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)
1,468 4,358
4,461 3,696
6,572 10,717
7,386 19,702
7,465 17,724
7,909 8,934
The least squares regression line of this data set is:
y=1.913x–390.094
How many square meters of floor space does this line predict for a convention with 2,044 attendees?
Round your answer to the nearest integer.
square meters

Answer 1

To predict the floor space required for a convention with 2,044 attendees using the least squares regression line \( y = 1.913x - 390.094 \), we substitute \( x = 2,044 \) into the equation:

\[
y = 1.913(2044) - 390.094
\]

Now, calculate \( 1.913 \times 2044 \):

\[
1.913 \times 2044 = 3,913.372
\]

Next, subtract 390.094 from this result:

\[
y = 3,913.372 - 390.094 = 3,523.278
\]

Now, round the result to the nearest integer:

\[
y \approx 3,523
\]

Thus, the predicted floor space required for a convention with 2,044 attendees is approximately **3,523 square meters**.