Collinearity is sometimes described as a problem with the data, not the model. R
ID: 3311346 • Letter: C
Question
Collinearity is sometimes described as a problem with the data, not the model. Rather than having data that fill the scatterplot of x, on x2, the data concentrate along a diagonal. For example, the plot to the right shows monthly percentage changes in the whole stock market and a certain stock index. The data span the period running from 1994 through 2002. Complete parts (a) through (c). 5- 0 5- 10 .2 0- 20 15 -10 -5 Market % Change (a) Data for two months (November and December of 1996) deviate from the pattern evident in other months. What makes these months unusual? O A. In both months the entire market had greater returns than the specific index. B. In one of the two months the entire market had greater returns than the specific index. The opposite happened in the other month O C. In both months the specific index had greater returns than the entire market. (b) If you were to use both returns on the market and those on the individual index as explanatory variables in the same regression, are these two months leveraged? O A. Yes. These months are different combinations of the two explanatory variables O B. No. These months are different combinations of the two explanatory variables. O C. No. The leverage of these months in such a regression would cancel each other out. O D. The month that is more of an outlier is leveraged, but the other is not. (c) Would you want to use these months in the regression or exclude these from the multiple regression? O A. O B. C. These months should not be used in the regression in order to reduce the correlation between the explanatory variables. These months should not be used in the regression because they are outliers. These months should be used in the regression because hese points re uce the corre ation between the ex ara to variablesExplanation / Answer
(a) These months are unusual because in one of the two
months the entire market had greater returns than the specific
index. The opposite happened in the other month.
Hence, Option (B) is the correct choice. (Ans).
(b) These two months are not leveraged, as these two months
are different combinations of the two explanatory variables.
Hence, Option (B) is the correct choice. (Ans).
(c) We should not exclude these two months from multiple
linear regression, as, these points reduce correlation between
explanatory variables. Hence, Option (C) is the correct choice.
(Ans).