In a study of several companies going public for the first time, a researcher is

Question

In a study of several companies going public for the first time, a researcher is particularly interested in the relationship between the size of the offering and the price per share. A sample of 15 companies that recently went public revealed the following estimated regression equation: Conduct a test to determine whether the slope of the regression line is zero (let alpha =0.05). Determine the coefficient of determination. Do you think the researcher should be satisfied with using the size of the offering as the independent variable?

Explanation / Answer

a)

Using technology, we get the correlation,              
              
r =    0.466060917          
              
              
As t = r sqrt [(n - 2) / (1 - r^2)], then              
              
t =    1.899295317          
              
As alpha =    0.05          

df = n -2 =    13          
              
Then              
              
tcrit =    2.160368656          
              
As t < 2.16, then there is no significant evidence that the slope of the regression line is not zero. [CONCLUSION]

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b)  

Thus, the coefficient of determination is                      
r^2 =    0.217212778          

As only 21.72% of the variation in y is explained by x, then I think the researcher would not be happy.

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