## Related questions with answers

The following table provides information on the 10 NASDAQ companies with the largest percentage of their stocks traded on July 6, 2009. Specifically, the table gives the information on the percentage of stocks traded and the change (in dollars per share) in each stock's price.

Stock | Percentage Traded | Change ($) |
---|---|---|

Matrixx | 19.6 | -0.43 |

SpectPh | 14.7 | -1.10 |

DataDom | 12.4 | 0.85 |

CardioNet | 9.3 | -0.11 |

DryShips | 9.0 | -0.42 |

DynMatl | 8.0 | -1.16 |

EvrgrSlr | 7.9 | -0.04 |

EagleBulk | 7.9 | -0.11 |

Palm | 7.8 | -0.02 |

CentAl | 7.4 | -0.57 |

a. With percentage traded as an independent variable and the change in the stock's price as a dependent variable, compute$S S_{x x}, S S_{y y}$, and$S S_{x y}$.

b. Construct a scatter diagram for these data. Does the scatter diagram exhibit a negative linear relationship between the percentage of stock traded and the change in the stock's price?

c. Find the regression equation$ $\hat{y}$=a+b x$.

d. Give a brief interpretation of the values$a$and$b$calculated in part$ $\mathrm{c}.

e. Compute the correlation coefficient$r$.

f. Predict the change in a stock's price if$8.6 \%$ of the stock's shares are traded on a day. Using part b, how reliable do you think this prediction will be? Explain.

Solution

VerifiedPart **a)**:

The values of the sum of squares $SS_{xx}$, $SS_{yy}$, and $SS_{xy}$ for the sample data are given by

$\begin{align*} SS_{xx}&=\sum x^2-\dfrac{(\sum x)^2}{n}\\ SS_{yy}&=\sum y^2-\dfrac{(\sum y)^2}{n}\\ SS_{xy}&=\sum xy-\dfrac{(\sum x)(\sum y)}{n} \end{align*}$

where $x$ is the value of the independent variable, $y$ is the value of the dependent variable, and $n$ is the sample size.

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