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 + X1 + B,X2 + B3X3 + B.X4+U, the estimate we get for 8, is what we would have obtained by regressing Y on the part of X, that has nothing to do with X2, X3, X4, and U. 2 2. In a OLS output ý=.5+1.2log(x), 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.c. the fraction of those in the labor force who are unemployed) is an example of a continuous random variable. 5. The mull 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

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@ The answer is true. This is exactly what the frisch- waugh - Lovell the stem states. It gives a Proof of how the same estimate for B. . Can be detor obtained by using the residual segrersion analysis as mentioned in the question 9 - 0.5 +1.2104 (0) d drogx d 1.2 - 1.2 dx 7 1.2 dý da 100 x 100 0.012 dy lilher drix -X100 dy to chang in a The Interprelation: 2:of slope coefficient is 0.012 1100 14 increase unit increases in y due to in x. Given interpretation is NOT TRUE

an any value between its minimum value it monimu The answer false is alucys close to As an unbiased estimator the true parameter we always prefer an unbiase d estimaton as it contains Zeno bias. True That the rate of unemployment is an example of continuous random variable .if variable can take any value, it is called a continuous variable in case of vrate of unemployment in Calgary it con take value from o to 100 Hence, A continuous variable which can take on an uncountable set of value is one This statement is true If a null hypothesis is true and if we reject it after a hypothesis test. it means that we are certain that null hypothesis is false.