A researcher notes that, in a certain region, 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 besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. 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 births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. 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. The coefficient of determination is 3.___? (Round to three decimal places as needed.) This value indicates that 4.___ of the sample variation in number of software millionaire birthdays is explained by the linear relationship with the number of CEO birthdays. (Round to one decimal place as needed.) c. 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. Yes/No, because the coefficient of correlation r=____ indicates that there is a strong/weak positive/negative linear relationship between the number of software millionaire birthdays and the number of CEO birthdays. That is, as the number of software millionaire birthdays increases, the number of CEO birthdays decreases/increases. Therefore, the software industry is/is not unique with respect to producing millionaires in a decade. (Round to three decimal places as needed.)

A researcher notes that, in a certain region, 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 besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. 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 births in the region. Interpret the result. The coefficient of determination is 1._? (Round to three decimal places as needed.) This value indicates that 2. of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. 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. The coefficient of determination is 3._? (Round to three decimal places as needed.) This value indicates that 4._ of the sample variation in number of software millionaire birthdays is explained by the linear relationship with the number of CEO birthdays. (Round to one decimal place as needed.) c. 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. Yes/No, because the coefficient of correlation r=__ indicates that there is a strong/weak positive/negative linear relationship between the number of software millionaire birthdays and the number of CEO birthdays. That is, as the number of software millionaire birthdays increases, the number of CEO birthdays decreases/increases. Therefore, the software industry is/is not unique with respect to producing millionaires in a decade. (Round to three decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 6SGR

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a. 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 births in the region. Interpret the result.

The coefficient of determination is 1.___?

(Round to three decimal places as needed.)

This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the

linear relationship with the total number of births in the region.

(Round to one decimal place as needed.)

b. 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.

The coefficient of determination is

3.___?

(Round to three decimal places as needed.)

This value indicates that 4.___ of the sample variation in number of software millionaire birthdays is explained by the

linear relationship with the number of CEO birthdays.

(Round to one decimal place as needed.)

c. 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.

Yes/No, because the coefficient of correlation r=____

indicates that there is a strong/weak positive/negative linear

relationship between the number of software millionaire birthdays and the number of CEO birthdays. That is, as the number of software millionaire birthdays increases, the number of CEO birthdays decreases/increases. Therefore, the software industry

is/is not unique with respect to producing millionaires in a decade.

(Round to three decimal places as needed.)

**Decade and Birth Data Analysis**

This table presents data detailing the total number of births in millions for a specific region across six decades, alongside statistics concerning the number of birthdays of software millionaires and CEOs from a sample of 70 companies. Each column provides unique insights into demographics and influential individuals over time.

| Decade | Total Births in Region (millions) | Number of Software Millionaire Birthdays | Number of CEO Birthdays (in a random sample of 70 companies) |
|--------|----------------------------------|----------------------------------------|------------------------------------------------------------|
| 1920 | 28.344 | 3 | 1 |
| 1930 | 24.214 | 1 | 5 |
| 1940 | 31.241 | 11 | 21 |
| 1950 | 40.149 | 14 | 37 |
| 1960 | 38.707 | 8 | 6 |
| 1970 | 33.665 | 4 | 0 |

### Discussion:

- **Total Births in Region:** Indicates a fluctuating population growth trend, peaking in the 1950s, which might suggest post-war population booms and subsequent declines.

- **Software Millionaire Birthdays:** Highest occurrences in the 1940s and 1950s, potentially reflecting the emergence and maturation of the software industry in later years.

- **CEO Birthdays:** Peaks in the 1950s suggest a significant number of prominent business leaders were born in this decade, possibly correlating with economic booms and increases in educational opportunities for business leadership during that period.

This analysis demonstrates how birth data can relate to significant socioeconomic trends and the emergence of industry leaders.

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