A publishing company is attempting to develop a model that it can use to help predict textbook sales for books it is considering for future publication. The marketing department has collected data on six variables from a random sample of 15 books. These variables are as follows:

Y: Number of Volumes sold (1000s).

X1: Number of Pages.

X2: Number of competing books.

X3: Advertising Budget ($1000s).

X4: Age of the Author.

X5: Production Expenditures ($1000s).

X6: Number of Reviewers.

In addition to these variables, the type of book sold is incorporated in the model. The company produces only three types of books which are: Biology, Statistics, or Physics, as follows:

X7: 1=If a Biology book, 0 otherwise.

X8: 1=If a Statistics book, 0 otherwise.

Regression Analysis: Y versus X1, X2, X3, X4, X5, X6, X7, X8

The regression equation is

Y = - 104 + 0.123 X1 - 0.55 X2 + 1.16 X3 + 1.34 X4 + 0.58 X5 + 1.61 X6 - 20.9 X7 - 29.6 X8

Predictor Coef SE Coef T P VIF

Constant -103.69 37.57 -2.76 0.033

X1 0.12302 0.09192 1.34 0.229 8.4

X2 -0.553 2.864 -0.19 0.853 4.0

X3 1.1649 0.7447 1.56 0.169 4.4

X4 1.3393 0.7707 1.74 0.133 2.0

X5 0.580 1.011 0.57 0.587 15.5

X6 1.613 6.837 0.24 0.821 5.8

X7 -20.95 19.09 -1.10 0.315 2.7

X8 -29.56 16.21 -1.82 0.118 1.6

S = 22.27 R-Sq = 91.9% R-Sq(adj) = 81.0%

Analysis of Variance

Source DF SS MS F P

Regression 8 33671.6 4209.0 8.48 0.009

Residual Error 6 2976.8 496.1

Total 14 36648.4

Durbin-Watson statistic = 2.14

Predicted Values for New Observations

New Obs Fit SE Fit 99.0% CI 99.0% PI

1 51.05 25.40 (-43.10, 145.21) ( -74.19, 176.29)X

X denotes a row with X values away from the center

Values of Predictors for New Observations

New Obs X1 X2 X3 X4 X5 X6 X7 X8

1 204 3.00 30.0 50.0 34.0 6.00 0.0 0.0

From the Minitab outputs above, answer the following questions:

1. How much of the total variation in the number of volumes sold is explained by the variation in these six explanatory variables?

2. Would you conclude that the model is significant at 2.5% level of significance? Explain in detail.

3. Which of the predictors can be concluded to be significant in explaining the variation in the number of the volumes sold? Explain. Using = 0.05.

4. Find 99% C.I. for the regression coefficient of Advertising Budget, and interpret this C.I.

5. Based on your solution in part (e), can you conclude that the Advertising Budget is significant? Why?

Since 0 included in the C.I. the Advertising Budget is not significant

6. Estimate the number of volumes sold for a book with each of the following given information and indicate which book the predicted value is for
7. Find a 99% C.I. for the number of volumes sold for a book with 204 pages, 3 competing books, $30,000 advertising budget, 50 years old of the author, $34,000 production expenses, 6 reviewers, and it is a Physics book.

1) (X1, X2, , X8) = (204, 3, 30000, 50, 34000, 6, 1, 1)
Which book (Biology, Statistics, Physics, or not possible)?
2) (X1, X2, , X8) = (204, 3, 30000, 50, 34000, 6, 0.5, 1)
Which book (Biology, Statistics, Physics, or not possible)?
3) (X1, X2, , X8) = (204, 3, 30000, 50, 34000, 6, 0, 0)
Which book (Biology, Statistics, Physics, or not possible)?