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.
the least squares regression line of this data set is:
y = 1.514x + 1,658.548
how many square meters of floor space does this line predict for a convention with 6,221
attendees?
round your answer to the nearest integer.
square meters

Explanation:

Step1: Substitute the value of \(x\) into the regression equation

Given the regression line \(y = 1.514x+1658.548\) and \(x = 6221\).
Substitute \(x = 6221\) into the equation: \(y=1.514\times6221 + 1658.548\).

Step2: Calculate the product

First, calculate \(1.514\times6221\).
\(1.514\times6221=(1.5 + 0.014)\times6221=1.5\times6221+0.014\times6221=9331.5+87.094 = 9418.594\).

Step3: Calculate the sum

Then, find \(y\): \(y=9418.594+1658.548\).
\(y = 11077.142\).

Step4: Round the result

Round \(11077.142\) to the nearest integer.

Answer:

\(11077\)