Comparing the three regression results, which X variable explains Y the best?(0.5 mark). Why that is the case?[Note: you may link it with market efficiency](1 mark)

22. US monetary policy can be measured by changes in the Federal funds rate, which are announced by the Federal Open Market Committee (FOMC) meetings. Given the importance of monetary policy to the whole economy, investors pay special attention to the FOMC announcements. We have collected data on FOMC announcements from 1989 to 2007 and the aggregate stock market reactions to it. Here is a list of variables: . Return: S&P 500 index return on the announcement date (in percentage) . Total change: change of Federal fund rate (in bps) - Expected: investors' expected change of Federal fund rate, which is estimated based on the futures contracts written on the Federal fund rate (in bps) - Surprise: the difference between Total change and Expected, which measures the change that is out of expectation of investors (in bps) - Scheduled: equals to 1 if the FOMC is scheduled, and 0 if not. With this dataset, we have run three separate regressions: In the first regression, Y is Return, X is Total change; In the second regression, Y is Return, X is Expected; In the third regression, Y is Return, X is Surprise. The results are presented as below: Return Regression Model 1 Regression Model 2 Re total.change -0.57721 (0.37161) expected 0.2531 (0.4536) surprise Constant 0.26826** 0.2855*** (0.08162) (0.0814) Observations 171 171 R-squared 0.01408 0.001839 Adjusted R-squared 0.008241 -0.004067 Residual Standard Error 1.058 (df-169) 1.064 (df=169) F-statistic 2.413 (df =1; 169) 0.3114 (df-=1; 169) 26 Note *p