Data on per capita consumption of beef, the price of beef, the price of lamb, the price of pork, and per capita disposable income for Australia, for the period 1949-1965, are given in the file "meat". All prices and income have been deflated, with 1953 as the base year. Consider the log-log demand curve.

ln (qb_t) = B₁+ B₂ln (pb_t) + B₃ln (pl_t) + B₄ln (pp_t) + B₅ln (pn_t) + et

qb_tis the per capita consumption of beef in year t (pounds), pb_tis the price of beef in year t (pence per pound), pl_tis the price of lamb in year t (pence per pound) pp_tis the price of pork in year t (pence per pound) pn_tis per capita disposable income in year t (Australian currency pounds)

(a) find computer output of the intercepts and regression using R studio, interpret intercepts b1 and b2

(b) Compute the estimated covariance matrix for the least-squares estimator and the standard errors. (USe R-studio to find this)

(c) Test hypothesis H_0:B2+B3=1 against H₁:B2 + B3 1 at alpha=5%

meat data

qb pn pb pl pp 121.3 355 25.68 20.01 45.74 124.3 380 26.3 18.74 53 131.6 426 30.19 22.45 57.9 118.9 353 33.13 27.11 56.56 119.7 354 31.61 20.69 55.25 114.6 361 30.15 18.89 55.69 116.5 380 32.23 19.16 50.62 119.1 391 31.8 20.1 52.36 128.9 380 30.76 20.6 53.96 125.1 368 32.08 19.46 51.78 117.6 385 33.34 17.9 51.01 98.4 403 36.66 17.86 54.64 85.4 406 39.71 19.14 53.04 93.3 411 37.79 18.03 49.47 100.4 427 38.38 18.82 53.7 104.9 459 39.1 19.04 55.22 98.8 469 39.84 20.63 56.03