Question

josie keeps detailed information about her model airplane collection. the data includes not only the characteristics of each model, but also the time it took to assemble it. she is thinking of buying a new model airplane and decided to look at this information to understand how long assembly might take.
from her data, josie found the number of pieces in each model, x, and how many minutes each took to assemble, y.
airplane model data summary

• the mean of the x - values is 85.600.
• the mean of the y - values is 54.867.
• the sample standard deviation of the x - values is 201.822.
• the sample standard deviation of the y - values is 6.492.
• the correlation coefficient of the data set is 0.959.

the least squares regression line of this data set is:
y = 0.031x + 52.226
how many minutes does this line predict a model with 223 pieces would take to assemble? round your answer to the nearest thousandth.
minutes

Explanation:

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

Given the regression equation \(y = 0.031x+52.226\) and \(x = 223\).
Substitute \(x = 223\) into the equation: \(y=0.031\times223 + 52.226\).

Step2: Calculate the product

First, calculate \(0.031\times223\).
\(0.031\times223=(0.03\times223)+(0.001\times223)=6.69+0.223 = 6.913\).

Step3: Calculate the sum

Then, calculate \(y\) by adding the result of the product to \(52.226\).
\(y=6.913 + 52.226=59.139\).

Answer:

\(59.139\)