Professor Asimov, continued Refer to the data in Exercise 12.9, relating x, the numb...

Professor Asimov, continued Refer to the data in Exercise 12.9, relating x, the number of books written by Professor Isaac Asimov, to y, the number of months he took to write his books (in increments of 100). The data are reproduced below.

a. Do the data support the hypothesis that β = 0? Use the p-value approach, bounding the p-value using Table 4 of Appendix I. Explain your conclusions in practical terms.

b. Use the ANOVA table in Exercise 12.9, part c, to calculate the coefficient of determination . What percentage reduction in the total variation is achieved by using the linear regression model?

c. Plot the data or refer to the plot in Exercise 12.9, part b. Do the results of parts a and b indicate that the model provides a good fit for the data? Are there any assumptions that may have been violated in fitting the linear model?

Reference:

Professor Asimov Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a 40-year career. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time.1 The data give the time in months required to write his books in increments of 100:

a. Assume that the number of books x and the time in months y are linearly related. Find the least-squares line relating y to x.

b. Plot the time as a function of the number of books written using a scatterplot, and graph the least squares line on the same paper. Does it seem to provide a good fit to the data points?

c. Construct the ANOVA table for the linear regression.