Use the data on annual catch of Gulf Menhaden, number of fishing vessels, and fishing effort. (a) Complete the analysis of variance for the regression of catch (Y) on fishing effort (X 1 ) and number...

(a) Complete the analysis of variance for the regression of catch (Y) on fishing effort (X₁) and number of vessels (X₂) with an intercept in the model. Determine the partial sums of squares for each independent variable. Estimate the standard errors for the regression coefficients and construct the Bonferroni confidence intervals for each using a joint confidence coefficient of 95%. Use the regression equation to predict the “catch” if number of vessels is limited to X₂
= 70 and fishing effort is restricted to X₁
= 400. Compute the variance of this prediction and the 95% confidence interval estimate of the prediction.

(b) Test the hypothesis that the variable “number of vessels” does not add significantly to the explanation of variation in “catch” provided by “fishing effort” alone (use α = .05). Test the hypothesis that “fishing effort” does not add significantly to the explanation provided by “number of vessels” alone.

(c) On the basis of the tests in Part (b) would you keep both X₁
and X₂
in the model, or would you eliminate one from the model? If one should be eliminated, which would it be? Does the remaining variable make a significant contribution to explaining the variation in “catch”?

(d) Suppose consideration is being given to controlling the annual catch by limiting either the number of fishing vessels or the total fishing effort. What is your recommendation and why?