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, debt ratio, and so on) were determined. When the multiple regression model with these 15 predictors was fit 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 at a significance level of .05. (The value 5.86 captures upper-tail area .05 under the F curve with 15 numerator df and 4 denominator df.)
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 here, how large would R2 have to be for the model to be judged useful at the .05 level of significance?
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