F I L E Consider a sample comprised o f firm s that were targets o f tender offers during the period 1978– 1985. Conduct an analysis where the response variable represents the num ber o f bids (Bids) received prior to the takeover of the firm . The explanatory variables include the bid prem ium (Premium)

and firm size (Size). It is generally believed that a high initial bid prem ium , defined as the percentage excess o f the firm's stock price, w ould deter subsequent bids. Moreover, while tender offers for large firms are likely to receive more media coverage and thereby attract the attention o f opportunistic bidders, it also is a wealth constraint to potential bidders. A portion o f the data is shown in the accompanying table; see the text website for the com plete data set, labeled Bids.

Bids Premium Size (in $ billions)

3 1.1905 0.7668 1 1.0360 0.1625 2 1.0329 3.4751 SOURCE: C o m p u s ta t a n d T he W a ll S tre e t J o u rn a l In d e x .

a. Estimate the model, Bids = β 0+ β1 Premium + β 2Size +

β 2Size2 + ε.

b. Justify the inclusion of the quadratic term in the model.

c. Find the predicted number of bids for a firm that has a bid premium of 1.2 and firm size of $4, 8 , 12, and 16 billion, respectively. What firm size is likely to get the highest number of bids?