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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

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.

a. Produce a residual plot and a normal probability plot of the residuals. Copy and paste them into your document.

b. 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?

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