Question

read the following description of a data set.
the owner of a bicycle store wonders if the employees who take the longest lunch breaks also make the fewest bicycle sales.
one day, she notes the length of each salespersons lunch break (in minutes), x, as well as the number of bicycles he or she sold that day, y.
the least squares regression line of this data set is:
y = -0.053x + 8.089
if a salesperson takes a 29 minute lunch break, how many bicycles does this line predict he or she will sell that day?
round your answer to the nearest integer.
bicycles

Explanation:

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

Given the regression line \(y = - 0.053x+8.089\) and \(x = 29\).
Substitute \(x = 29\) into the equation: \(y=-0.053\times29 + 8.089\).

Step2: Calculate the value of \(y\)

First, calculate \(-0.053\times29=-1.537\).
Then, \(y=-1.537 + 8.089=6.552\).

Step3: Round the result

Round \(6.552\) to the nearest integer. Since \(0.552\gt0.5\), we round up. So \(y\approx7\).

Answer:

$7$