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, computeSSxx,SSyyS S_{x x}, S S_{y y}, andSSxyS 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$ y^\hat{y}=a+b x$.

d. Give a brief interpretation of the valuesaaandbbcalculated in part$ $\mathrm{c}.

e. Compute the correlation coefficientrr.

f. Predict the change in a stock's price if8.6%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.


Answered 1 year ago
Answered 1 year ago
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Part a):

The values of the sum of squares SSxxSS_{xx}, SSyySS_{yy}, and SSxySS_{xy} for the sample data are given by

SSxx=x2(x)2nSSyy=y2(y)2nSSxy=xy(x)(y)n\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 xx is the value of the independent variable, yy is the value of the dependent variable, and nn is the sample size.

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