119. A sample of n  20 companies was selected, and the values of y  stock price and k  15 predictor variables (such as quarterly dividend, previous year s earnings, and debt ratio) were determined.

When the multiple regression model using these 15 predictors was t to the data, R2  .90 resulted.

a. Does the model appear to specify a useful relationship between y and the predictor variables?

Carry out a test using signi cance 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 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 signi cance?