In a study of several companies going public for the first t

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?

Solution

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.