Question

a software developer is looking for ways to predict how many bugs will appear in future projects. she used a bug - tracking database to analyze several recent projects. from the database, she recorded the number of lines of code for each project, x. she also looked up the number of bugs that had been found in each projects code, y. the least squares regression line of this data set is: y = 0.029x + 205.793 how many bugs does this line predict would be found in a project with 5,771 lines of code? round your answer to the nearest integer.

Explanation:

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

Given \(x = 5771\) and the regression line \(y=0.029x + 205.793\).
Substitute \(x\) into the equation: \(y=0.029\times5771+ 205.793\).

Step2: Calculate the product

First, calculate \(0.029\times5771\).
\(0.029\times5771=(0.03 - 0.001)\times5771=0.03\times5771-0.001\times5771=173.13 - 5.771 = 167.359\).

Step3: Calculate the sum

Then, find \(y\): \(y = 167.359+205.793\).
\(y=373.152\).

Step4: Round to the nearest integer

Since \(373.152\approx373\) (because the decimal part \(0.152<0.5\)).

Answer:

\(373\)