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Consider the Following Model y=β0+β1x+Ewhere yy = \beta _ { 0 } + \beta _ { 1 } x + \mathrm { E } _ { \text {where } } \mathrm { y }

question 43

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Consider the following model y=β0+β1x+Ewhere yy = \beta _ { 0 } + \beta _ { 1 } x + \mathrm { E } _ { \text {where } } \mathrm { y } is the daily rate of return of a stock, and xx is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard \& Poor's (S\&P) 500 Composite Index. Using a random sample of n=12n = 12 days from 1980, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of β^1\hat { \beta } _ { 1 } is shown to the right of each least squares prediction equation.
 Firm  Estimated Market Model  Estimated Standard Error of β1 Company A y=.0010+1.40x.03 Company B y=.00051.21x.06 Company C y=.0010+1.62x1.34 Company D y=.0013+.76x.15\begin{array}{llc}\hline \text { Firm } & \text { Estimated Market Model } & \text { Estimated Standard Error of } \beta 1 \\\hline \text { Company A } & y=.0010+1.40 x & .03 \\\text { Company B } & y=.0005-1.21 x & .06 \\\text { Company C } & y=.0010+1.62 x & 1.34 \\\text { Company D } & y=.0013+.76 x & .15 \\\hline\end{array}

For which of the three stocks, Companies B, C, or D, is there evidence (at α=.05\alpha = .05 ) of a positive linear relationship between yy and xx ?


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