you are analyzing the variables that explain the returns on the stock of the Boeing Com- pany. Because overall market returns are likely to explain a part of the returns on Boeing, you decide to include the returns on a value-weighted index of all the companies listed on the nySe, aMeX, and naSdaQ as an
you are analyzing the variables that explain the returns on the stock of the Boeing Com- pany. Because overall market returns are likely to explain a part of the returns on Boeing, you decide to include the returns on a value-weighted index of all the companies listed on the nySe, aMeX, and naSdaQ as an independent variable. Further, because Boeing is a large company, you also decide to include the returns on the S&P 500 index, which is a value-weighted index of the larger market-capitalization companies. Finally, you decide to include the changes in the uS dollar’s value. to conduct your test, you have collected the following data for the period 1990–2002.
Rt = monthly return on the stock of Boeing in month t RALLt = monthly return on a value-weighted index of all the companies listed on the nySe, aMeX, and naSdaQ in month t RSPt = monthly return on the S&P 500 index in month t ΔXt = change in month t in the log of a trade-weighted index of the foreign exchange value of the uS dollar against the currencies of a broad group of major uS trading partners The following table shows the output from regressing the monthly return on Boeing stock on the three independent variables.
regression of Boeing returns on Three explanatory Variables: Monthly data, January 1990–december 2002
intercept
RALLt RSPt ΔXt
anoVa
df
total
Coefficient
0.0026 −0.1337 0.8875 0.2005
t-Statistic
0.3939 −0.2150 1.3961 0.3714
MSS
0.0573 0.0059
Standard error
0.0066 0.6219 0.6357 0.5399
SS
regression 3 0.1720 residual 152 0.8947
155 1.0667
residual standard error R-squared observations 156
Source: FactSet, Federal reserve Bank of Philadelphia.
0.0767 0.1610
From the t-statistics, we see that none of the explanatory variables is statistically significant at the 5 percent level or better. you wish to test, however, if the three variables jointly are statistically related to the returns on Boeing. a. your null hypothesis is that all three population slope coefficients equal 0—that the
three variables jointly are statistically not related to the returns on Boeing. Conduct
the appropriate test of that hypothesis. B. examining the regression results, state the regression assumption that may be violated
in this example. explain your answer. C. State a possible way to remedy the violation of the regression assumption identified in
Part B.
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