a predictive linear regression model to estimate weight of the fish from its length (length1, length2, length3), height and width using the data source

Fit a predictive linear regression model to estimate weight of the fish from its length (length1, length2, length3), height and width using the data source fish.xls provided to you. Use only 70% of the data as training set (15 points) -Report the coefficients values by using the standard Least Square Estimates -What is the standard error of the estimated coefficients, R-squared term, and the 95% confidence interval? -Is there any dependence between the length and weight of the fish?

Q2 Using the data source in Q1(only 70% of the data points as training set), fit the Ridge and Lasso Regression Models (15 points) - Report the coefficients for both the models. - Report the attribute(s) least impacting the weight of the fish. Justify your answer.

Q3 Using remaining 30% of the data in Q1 first , test the trained regression models in Q1 and Q2 and report their performance (model accuracy) using MSE (mean square error) and R-squared metrics. Which model is performing the best? Explain your answer. (20 points)

fish.xls file is below as text format

Species	Weight	Length1	Length2	Length3	Height	Width
Bream	242	23.2	25.4	30	11.52	4.02
Bream	290	24	26.3	31.2	12.48	4.3056
Bream	340	23.9	26.5	31.1	12.3778	4.6961
Bream	363	26.3	29	33.5	12.73	4.4555
Bream	430	26.5	29	34	12.444	5.134
Bream	450	26.8	29.7	34.7	13.6024	4.9274
Bream	500	26.8	29.7	34.5	14.1795	5.2785
Bream	390	27.6	30	35	12.67	4.69
Bream	450	27.6	30	35.1	14.0049	4.8438
Bream	500	28.5	30.7	36.2	14.2266	4.9594
Bream	475	28.4	31	36.2	14.2628	5.1042
Bream	500	28.7	31	36.2	14.3714	4.8146
Bream	500	29.1	31.5	36.4	13.7592	4.368
Bream	340	29.5	32	37.3	13.9129	5.0728
Bream	600	29.4	32	37.2	14.9544	5.1708
Bream	600	29.4	32	37.2	15.438	5.58
Bream	700	30.4	33	38.3	14.8604	5.2854
Bream	700	30.4	33	38.5	14.938	5.1975
Bream	610	30.9	33.5	38.6	15.633	5.1338
Bream	650	31	33.5	38.7	14.4738	5.7276
Bream	575	31.3	34	39.5	15.1285	5.5695
Bream	685	31.4	34	39.2	15.9936	5.3704
Bream	620	31.5	34.5	39.7	15.5227	5.2801
Bream	680	31.8	35	40.6	15.4686	6.1306
Bream	700	31.9	35	40.5	16.2405	5.589
Bream	725	31.8	35	40.9	16.36	6.0532
Bream	720	32	35	40.6	16.3618	6.09
Bream	714	32.7	36	41.5	16.517	5.8515
Bream	850	32.8	36	41.6	16.8896	6.1984
Bream	1000	33.5	37	42.6	18.957	6.603
Bream	920	35	38.5	44.1	18.0369	6.3063
Bream	955	35	38.5	44	18.084	6.292
Bream	925	36.2	39.5	45.3	18.7542	6.7497
Bream	975	37.4	41	45.9	18.6354	6.7473
Bream	950	38	41	46.5	17.6235	6.3705
Roach	40	12.9	14.1	16.2	4.1472	2.268
Roach	69	16.5	18.2	20.3	5.2983	2.8217
Roach	78	17.5	18.8	21.2	5.5756	2.9044
Roach	87	18.2	19.8	22.2	5.6166	3.1746
Roach	120	18.6	20	22.2	6.216	3.5742
Roach	0	19	20.5	22.8	6.4752	3.3516
Roach	110	19.1	20.8	23.1	6.1677	3.3957
Roach	120	19.4	21	23.7	6.1146	3.2943
Roach	150	20.4	22	24.7	5.8045	3.7544
Roach	145	20.5	22	24.3	6.6339	3.5478
Roach	160	20.5	22.5	25.3	7.0334	3.8203
Roach	140	21	22.5	25	6.55	3.325
Roach	160	21.1	22.5	25	6.4	3.8
Roach	169	22	24	27.2	7.5344	3.8352
Roach	161	22	23.4	26.7	6.9153	3.6312
Roach	200	22.1	23.5	26.8	7.3968	4.1272
Roach	180	23.6	25.2	27.9	7.0866	3.906
Roach	290	24	26	29.2	8.8768	4.4968
Roach	272	25	27	30.6	8.568	4.7736
Roach	390	29.5	31.7	35	9.485	5.355
Whitefish	270	23.6	26	28.7	8.3804	4.2476
Whitefish	270	24.1	26.5	29.3	8.1454	4.2485
Whitefish	306	25.6	28	30.8	8.778	4.6816
Whitefish	540	28.5	31	34	10.744	6.562
Whitefish	800	33.7	36.4	39.6	11.7612	6.5736
Whitefish	1000	37.3	40	43.5	12.354	6.525
Parkki	55	13.5	14.7	16.5	6.8475	2.3265
Parkki	60	14.3	15.5	17.4	6.5772	2.3142
Parkki	90	16.3	17.7	19.8	7.4052	2.673
Parkki	120	17.5	19	21.3	8.3922	2.9181
Parkki	150	18.4	20	22.4	8.8928	3.2928
Parkki	140	19	20.7	23.2	8.5376	3.2944
Parkki	170	19	20.7	23.2	9.396	3.4104
Parkki	145	19.8	21.5	24.1	9.7364	3.1571
Parkki	200	21.2	23	25.8	10.3458	3.6636
Parkki	273	23	25	28	11.088	4.144
Parkki	300	24	26	29	11.368	4.234
Perch	5.9	7.5	8.4	8.8	2.112	1.408
Perch	32	12.5	13.7	14.7	3.528	1.9992
Perch	40	13.8	15	16	3.824	2.432
Perch	51.5	15	16.2	17.2	4.5924	2.6316
Perch	70	15.7	17.4	18.5	4.588	2.9415
Perch	100	16.2	18	19.2	5.2224	3.3216
Perch	78	16.8	18.7	19.4	5.1992	3.1234
Perch	80	17.2	19	20.2	5.6358	3.0502
Perch	85	17.8	19.6	20.8	5.1376	3.0368
Perch	85	18.2	20	21	5.082	2.772
Perch	110	19	21	22.5	5.6925	3.555
Perch	115	19	21	22.5	5.9175	3.3075
Perch	125	19	21	22.5	5.6925	3.6675
Perch	130	19.3	21.3	22.8	6.384	3.534
Perch	120	20	22	23.5	6.11	3.4075
Perch	120	20	22	23.5	5.64	3.525
Perch	130	20	22	23.5	6.11	3.525
Perch	135	20	22	23.5	5.875	3.525
Perch	110	20	22	23.5	5.5225	3.995
Perch	130	20.5	22.5	24	5.856	3.624
Perch	150	20.5	22.5	24	6.792	3.624
Perch	145	20.7	22.7	24.2	5.9532	3.63
Perch	150	21	23	24.5	5.2185	3.626
Perch	170	21.5	23.5	25	6.275	3.725
Perch	225	22	24	25.5	7.293	3.723
Perch	145	22	24	25.5	6.375	3.825
Perch	188	22.6	24.6	26.2	6.7334	4.1658
Perch	180	23	25	26.5	6.4395	3.6835
Perch	197	23.5	25.6	27	6.561	4.239
Perch	218	25	26.5	28	7.168	4.144
Perch	300	25.2	27.3	28.7	8.323	5.1373
Perch	260	25.4	27.5	28.9	7.1672	4.335
Perch	265	25.4	27.5	28.9	7.0516	4.335
Perch	250	25.4	27.5	28.9	7.2828	4.5662
Perch	250	25.9	28	29.4	7.8204	4.2042
Perch	300	26.9	28.7	30.1	7.5852	4.6354
Perch	320	27.8	30	31.6	7.6156	4.7716
Perch	514	30.5	32.8	34	10.03	6.018
Perch	556	32	34.5	36.5	10.2565	6.3875
Perch	840	32.5	35	37.3	11.4884	7.7957
Perch	685	34	36.5	39	10.881	6.864
Perch	700	34	36	38.3	10.6091	6.7408
Perch	700	34.5	37	39.4	10.835	6.2646
Perch	690	34.6	37	39.3	10.5717	6.3666
Perch	900	36.5	39	41.4	11.1366	7.4934
Perch	650	36.5	39	41.4	11.1366	6.003
Perch	820	36.6	39	41.3	12.4313	7.3514
Perch	850	36.9	40	42.3	11.9286	7.1064
Perch	900	37	40	42.5	11.73	7.225
Perch	1015	37	40	42.4	12.3808	7.4624
Perch	820	37.1	40	42.5	11.135	6.63
Perch	1100	39	42	44.6	12.8002	6.8684
Perch	1000	39.8	43	45.2	11.9328	7.2772
Perch	1100	40.1	43	45.5	12.5125	7.4165
Perch	1000	40.2	43.5	46	12.604	8.142
Perch	1000	41.1	44	46.6	12.4888	7.5958
Pike	200	30	32.3	34.8	5.568	3.3756
Pike	300	31.7	34	37.8	5.7078	4.158
Pike	300	32.7	35	38.8	5.9364	4.3844
Pike	300	34.8	37.3	39.8	6.2884	4.0198
Pike	430	35.5	38	40.5	7.29	4.5765
Pike	345	36	38.5	41	6.396	3.977
Pike	456	40	42.5	45.5	7.28	4.3225
Pike	510	40	42.5	45.5	6.825	4.459
Pike	540	40.1	43	45.8	7.786	5.1296
Pike	500	42	45	48	6.96	4.896
Pike	567	43.2	46	48.7	7.792	4.87
Pike	770	44.8	48	51.2	7.68	5.376
Pike	950	48.3	51.7	55.1	8.9262	6.1712
Pike	1250	52	56	59.7	10.6863	6.9849
Pike	1600	56	60	64	9.6	6.144
Pike	1550	56	60	64	9.6	6.144
Pike	1650	59	63.4	68	10.812	7.48
Smelt	6.7	9.3	9.8	10.8	1.7388	1.0476
Smelt	7.5	10	10.5	11.6	1.972	1.16
Smelt	7	10.1	10.6	11.6	1.7284	1.1484
Smelt	9.7	10.4	11	12	2.196	1.38
Smelt	9.8	10.7	11.2	12.4	2.0832	1.2772
Smelt	8.7	10.8	11.3	12.6	1.9782	1.2852
Smelt	10	11.3	11.8	13.1	2.2139	1.2838
Smelt	9.9	11.3	11.8	13.1	2.2139	1.1659
Smelt	9.8	11.4	12	13.2	2.2044	1.1484
Smelt	12.2	11.5	12.2	13.4	2.0904	1.3936
Smelt	13.4	11.7	12.4	13.5	2.43	1.269
Smelt	12.2	12.1	13	13.8	2.277	1.2558
Smelt	19.7	13.2	14.3	15.2	2.8728	2.0672
Smelt	19.9	13.8	15	16.2	2.9322	1.8792

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