solution

Software millionaires and birthdays. Refer to Exercise 11.40 (p. 662) and the study of software millionaires and their birthdays. Recall that simple linear regression was used to model number (y) of software millionaire birthdays in a decade as a straight-line function of number () of CEO birthdays.

a. Consider a future decade where the number of CEO birthdays (in a random sample of 70 companies) is 25. Find a 95% prediction interval for the number of software millionaire birthdays in this decade. Interpret the result.

b. Consider another future decade where the number of CEO birthdays (in a random sample of 70 companies) is 10. Will the 95% prediction interval for the number of software millionaire birthdays in this decade be narrower or wider than the interval, part b? Explain.

Exercise 11.40

Software millionaires and birthdays. Refer to Exercise 11.23 (p. 655) and the study of software millionaires and their birthdays. The data are reproduced on p. 663.

a. Find SSE, s2, and s for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of U.S. births.

b. Find SSE, s2, and s for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to number (x) of CEO birthdays.

c. Which of the two models’ fit will have smaller errors of prediction? Why?

Exercise 11.23

Software millionaires and birthdays. In Outliers: The Story of Success (Little, Brown, 2008), the author notes that a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will be successful? On his Web blog (www.measuringusability .com), statistical consultant Jeff Sauro investigated this question by analyzing the data shown in the table on the next page.

a. Fit a simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of U.S. births. Give the least squares prediction equation.

b. Practically interpret the estimated y-intercept and slope of the model, part a.

c. Predict the number of software millionaire birthdays that will occur in a decade where the total number of U.S. births is 35 million.

d. Fit a simple linear regression model relating number (y) of software millionaire birthdays in a decade to number (x) of CEO birthdays. Give the least squares prediction equation.

e. Practically interpret the estimated y-intercept and slope of the model, part d.

f. Predict the number of software millionaire birthdays that will occur in a decade in which the number of CEO  birthdays (from a random sample of 70 companies) is 10.

 
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