There is substantial cross-sectional variation in the number of financial analysts who follow a company. Suppose you hypothesize that a company’s size (market cap) and financial risk (debt-to-equity ratios) influence the number of financial analysts who follow a company. You formulate the following regression model:
(Analyst following) i = b0 + b1Size i + b2(D/E) i + ε i
Where
(Analyst following) i = the natural log of (1 + n), where n i is the number of analysts following company i
Size i = the natural log of the market capitalization of company i in millions of dollars
(D/E) i = the debt-to-equity ratio for company i
In the definition of Analyst following, 1 is added to the number of analysts following a company because some companies are not followed by any analysts, and the natural log of 0 is indeterminate. The following table gives the coefficient estimates of the above regression model for a randomly selected sample of 500 companies. The data are for the year 2002.
Coefficient Estimates from Regressing Analyst Following on Size and Debt-to-Equity Ratio
A. Consider two companies, both of which have a debt-to-equity ratio of 0.75. The first company has a market capitalization of $100 million, and the second company has a market capitalization of $1 billion. Based on the above estimates, how many more analysts will follow the second company than the first company?
B. Suppose the p-value reported for the estimated coefficient on (D/E)i is 0.00236. State the interpretation of 0.00236.
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