Consider the Following Model $y = \beta _ { 0 } + \beta _ { 1 } x + \mathrm { E } _ { \text {where } } \mathrm { y }$

question 43

Multiple Choice

Consider the following model $y = \beta _ { 0 } + \beta _ { 1 } x + \mathrm { E } _ { \text {where } } \mathrm { y }$ is the daily rate of return of a stock, and $x$ 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 $n = 12$ days from 1980, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of $\hat { \beta } _ { 1 }$ is shown to the right of each least squares prediction equation.
$\begin{array}{llc}\hline \text { Firm } & \text { Estimated Market Model } & \text { Estimated Standard Error of } \beta 1 \\\hline \text { Company A } & y=.0010+1.40 x & .03 \\\text { Company B } & y=.0005-1.21 x & .06 \\\text { Company C } & y=.0010+1.62 x & 1.34 \\\text { Company D } & y=.0013+.76 x & .15 \\\hline\end{array}$

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

• A) Companies B and D only
• B) Company D only
• C) Companies B and C only
• D) Company C only

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