Question

read the following description of a data set.
marshalls landscape architecture firm won a contract to design a new public playground in seville. to decide how many swings to include, marshall collected information about other playgrounds in the city.
for each playground, he recorded the area (in square meters), x, and the number of swings, y.
the least squares regression line of this data set is:
y = 0.084x + 7.088
how many swings does this line predict a 20.46 square meter playground would have?
round your answer to the nearest integer.
swings
save answer

Explanation:

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

Given the regression line \(y = 0.084x+7.088\) and \(x = 20.46\).
Substitute \(x = 20.46\) into the equation: \(y=0.084\times20.46 + 7.088\).
First, calculate \(0.084\times20.46\):
\(0.084\times20.46=(0.08\times20.46)+(0.004\times20.46)=1.6368+0.08184 = 1.71864\).

Step2: Calculate the value of \(y\)

Now, find \(y\): \(y=1.71864 + 7.088=8.80664\).

Step3: Round the result

Round \(y = 8.80664\) to the nearest integer.
Since the decimal part \(0.80664>0.5\), we round up.

Answer:

\(9\)