Question

In: Statistics and Probability

A researcher notes that, in a certain country, a disproportionate number of software millionaires were born...

A researcher notes that, in a certain country, 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? The researcher investigated this question by analyzing the data shown in the accompanying table.

Decade	Total_Births_in_Country_(millions)	Number_of_Software_Millionaire_Birthdays	Number_ of_CEO_Birthdays_(in_a_random_sample_of_70_companies)
1920	28.365	2	3
1930	24.207	1	2
1940	31.406	11	21
1950	40.619	16	33
1960	38.972	9	7
1970	33.787	4	0

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

y^ = _______ +________x (Round to two decimal places as needed.)

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

Give a practical interpretation of the estimated y-intercept of the line. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. For a decade with 0 software millionaire birthdays, the total number of births in this country is estimated be ___ million. (Round to two decimal places as needed.)

B. For a decade with 0 total births in this country, the number of software millionaire birthdays is estimated be ___. (Round to two decimal places as needed.)

C. The y-intercept does not have a practical interpretation.

Give a practical interpretation of the estimated slope of the line. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. For each additional unit increase in the total number of births in this country, the number of software millionaire birthdays is estimated to decrease by ____ .

(Round to two decimal places as needed.)

B. For each additional unit increase in the total number of births in this country, the number of software millionaire birthdays is estimated to increase by _____.

(Round to two decimal places as needed.)

C. The slope does not have a practical interpretation.

c. Predict the number of software millionaire birthdays that will occur in a decade where the total number of births in this country is 26 million.

____________ software millionaire birthdays (Round to two decimal places as needed.)

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.

y^ = _______ + (________)x (Round to two decimal places as needed.)

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

Give a practical interpretation of the estimated y-intercept of the line. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. For a decade with 0 software millionaire birthdays, the number of CEO birthdays (from a random sample of 70 companies) is estimated be __. (Round to two decimal places as needed.)

B. For a decade with 0 CEO birthdays (from a random sample of 70 companies), the number of software millionaire birthdays is estimated be __. (Round to two decimal places as needed.)

C. The y-intercept does not have a practical interpretation.

Give a practical interpretation of the estimated slope of the line. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. For each additional unit increase in the number of CEO birthdays, the number of software millionaire birthdays is estimated to increase by __. (Round to two decimal places as needed.)

B. For each additional unit increase in the number of CEO birthdays, the number of software millionaire birthdays is estimated to decrease by __. (Round to two decimal places as needed.)

C. The slope does not have a practical interpretation.

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 19.

___ software millionaire birthdays (Round to two decimal places as needed.)

Expert Solution

orchestra answered 2 years ago

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