Data:

FisheryID	Biomass	Metal	Species	Area
1	458	0.081	11	147
2	395	0.755	11	167
3	443	0.341	7	203
4	511	0.388	8	218
5	375	0.355	10	176
6	513	0.303	14	166
7	374	0.685	5	144
8	541	0.399	10	183
9	338	0.424	14	160
10	400	0.499	11	161
11	414	0.344	8	143
12	371	0.373	12	145
13	430	0.498	12	150
14	432	0.333	9	167
15	452	0.322	12	157
16	457	0.844	8	187
17	368	0.612	10	151
18	527	0.161	7	205
19	440	0.518	10	183
20	410	0.773	10	170
21	406	0.366	11	145
22	577	0.332	11	176
23	377	0.325	12	154
24	423	0.359	15	155
25	349	0.313	7	133
26	538	0.087	6	182
27	338	0.504	10	148
28	408	0.211	6	156
29	389	0.661	10	136

Consider the explanatory variables [heavy metal concentration (Metal - measured in mg/g), number of fish species in the fishery (Species), and the area of the fishery (Area - measured in acres)] and use them to attempt to predict a fishery's total biomass (Biomass - measured in g/m2). The data set is included on Blackboard as Fisheries.csv. It includes a random sample of 29 wild fisheries.

Run simple linear regression analysis using Area as the explanatory and Biomass as the response variable. Use it to answer all the questions below.

1. Produce a residual plot and a normal probability plot of the residuals. Copy and paste them into your document. Report t-test
2. Discuss any violations of the model assumptions using the graphs from part

c. Is it meaningful to interpret the y-intercept in this problem? Why or why not?

d. Interpret the slope of the regression line (in context of this data set).

e. Report the 95% confidence interval for the slope.

f. Test whether the slope is significant using a significance level of 0.05. State the null and alternative hypotheses, the test statistic, and the p-value. Make a decision in terms of the problem.

g. State and interpret the coefficient of determination.

h. Predict the Biomass of a fishery that is 165 acres. Show your calculations.

i) Produce a 95% confidence interval for the mean Biomass of all 165 acre fisheries.

j) Produce a 95% prediction interval for the Biomass of a single 165 acre fishery.

k) Predict the Biomass of a fishery that is 215 acres. Show your calculations.

l) Produce a 95% confidence interval for the mean Biomass of all 215 acre fisheries.

m) Produce a 95% prediction interval for the Biomass of a single 215 acre fishery.

n) Compare the confidence intervals in parts i) and j). Which has the smallest width? Is this surprising? Why or why not?