A sample of companies was selected, and the values of price and variables (such as quarterly dividend, previous year’s earnings, and debt ratio) were determined. When the multiple regression model using these 15 predictors was fit to the data, resulted.

a. Does the model appear to specify a useful relationship between y and the predictor variables? Carry out a test using significance level .05. [Hint: The F critical value for 15 numerator and 4 denominator df is 5.86.]

b. Based on the result of part (a), does a high R2 value by itself imply that a model is useful? Under what R2 5 .90 y 5 stock k 5 15 n 5 20 Rk 2

Rk 2

xi xj xj 2

Rk 2

Bibliography 593 circumstances might you be suspicious of a model with a high R2 value?

c. With n and k as given previously, how large would R2 have to be for the model to be judged useful at the .05 level of significance?