NO.PZ2023040502000027
问题如下：
Charlent regresses monthly total returns of the
Bangkok SET Index on one-month Libor (for a US dollar–denominated contract).
The period of the study is from July 2006 to December 2013. To improve the
statistical validity of the variables, for both the SET Index and Libor, Charlent
uses the natural logarithms of one plus the monthly returns in the regression
calculation.
Charlent next regresses the natural logarithm of one plus the SET Index monthly returns on the natural logarithm of one plus Libor, the natural logarithm of one plus the effective Fed funds rate, and the $/£ exchange rate. The results are reported in the following Exhibit.
Then report the pairwise
correlations of the variables used in the second regression.
Geoffrey
Small states that the highly significant F-statistic of the second regression
along with the increased R2 of the second
regression means that the addition of the Fed funds rate and the $/£ exchange
rate to the analysis provides more reliable estimates of linear associations
than the first regression.
Regarding Geoffrey Small’s statement about the
second regression, which of the following is most accurate?
选项：
A.It is true that the second regression has
substantially greater explanatory power than the first regression.
The second regression displays multicollinearity.
The F-statistic of the second regression is likely
underestimated.
解释：
The high pairwise
correlations of Exhibit 5, especially the correlation between Libor and Fed
funds, suggest a multicollinearity problem. In the presence of
multicollinearity, R2s and F-statistics are overstated, and
estimates of the coefficients become extremely imprecise and unreliable.
1、本题我有一个疑惑的点，就是对于第二个模型，确实adjusted R^2变大的，两个模型的样本量也相同，所以其实解释力度是提高了的，那么A为什么是错的？
2、我自己的理解是由于多重共线，所以无法判断x对Y的实际影响，导致R^2和AR^2是不准确的，可以这么理解吗？
3、如果我的理解没有错，更进一步，异方差、序列相关是否也有类似的性质？
