Question
Read the following description of a data set.
A publishing company is interested in the relationship between a customer's educational background and book-buying habits. As part of his summer internship at the company, David designed a survey to investigate this relationship.
The survey asked each person how many years of education they had completed, x, and how many books they had purchased last year, y.
The least squares regression line of this data set is:
y=1.769x+40.794
How many books does this line predict a person with 21 years of education would have purchased last year?
Round your answer to the nearest integer.
books
A publishing company is interested in the relationship between a customer's educational background and book-buying habits. As part of his summer internship at the company, David designed a survey to investigate this relationship.
The survey asked each person how many years of education they had completed, x, and how many books they had purchased last year, y.
The least squares regression line of this data set is:
y=1.769x+40.794
How many books does this line predict a person with 21 years of education would have purchased last year?
Round your answer to the nearest integer.
books
Answers
Answered by
GPT-4o mini
To predict the number of books a person with 21 years of education would have purchased using the least squares regression line \( y = 1.769x + 40.794 \), we can substitute \( x = 21 \) into the equation.
\[
y = 1.769(21) + 40.794
\]
Calculating \( 1.769 \times 21 \):
\[
1.769 \times 21 = 37.185
\]
Now, adding \( 40.794 \):
\[
y = 37.185 + 40.794 = 77.979
\]
Rounding \( 77.979 \) to the nearest integer gives:
\[
\text{Predicted number of books} = 78
\]
Thus, the predicted number of books that a person with 21 years of education would have purchased last year is **78 books**.
\[
y = 1.769(21) + 40.794
\]
Calculating \( 1.769 \times 21 \):
\[
1.769 \times 21 = 37.185
\]
Now, adding \( 40.794 \):
\[
y = 37.185 + 40.794 = 77.979
\]
Rounding \( 77.979 \) to the nearest integer gives:
\[
\text{Predicted number of books} = 78
\]
Thus, the predicted number of books that a person with 21 years of education would have purchased last year is **78 books**.