In Chapter 16, Exercise 53 predicted the annual value of the Maine lobster industry catch from the number of licensed lobser fishers. The lobster industry is an important one in Maine, with annual landings worth about $300,000,000 and employment consequences that extend throughout the state€™s economy. We saw in Chapter 16 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). The predictors are number of Traps (millions), number of licensed Fishers, and Pounds/Trap during the years 1957 to 2012.
Dependent variable is: LogValue
R squared = 97.5% R squared (adjusted) = 97.4%
s = 0.0801 with 56 - 4 = 52 degrees of freedom

a) Write the regression model.
b) Are the assumptions and conditions met?
c) Interpret the coefficient of Fishers. 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?

Source Residual Variable Coeff Sum of Squares df Mean Square F-ratio 690.108 Regression 13.2861 3 4.4287 52 0.00642 0.33370 SE(Coeff) t ratio P-value 9.77