Consider a sample comprised of firm s that were targets of tender offers during the period 1978- 1985. Conduct an analysis where the response variable represents the number of bids (Bids) received prior to the takeover of the firm. The explanatory variables include the bid premium (Premium) and firm size (Size). It is generally believed that a high initial bid premium, defined as the percentage excess of the firm's stock price, would deter subsequent bids. Moreover, while tender offers for large firms are likely to receive more media coverage and thereby attract the attention of opportunistic bidders, it also is a wealth constraint to potential bidders. A portion of the data is shown in the accompanying table; see the text website for the complete data set, labeled Bids.
a. Estimate the model, Bids = β0 + β1 Premium + β2 Size + β2 Size2 + 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?