Question

Question 2: Indicate whether each of the following statements is true or false and explain concisely why. 1. The Frisch-Waugh-Lovell theorem states that in a multiple linear re- gression Y = Bo + B1X1 + B2X2 + B3X3 + X4 +U, the estimate B1 we get for B1 is what we would have obtained by regressing Y on the part of Xị that has nothing to do with X2, X3, X4, and U. 2 2. In a OLS output ý=.5+1.2log(0), the slope 1.2 is correctly interpreted as “a 1.2 percent increase in x is associated with a 1 unit increase in y, on average." 3. An estimate from an unbiased estimator may be closer to the true parameter, but may also be further away from the true parameter, when compared to an estimate from a biased estimator. 4. The rate of unemployment in Calgary (i.e. the fraction of those in the labor force who are unemployed) is an example of a continuous random variable. 5. The null hypothesis is initially presumed to be true. If we reject it after a hypothesis test, it means we are certain the null hypothesis is false.

Answer 1

Answer- Given that - The Answer is true. This is exactly cohat the frisch- waugh - Lovell theorum states. It gives a proof of how the same estimate for B, can be obtained by using the resdual regression analysis mentioned in the question. as ĝ=0 =0.5+1.210g (30) d - 1.2 2 logx d 1.2 dx d dx X100 12 100 d = 0.012 dx x 100 where da *100 Y. Change inx. The interpretation of slope coefficient is 0.012. unit in y due to ly. increase inx, increase given interpretation is not true. The answer is False. as an unbiased estimator is always close to the true parameter. we always prefer an unbiased estimator as it contains zero bias. 4 ) True. That the rate of of unemployment is an example continuous random variable. if a variable can take on any

value between its minimum value and its maximum value, it is called a continuous variable in case of rate of unema ployment in calgary it can take any value from oto 100- hence, A continuous variable is one which can take on an uncountable set of values.. 5) The above statement is true. If a null hypothesis is true and if we reject it after a hypothesis test it means that coe are certain hypothesis is false that null