Lena Pilchard, research associate for Eiffel Investments, is attempting to measure the value added to the Eiffel Investments portfolio from the use of 1-year earnings growth forecasts developed by professional analysts.

Pilchard's supervisor, Edna Wilms, recommends a portfolio allocation strategy that overweights neglected firms. Wilms cites studies of the "neglected firm effect," in which companies followed by a small number of professional analysts are associated with higher returns than firms followed by a larger number of analysts. Wilms considers a company covered by three or fewer analysts to be "neglected."

Pilchard also is aware of research indicating that, on average, stock returns for small firms have been higher than those earned by large firms. Pilchard develops a model to predict stock returns based on analyst coverage, firm size, and analyst growth forecasts. She runs the following cross-sectional regression using data for the 30 stocks included in the Eiffel Investments portfolio:

Ri = b0 + b,COVERAGEi + b2 LN(SIZEi) + b3(FORECASTi) + ei

where:

Ri = the rate of return on stock i

COVERAGEi = one if there are three or fewer analysts covering stock

i, and equals zero otherwise

LN(SIZEi) = the natural logarithm of the market capitalization

(stock price times shares outstanding) for stock i,

units in millions

FORECASTi = the 1-year consensus earnings growth rate forecast for stock i

Pilchard derives the following results from her cross-sectional regression:

The standard error of estimate in Pilchard's regression equals 1.96 and the regression sum of squares equals 400.

Wilrus provides Pilchard with the following values for analyst coverage, firm size, and earnings growth forecast for Eggmann Enterprises, a company that Eiffel Investments is evaluating.

Wilms asks Pilchard to derive the lowest possible value for the coefficient on the FORECAST variable using a 99% confidence interval. The appropriate lower bound for the FORECAST coefficient is closest to;