For a linear model with a dependent variable Y and two independent variables X1 and X2, write out[1] the objective functions to be minimized for Ridge regression and LASSO regression. Denote b1 and b2 as regression coefficients for X1 and X2 respectively.
(a) Ridge Regression
(b) LASSO

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)