Question
Read the following description of a data set.
Vivian's landscape architecture firm won a contract to design a new public playground in Seville. To decide how many swings to include, Vivian collected information about other playgrounds in the city.
For each playground, she recorded the area (in square meters), x, and the number of swings, y.
The least squares regression line of this data set is:
y=0.098x+3.442
How many swings does this line predict a 21 square meter playground would have?
Round your answer to the nearest integer.
swings
Vivian's landscape architecture firm won a contract to design a new public playground in Seville. To decide how many swings to include, Vivian collected information about other playgrounds in the city.
For each playground, she recorded the area (in square meters), x, and the number of swings, y.
The least squares regression line of this data set is:
y=0.098x+3.442
How many swings does this line predict a 21 square meter playground would have?
Round your answer to the nearest integer.
swings
Answers
Answered by
GPT-4o mini
To predict the number of swings for a 21 square meter playground using the least squares regression line equation \( y = 0.098x + 3.442 \), we can substitute \( x = 21 \) into the equation.
\[
y = 0.098(21) + 3.442
\]
Calculating \( 0.098 \times 21 \):
\[
0.098 \times 21 = 2.058
\]
Now, adding this value to 3.442:
\[
y = 2.058 + 3.442 = 5.5
\]
Rounding to the nearest integer, the predicted number of swings for a 21 square meter playground is:
\[
\boxed{6}
\]
\[
y = 0.098(21) + 3.442
\]
Calculating \( 0.098 \times 21 \):
\[
0.098 \times 21 = 2.058
\]
Now, adding this value to 3.442:
\[
y = 2.058 + 3.442 = 5.5
\]
Rounding to the nearest integer, the predicted number of swings for a 21 square meter playground is:
\[
\boxed{6}
\]