Question
Use the least squares regression line of this data set to predict a value.
Fans of the science fiction television show Space Cruiser Zeta are hosting a convention. To figure out how much space the event will require, an employee at the convention center looked at the space requirements for previous conventions.
For each convention, the employee recorded the number of attendees, x, and the floor space required (in square meters), y.
Attendees Floor space (in square meters)
2,313 2,138
2,966 7,310
5,237 6,761
6,052 17,763
6,294 6,670
9,591 16,832
The least squares regression line of this data set is:
y=1.812x–220.218
How many square meters of floor space does this line predict for a convention with 7,659 attendees?
Round your answer to the nearest integer.
square meters
Fans of the science fiction television show Space Cruiser Zeta are hosting a convention. To figure out how much space the event will require, an employee at the convention center looked at the space requirements for previous conventions.
For each convention, the employee recorded the number of attendees, x, and the floor space required (in square meters), y.
Attendees Floor space (in square meters)
2,313 2,138
2,966 7,310
5,237 6,761
6,052 17,763
6,294 6,670
9,591 16,832
The least squares regression line of this data set is:
y=1.812x–220.218
How many square meters of floor space does this line predict for a convention with 7,659 attendees?
Round your answer to the nearest integer.
square meters
Answers
Answered by
GPT-4o mini
To predict the floor space required for a convention with 7,659 attendees using the least squares regression line \( y = 1.812x - 220.218 \), we need to substitute \( x = 7659 \) into the equation.
1. Substitute \( x \) into the equation:
\[
y = 1.812 \times 7659 - 220.218
\]
2. Calculate \( 1.812 \times 7659 \):
\[
1.812 \times 7659 \approx 13841.508
\]
3. Now, subtract \( 220.218 \) from the result:
\[
y \approx 13841.508 - 220.218 \approx 13621.290
\]
4. Round the result to the nearest integer:
\[
y \approx 13621
\]
Thus, the least squares regression line predicts that approximately **13,621 square meters** of floor space will be required for a convention with 7,659 attendees.
1. Substitute \( x \) into the equation:
\[
y = 1.812 \times 7659 - 220.218
\]
2. Calculate \( 1.812 \times 7659 \):
\[
1.812 \times 7659 \approx 13841.508
\]
3. Now, subtract \( 220.218 \) from the result:
\[
y \approx 13841.508 - 220.218 \approx 13621.290
\]
4. Round the result to the nearest integer:
\[
y \approx 13621
\]
Thus, the least squares regression line predicts that approximately **13,621 square meters** of floor space will be required for a convention with 7,659 attendees.