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Software millionaires and birthdays. In Outliers: The
Chapter 11, Problem 19E(choose chapter or problem)
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.
Data for Exercise 11.19
\(\begin{array}{cccc} \hline \text { Decade } & \begin{array}{c} \text { Total U.S. Births } \\ \text { (millions) } \end{array} & \begin{array}{c}
\text { Number of Software } \\ \text { Millionaire Birthdays } \end{array} & \begin{array}{c} \text { Number of CEO Birthdays (in a random sample } \\ \text { of } 70 \text { companies from the Fortune } 500 \text { list) } \end{array} \\ \hline 1920 & 28.582 & 3 & 2 \\ 1930 & 24.374 & 1 & 2 \\ 1940 & 31.666 & 10 & 23 \\ 1950 & 40.530 & 14 & 38 \\ 1960 & 38.808 & 7 & 9 \\ 1970 & 33.309 & 4 & 0 \\ \hline \end{array}\)
Source: Sauro, J. “Were most software millionaires born around 1955?” Measuring Usability, November 17, 2010. Copyright © 2010 by Measuring Usability LLC. Reprinted with permission.
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 where the number of CEO birthdays (from a random sample of 70 companies) is 10.
Questions & Answers
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QUESTION:
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.
Data for Exercise 11.19
\(\begin{array}{cccc} \hline \text { Decade } & \begin{array}{c} \text { Total U.S. Births } \\ \text { (millions) } \end{array} & \begin{array}{c}
\text { Number of Software } \\ \text { Millionaire Birthdays } \end{array} & \begin{array}{c} \text { Number of CEO Birthdays (in a random sample } \\ \text { of } 70 \text { companies from the Fortune } 500 \text { list) } \end{array} \\ \hline 1920 & 28.582 & 3 & 2 \\ 1930 & 24.374 & 1 & 2 \\ 1940 & 31.666 & 10 & 23 \\ 1950 & 40.530 & 14 & 38 \\ 1960 & 38.808 & 7 & 9 \\ 1970 & 33.309 & 4 & 0 \\ \hline \end{array}\)
Source: Sauro, J. “Were most software millionaires born around 1955?” Measuring Usability, November 17, 2010. Copyright © 2010 by Measuring Usability LLC. Reprinted with permission.
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 where the number of CEO birthdays (from a random sample of 70 companies) is 10.
ANSWER:Step 1 of 15
a)
Obtain a fitted linear regression model.
The equation of a straight-line model relating the number (y) of software millionaire birthdays in a decade to the total number (x) of U.S. births is given below:
\(y=\beta_{0}+\beta_{1} x+\varepsilon\)
Where, y = response variable (Millionaire births)
x = explanatory variable (Total births)
\(\beta_{0}=\) y-intercept
\(\beta_{1}=\) slope of the line
\(\varepsilon=\) random error component
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