Lobsters 2016, revisited. In Chapter 17, Exercise 53 predicted the annual value of the Maine lobster industry catch from the number of licensed lobster fishers. The lobster industry is an important one in Maine, with annual landings worth more than $500,000,000 and employment consequences that extend throughout the state’s economy.

We saw in Chapter 17 that it was best to transform Value by logarithms. Here’s a more sophisticated multiple regression to predict the logValue from other variables published by the Maine Department of Marine Resources (maine

.gov/dmr/commercial-fishing/landings/documents/lobster

.table.pdf). The predictors are number of Traps (millions), number of licensed Fishers, and Pounds/Trap during the years 1950 to 2016. (If you wish to replicate this regression in your statistics package, you have to compute Pounds(M)/

Traps(M) as the third predictor variable.)

Response variable is: LogValue R squared = 96.9% R squared (adjusted) = 96.8%

s = 0.1036 with 67 - 4 = 63 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept 6.73738 0.1057 63.7 60.0001 Traps(M) 0.607250 0.0138 43.9 60.0001 License holders

-0.000042 0.0000

-3.47 0.0010 Pounds/Trap 0.000474 0.0013 3.64 0.0006

a) Write the regression model.

b) Are the assumptions and conditions met?

c) Interpret the coefficient of License Holders. Would you expect that restricting the number of lobstering licenses to even fewer fishers would increase the value of the harvest?

d) State and test the standard null hypothesis for the coefficient of Pounds/Trap. Scientists claim that this is an important predictor of the harvest. Do you agree?

Transcribed Image Text:

Residuals Residuals 0.250 0.125- 0.000+ -0.125- 0.250+ 0.125 0.000 -0.125 7.2 7.6 8.0 8.4 Predicted -1.25 0.00 + 1.25 Nscores