2. The file hw3_stream.xlsx contains data on the characteristics and macroinvertebrate abundance for a number of sampling locations along streams in Chester County, PA. I have reduced the information in the original data set to contain abundance of three macroinvertebrate groups (mayfly, stonefly and caddisfly) and 9 potential predictor variables.

(a) Perform a normality check on the independent and dependent variables. Are there any that warrant transformation and which transformation would you use? Provide histograms or qq-plots to justify your decision regarding transformations. Make the recommended transformations prior to proceeding to part b.

(b) Run a multivariate regression where mayfly, caddisfly and stonefly abundance are the dependent variables and the other 9 variables are the independent variables. Do not include interaction terms. Provide the output and a summary of the overall model fit (both the individual regressions and the test of the joint distribution) and interpret the estimates of the individual regression coefficients and significance values (p-values). Provide an assessment of whether this regression model provides a good fit to the data - provide any relevant output from your analysis to back-up your assessment.

(c) Plot and interpret the residuals vs. the predicted values from your model. Provide an interpretation of those residual plots.

mayfly	caddisfly	stonefly	SmallStreamIBI	Species_Richness	Shannon_Diversity_Index	TotalHabitatScore	TotalWatershedArea	Pct_developed	Pct_deciduous	Pct_pasture	Pct_rowcrop
8	50	28	54.83	20	2.41	181	2.05	27.3	31.2	17.9	4.8
5	20	10	39.03	21	1.79	137	3.33	30.2	32.1	17.5	3.7
112	13	1	52.92	17	1.98	132	4.77	9.0	19.3	52.4	13.3
93	8	4	52.64	23	1.85	182	11.22	11.9	18.3	44.0	17.6
147	43	2	65.63	22	1.64	189	2.80	8.3	18.8	48.4	16.8
0	30	2	24.96	11	0.92	140	1.12	61.0	9.3	0.0	3.1
0	27	0	25.87	15	1.40	158	4.03	47.8	19.7	3.4	2.7
9	14	0	31.90	15	1.66	169	3.19	42.1	20.8	13.2	6.5
0	10	5	26.67	13	1.48	163	8.50	46.5	13.0	3.1	1.7
1	18	4	34.43	17	1.95	163	8.50	46.5	13.0	3.1	1.7
0	9	2	29.89	14	0.92	183	1.74	36.2	27.6	7.2	1.3
0	9	0	15.28	5	0.76	137	6.61	41.8	14.4	2.8	0.4
0	42	1	24.56	11	1.27	143	3.64	46.9	27.4	5.8	0.6
16	14	120	65.98	22	1.76	143	3.43	16.4	22.2	13.0	16.1
4	25	48	61.57	20	1.97	150	3.17	10.0	23.6	21.0	32.1
5	30	81	62.41	27	2.61	104	1.80	17.7	48.2	18.1	3.2
5	13	0	24.46	13	1.41	160	4.01	31.2	26.7	8.3	5.6
5	32	0	27.79	13	1.67	160	4.01	31.2	26.7	8.3	5.6
25	13	1	30.06	12	1.80	177	2.61	23.1	19.0	2.3	4.0
17	7	0	23.66	10	1.53	161	6.64	31.1	27.5	5.9	4.3
41	5	2	27.57	13	1.39	162	7.05	29.4	28.4	0.9	0.2
30	43	0	26.40	11	1.88	125	11.81	29.8	26.5	5.3	4.7
133	26	16	47.13	19	1.72	168	1.09	34.3	45.4	0.0	0.0
33	5	0	27.77	15	1.72	157	22.82	28.6	28.1	5.0	3.2
8	10	0	28.53	11	1.10	157	2.03	6.6	47.8	7.4	19.7
72	14	12	75.91	28	2.58	156	5.80	6.5	57.6	5.2	11.5
73	55	49	75.10	15	2.18	177	2.08	6.0	70.7	3.4	3.8
75	9	2	47.47	20	2.27	150	10.28	17.2	30.2	18.0	20.4
121	17	5	71.17	27	2.08	170	19.03	7.6	60.9	7.6	8.5
95	18	14	75.11	31	2.58	170	19.03	7.6	60.9	7.6	8.5
70	67	22	83.72	29	2.62	159	2.98	9.6	46.6	18.0	7.8
122	47	22	85.62	31	2.17	161	4.98	9.5	49.3	17.9	6.8
38	2	5	55.54	23	2.44	173	38.70	10.3	51.0	12.3	11.7
50	16	10	66.29	27	2.63	184	47.79	10.2	49.6	14.0	11.0
86	23	13	72.30	28	2.78	161	3.20	10.4	33.2	19.7	16.9
57	30	10	74.56	32	2.61	161	6.52	10.2	40.0	18.9	14.3
6	81	0	44.86	19	2.30	153	1.80	15.3	32.4	15.5	16.6
10	17	2	60.80	17	1.37	162	59.03	10.6	46.4	16.3	11.4
62	42	13	66.94	24	2.47	179	12.28	15.9	36.5	19.3	8.6
22	11	27	80.00	22	2.41	172	62.84	11.0	44.8	17.5	11.3
28	41	45	62.30	24	2.51	161	2.04	38.5	16.9	12.7	2.9
12	64	38	53.30	21	2.49	161	2.04	38.5	16.9	12.7	2.9
57	64	28	67.83	25	2.53	157	2.30	24.3	13.3	30.7	9.8
31	47	13	59.36	20	2.41	168	2.90	15.8	61.6	7.8	1.3
1	115	4	49.48	20	2.25	155	1.18	10.0	33.9	8.1	6.9
0	120	2	44.01	17	2.13	121	0.47	2.3	23.8	20.9	12.5
0	85	0	42.37	17	1.86	161	0.47	2.3	23.8	20.9	12.5
28	22	63	73.00	22	2.52	165	69.08	13.3	42.0	17.2	10.5
3	66	0	46.63	18	1.84	187	2.87	5.2	19.9	34.3	31.8
2	55	10	56.93	22	2.30	160	3.13	27.6	23.5	23.3	17.2
26	60	24	64.43	25	2.62	182	1.18	10.0	33.9	8.1	6.9
3	44	26	50.82	17	2.13	136	3.13	27.6	23.5	23.3	17.2
4	42	0	46.45	15	1.59	128	10.40	13.2	15.9	31.7	26.1
34	50	9	60.07	23	2.14	202	10.40	13.2	15.9	31.7	26.1
14	46	0	40.64	19	2.07	160	3.17	12.0	13.0	28.7	28.1
25	79	19	53.64	24	2.33	159	3.13	27.6	23.5	23.3	17.2
64	51	20	76.16	29	2.60	183	2.90	15.8	61.6	7.8	1.3
1	36	0	34.15	15	1.72	169	3.17	12.0	13.0	28.7	28.1
9	93	0	36.56	20	2.04	135	3.17	12.0	13.0	28.7	28.1
1	5	136	43.22	12	1.00	157	0.28	42.7	5.2	7.9	0.2
8	14	1	35.32	14	1.18	195	40.86	20.1	21.4	26.5	22.3
23	18	15	67.26	22	1.92	163	40.83	20.1	21.4	26.5	22.3
44	52	7	50.85	18	2.30	112	12.95	16.3	35.0	19.7	9.0
73	42	12	61.28	22	2.28	178	7.02	13.4	51.1	12.9	5.9
4	9	0	44.39	12	1.41	163	0.47	2.3	23.8	20.9	12.5
2	94	1	33.84	15	1.94	141	0.47	2.3	23.8	20.9	12.5
5	30	0	36.76	17	1.71	190	3.13	27.6	23.5	23.3	17.2
0	22	2	41.54	14	1.50	155	1.72	16.8	11.4	29.2	36.2
31	24	6	46.02	22	1.96	128	9.85	17.8	13.2	28.6	30.6
23	33	2	48.80	23	2.04	163	3.13	27.6	23.5	23.3	17.2
28	45	6	47.13	15	1.94	166	40.86	20.1	21.4	26.5	22.3
3	28	8	49.85	20	1.95	192	1.18	10.0	33.9	8.1	6.9
1	68	0	26.62	11	1.51	187	3.17	12.0	13.0	28.7	28.1
7	47	0	26.33	12	1.24	151	3.17	12.0	13.0	28.7	28.1
10	90	0	35.05	16	1.73	185	3.17	12.0	13.0	28.7	28.1
0	80	0	23.30	11	1.54	167	9.85	17.8	13.2	28.6	30.6
6	39	0	32.16	16	1.71	142	9.85	17.8	13.2	28.6	30.6
2	67	0	30.14	15	1.88	119	3.17	12.0	13.0	28.7	28.1
41	23	0	47.11	20	2.02	98	1.18	10.0	33.9	8.1	6.9
33	114	0	24.00	10	1.51	143	5.20	39.5	22.3	8.3	2.9
10	67	0	24.24	13	1.33	149	3.46	44.3	26.5	4.1	2.2
23	101	0	34.86	13	2.06	143	3.44	44.4	26.6	4.2	2.3
20	110	0	26.82	13	1.79	128	6.61	41.8	14.4	2.8	0.4
4	65	0	25.83	14	1.72	138	3.27	32.2	7.3	0.9	0.0
5	93	0	25.68	11	1.78	137	1.84	23.5	3.7	1.6	0.0
52	65	1	44.65	18	2.01	158	1.18	10.0	33.9	8.1	6.9
3	100	1	34.70	17	1.99	131	10.23	13.8	19.2	23.2	32.7
13	119	4	36.30	16	1.91	187	5.59	14.6	18.9	25.2	32.6
14	77	9	52.43	18	2.36	167	1.18	10.0	33.9	8.1	6.9
3	100	1	34.06	16	2.16	103	8.03	6.0	11.1	31.9	47.1
3	54	20	41.78	19	1.81	139	2.60	7.5	16.0	36.2	37.0
1	97	1	32.19	15	1.58	141	13.41	7.8	17.3	35.1	34.6
1	88	0	35.80	17	1.86	172	5.82	19.2	10.5	32.3	24.2
2	84	0	38.94	17	2.08	173	5.82	19.2	10.5	32.3	24.2
1	71	0	28.05	15	1.55	173	5.82	19.2	10.5	32.3	24.2
5	90	1	32.92	14	1.73	187	4.25	17.0	7.8	31.9	35.4
3	49	2	31.29	14	1.32	187	4.25	17.0	7.8	31.9	35.4
1	99	2	32.07	13	1.87	172	4.25	17.0	7.8	31.9	35.4
3	119	0	35.32	14	1.79	172	4.25	17.0	7.8	31.9	35.4
1	83	0	37.66	16	1.92	176	5.82	19.2	10.5	32.3	24.2
111	25	21	77.51	30	2.56	179	1.11	14.2	51.0	9.4	13.5
43	8	44	74.50	25	2.28	173	1.14	10.0	72.5	4.1	6.7
61	33	4	54.49	19	2.23	182	1.88	29.3	24.7	21.7	9.6
26	10	0	42.40	15	1.76	173	172.60	8.2	19.1	32.6	31.8
12	11	0	32.06	13	1.34	158	38.31	9.6	20.2	29.6	31.6
0	159	0	23.15	10	1.26	85	1.84	23.5	3.7	1.6	0.0
0	127	0	22.21	9	1.72	121	3.27	32.2	7.3	0.9	0.0
1	187	0	23.11	12	1.10	105	6.35	40.1	14.9	2.9	0.4
5	134	2	45.41	23	2.15	142	2.60	16.0	19.6	34.4	20.1
1	38	0	28.32	12	1.69	140	5.51	6.3	14.9	38.0	33.6
94	55	43	70.53	19	2.21	189	1.76	4.9	33.8	30.8	29.3
14	92	46	82.97	24	2.60	188	1.14	7.0	29.6	24.7	35.9
4	126	1	40.22	17	2.09	138	3.58	5.1	17.6	40.1	32.8
0	59	0	29.47	14	1.88	112	4.15	4.4	12.7	43.7	35.7
2	141	0	26.64	12	1.39	125	6.27	6.4	10.4	54.6	24.4
35	110	1	61.50	24	2.57	193	1.20	7.3	28.2	28.7	30.5
6	106	7	35.54	16	1.90	157	1.05	7.8	18.5	22.2	45.8
3	150	0	32.98	14	1.95	121	1.05	7.8	18.5	22.2	45.8
1	137	0	35.02	13	1.92	121	3.31	9.5	9.2	40.6	33.9
3	115	3	47.47	23	2.34	147	1.04	11.5	10.8	32.6	34.4
25	155	0	33.92	14	1.96	187	4.94	9.4	15.5	37.2	28.7
8	132	0	31.67	13	1.96	184	2.66	42.2	34.7	0.6	0.9
34	91	8	67.48	25	2.52	174	1.71	12.1	59.8	8.5	12.5
27	54	12	59.67	23	2.69	182	31.03	15.4	32.1	16.8	13.0