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 below.

a. Fit a simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of US births. Give the least squares prediction equation. DIAMND BDAYS Data for Exercise 11.112 Decade Total US Births (millions) Number of Software Millionaire Birthdays Number of CEO Birthdays (in a random sample of 70 companies from the Fortune 500 list) 1920 28.582 3 2 1930 24.374 1 2 1940 31.666 10 23 1950 40.530 14 38 1960 38.808 7 9 1970 33.309 4 0 Source: J. Sauro, “Were Most Software Millionaires Born Around 1955?” Measuring Usability, November 17, 2010. Copyright © 2010 by

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 US 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. g. 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 US births. h. 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 birth days. i. Which of the two models’ fit will have smaller errors of prediction? Why? j. Construct a 95% confidence interval for the slope of the model, E1y2 = b0 + b1x, where x = total number of US births and y = number of software millionaire birthdays. Give a practical interpretation of the interval. k. Construct a 95% confidence interval for the slope of the model, E1y2 = b0 + b1x, where x = number of CEO birthdays (in a sample of 70 companies) and y = number of software millionaire birthdays. Give a practical interpretation of the interval. l. Can you conclude that number of software millionaires born in a decade is linearly related to total number of people born in the United States? Number of CEOs born in the decade? m. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of US births. Interpret the result. n. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to number (x) of CEO birthdays. Interpret the result. o. The consulting statistician argued that the software industry appears to be no different from any other industry with respect to producing millionaires in a decade. Do you agree? Explain. p. 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. q. 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.