Company donations to charity. The amount a company donates to a charitable organization is often restricted by financial inflexibility at the firm. One measure of financial inflexibility is the ratio of restricted assets to total firm assets. A study published in the Journal of Management Accounting Research (Vol. 27, 2015) investigated the link between donation amount and this ratio. Data were collected on donations to 115,333 charities over a recent 10-year period, resulting in a sample of 419,225 firm-years. The researchers fit the quadratic model, E1y2 = b0 + b1x + b2x2 , where y = natural logarithm of total donations to charity by a firm in a year and x = ratio of restricted assets to the firm’s total assets in the previous year. [Note: This model is a simplified version of the actual model fit by the researchers.]

a. The researchers’ theory is that as a firm’s restricted assets increase, donations will initially increase. However, there is a point at which donations will not only diminish, but also decline as restricted assets increase. How should the researchers use the model to test this theory?

b. The results of the multiple regression are shown in the table below. Use this information to test the researchers’ theory at a = .01. What do you conclude? bn 0 = 11.24 bn 1 = .365 bn 2 = -.279 R2 adj = .833 sbn0 = .017 sbn1 = .033 sbn2 = .039 n = 419,225