1. The daily production of electricity generated by a coal-fired power plant operating in the midwest can be represented as Yj = {Jll~m~JeE;

where Yj = quantity of electricity produced on day i, measured in megawatts, lj = quantity of labor input used on day i, measured in hundreds of hours, mj = units of fossil fuel input on day i, and ej - N(O, 0'2), the e/s being iid.

One hundred days of observations on the levels of inputs used and the quantity of electricity generated were collected. The following information is provided to you by the utility company, where Y. = In(y), and x. is a matrix consisting of a vector of 1 's followed by column vectors corresponding to the natural logarithms of labor and fuel levels.

Y:Y. = 288.93382, [

165.47200] x:y. = 180.32067 , 122.90436

[

.06156 -.05020 -.00177]

(x:x.tl = .09709 -.07284 .

(symmetric) .11537