This is written and solved ONLY using rStudio. But if you have an easier way to do it, that works:

Information:

The Long Term Resource Monitoring (LTRM) project has been conducting research and monitoring on the Upper Mississippi River System since 1986.

Here is a bit about the LTRM from their website: "Fishes of the Upper Mississippi River System have recreational and commercial value, conservation potential, and can be used to assess the ecological integrity of the aquatic ecosystem.

The objective of the standardized monitoring is to quantify the status and trends of fish populations and communities and identify relations with various other ecological attributes. The findings can be used to address fisheries management concerns.

The Long Term Resource Monitoring element uses a multigear and multihabitat sampling design to collect fish data in six study pools/reaches."

The file fish_data.rda is available at the bottom of the page, It contains length and weight measurements for a sample of 50 fish of four difference species of interest:

BHMW = Bullhead minnow,

BKCP = Black crappie,

BLGL = Bluegill,

BWFN = Bowfin.

Additionally, the file includes the date that the fish was observed.

Load packages

library(tidyverse) library(broom) library(car)

Question 1 (2 pts)

It is standard practice to plot and model the relationship between fish weight and length using a logarithm transformation on both variables. To see the reason for the use of these transformations, we are going to start by fitting a model without any transformation.

Fit a model for predicting weight based on length and species. Include the length by species interaction term. Create and inspect the 4-pack of model diagnostic plots.

What conditions fail based on the 4-pack of plots? Select all that apply.

Group of answer choices

L = Linear

I = Independent errors

N = Normally distributed errors

E = Equal variance of errors

Question 2 (2 pts)

Refit the model from question 1 with a log-transformation applied to both weight and length. Include the log(length) by species interaction term. Again, inspect the diagnostic plots. Call this model fit MOD_interact as we will refer to it later.

Have model conditions improved in comparison to the model based on non-transformed data?

a. Yes, all plots look ideal

b. Yes, there is improvement but there are still some concerns with normality and outliers

c. No, the model conditions look to be violated to the same degree as without the transformations

d. No, the model conditions look to be much worse with the transformations applied

Question 3 (2 pts)

Extract the residuals from your fit model using the residuals() function. Create a scatter plot of your model residuals (y) over time (x=fdate) to assess the assumed independence of model errors. Distinct patterns in the residuals over time (e.g.residuals trending upward over time) suggest a violation of the assumption of independent errors in linear regression.

Do you see any clear patterns in your plot of the residuals over time?

Yes / No

Question 4 (2 pts)

Make a plot that visualizes the interaction - weight on the y-axis (log-scale), length on the x-axis (log-scale), and fishcode showing the categorical predictor variable with a separate line fit for each category. You can do this with geom_abline or with geom_smooth with color/group set in the aes.

What best describes the nature of this interaction?

Group of answer choices

a. The four species seem to have the same slopes (no interaction)

b. The slopes are notably steeper for BLGL and BWFN than for BHMW and BKCP (interaction present)

c. The slope for BWFN is slightly shallower than for the other 3 species (interaction present)

Question 5 (2 pts)

Fit the model with no interaction term. Call this model MOD_additive.

Based on AIC values, which model is better?

Group of answer choices

a. MOD_interact

b. MOD_additive

c. Essentially no difference between the two models (AIC is identical to 3 decimal places)

Question 6 (2 pts)

Based on adjusted R2 values, which model is better?

Group of answer choices

a. MOD_interact

b. MOD_additive

c. Essentially no difference between the two models (adjusted R2 is identical to 3 decimal places)

Question 7 (2 pts)

Carry out a comparative ANOVA test H0: MOD_additive versus H1: MOD_interact. What is the associated p-value? (Fill in the blank, 4 decimal places)

p-value =

Question 8 (2 pts)

Using the interaction model, what is the predicted weight of a blue gill (BLGL) with a length of 100? Be mindful of the log transformation that the model has applied to length and weight. (Fill in the blank, 4 decimal places)

Predicted weight =

Here is the fish_data used in this exercise:

length	weight	fishcode	fdate
74	4	BHMW	2020-07-23
66	3	BHMW	2020-10-06
63	2	BHMW	2020-09-29
42	0.67	BHMW	2020-07-14
66	3	BHMW	2019-08-28
42	0.67	BHMW	2020-07-14
64	2	BHMW	2019-10-25
39	0.53	BHMW	2020-07-14
73	5	BHMW	2019-07-24
69	3	BHMW	2020-08-25
53	1	BHMW	2020-08-25
55	2	BHMW	2020-06-26
48	1.07	BHMW	2020-07-14
48	1	BHMW	2020-07-23
67	3	BHMW	2019-09-10
37	0.43	BHMW	2020-07-14
51	1	BHMW	2018-08-14
43	0.67	BHMW	2020-07-14
55	2	BHMW	2019-08-28
55	1	BHMW	2018-08-14
41	0.59	BHMW	2020-07-14
43	0.68	BHMW	2020-07-14
55	2	BHMW	2019-07-24
38	0.5	BHMW	2020-07-14
58	2	BHMW	2020-08-25
53	1	BHMW	2020-08-25
66	3	BHMW	2020-08-25
52	1	BHMW	2020-08-25
54	2	BHMW	2019-07-24
70	3	BHMW	2020-08-25
55	2	BHMW	2020-08-25
76	5	BHMW	2020-08-25
58	2	BHMW	2018-09-06
49	1	BHMW	2018-08-14
59	1	BHMW	2018-09-06
60	2	BHMW	2020-09-22
54	1	BHMW	2018-07-24
42	0.67	BHMW	2020-07-14
34	0.3	BHMW	2020-08-25
67	3	BHMW	2018-09-06
261	296	BKCP	2011-10-17
187	105	BKCP	1999-09-28
218	144	BKCP	2007-10-04
77	6	BKCP	2010-10-15
232	210	BKCP	1997-09-18
69	3	BKCP	1999-09-23
165	70	BKCP	1999-09-22
270	330	BKCP	1992-10-21
254	263	BKCP	2006-09-22
139	36	BKCP	2009-09-23
144	36	BKCP	2007-10-09
245	275	BKCP	1994-09-29
128	26	BKCP	2016-09-30
302	436	BKCP	1993-09-24
149	48	BKCP	1999-09-21
302	479	BKCP	2020-09-29
270	344	BKCP	1997-10-08
92	11	BKCP	1997-09-19
69	5	BKCP	2013-09-26
123	35	BKCP	1993-09-30
256	249	BKCP	2012-09-21
223	173	BKCP	1996-09-25
285	391	BKCP	2009-09-17
159	55	BKCP	1999-10-20
66	3	BKCP	2007-10-04
166	67	BKCP	2001-09-19
140	39	BKCP	2016-09-30
97	12	BKCP	2007-09-17
209	135	BKCP	2000-09-21
84	7	BKCP	2009-09-24
154	59	BKCP	1995-09-19
103	14	BKCP	2001-10-23
176	78	BKCP	2011-09-22
243	232	BKCP	2004-10-07
298	449	BKCP	2019-10-08
89	9	BKCP	2018-09-25
253	294	BKCP	2001-10-29
281	440	BKCP	2008-09-17
177	82	BKCP	1996-10-08
117	20	BKCP	2014-10-08
52	2	BLGL	2019-09-06
125	41	BLGL	2012-09-25
157	102	BLGL	2016-09-30
50	2	BLGL	2011-10-11
230	263	BLGL	2013-10-16
65	5	BLGL	2010-10-19
130	50	BLGL	2008-10-30
138	47	BLGL	2001-09-18
90	8	BLGL	2009-09-24
191	160	BLGL	2012-09-21
88	12	BLGL	2016-10-24
94	16	BLGL	2020-10-06
53	4	BLGL	2014-10-15
136	47	BLGL	2015-10-20
173	120	BLGL	2001-09-20
49	2	BLGL	2013-09-20
50	2	BLGL	2019-10-08
192	173	BLGL	2016-09-30
115	29	BLGL	2006-10-25
112	30	BLGL	2011-09-22
175	123	BLGL	2009-09-17
81	10	BLGL	1995-10-03
115	47	BLGL	2012-09-25
129	45	BLGL	2019-09-24
93	14	BLGL	2015-10-22
52	2	BLGL	2011-10-03
130	45	BLGL	2018-10-02
175	130	BLGL	2019-09-05
116	38	BLGL	2005-10-12
95	15	BLGL	2006-09-26
93	15	BLGL	2007-09-17
201	210	BLGL	2018-08-28
153	80	BLGL	2003-09-18
96	17	BLGL	2007-10-04
182	134	BLGL	2008-10-01
66	2	BLGL	2005-10-12
68	5	BLGL	2009-10-22
131	48	BLGL	2001-09-18
145	62	BLGL	2012-09-20
233	331	BLGL	2019-09-24
636	2428	BWFN	2020-09-02
204	84	BWFN	2019-08-22
474	1108	BWFN	2020-08-25
562	1449	BWFN	2019-07-09
568	2588	BWFN	2020-06-23
516	1298	BWFN	2020-08-18
608	1965	BWFN	2020-08-19
504	1246	BWFN	2019-08-22
500	1083	BWFN	2020-08-25
547	1404	BWFN	2020-10-02
633	2110	BWFN	2020-07-14
617	1760	BWFN	2020-09-29
632	2138	BWFN	2019-07-03
598	2042	BWFN	2020-07-07
554	1529	BWFN	2020-08-25
583	1766	BWFN	2019-09-24
585	1887	BWFN	2020-07-22
541	1602	BWFN	2019-08-22
545	1412	BWFN	2020-10-02
582	1697	BWFN	2020-10-02
629	2152	BWFN	2019-07-03
501	1048	BWFN	2020-10-02
572	1572	BWFN	2020-10-02
523	1117	BWFN	2020-09-29
603	1924	BWFN	2019-07-03
512	1202	BWFN	2020-08-25
558	1552	BWFN	2020-10-06
592	1908	BWFN	2020-10-02
222	119	BWFN	2019-08-22
637	2563	BWFN	2020-09-22
656	2496	BWFN	2020-07-07
559	1516	BWFN	2020-07-07
518	1225	BWFN	2020-10-02
712	3260	BWFN	2020-10-02
628	2438	BWFN	2020-07-23
531	1418	BWFN	2020-07-07
625	1946	BWFN	2020-08-25
582	1623	BWFN	2019-08-22
577	1729	BWFN	2020-10-02
517	1330	BWFN	2019-07-03