A sample of n = 20 companies was selected, and the values of y = stock price and k = 15 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, R2 = .90 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 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?
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