Problem 1 -20ptsConstruct the likelihood function πΏ(π½0,π½1,π2)of:π(ππ,π½0,π½1,π2)=1β2ππ2exp[β12(ππβπ½0βπ½1π₯ππ)2]Where ππ~π(π½0+π½1π₯π,π2)and estimateπ½0,π½1andπ2in ππ=π½0+π½1π₯π+ππ, where ππ~π(0,π2),using the MLE. Compare the least squares estimators with the MLE.Problem 2-20ptsThe marketing department of Coca Colawanted to analyze the relationship between the price of Coke and the demand forit. They were concerned that if they continue increasing the price, people will switch to Pepsi. Calculate π½0Μand π½1Μfor the following data and give interpretation for the results.WeekPriceDemand in quantity117.7647225.3739322.8343417.7649525.3741Problem 3 (20 pts)
In problem 2 test the hypothesis that π½1Μβ 0at 5% level of significance, using the rejection region method. What conclusion you can provide, based on that test.Problem 4(20pts)For the data set in problem 2 construct95% confidence intervals for π½1Μand explain the results. Does the interval include zero, if no explain what does this mean?Problem 5(20pts)Provide a proof that π½1Μis an unbiased estimator for π½1.Bonus question(10pts)Name all of the assumptions that you know for the linear regression model.