Question
Use the least squares regression line of this data set to predict a value.
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 project's code, y.
Lines of code Bugs
516 239
1,696 252
11,448 390
11,508 235
17,936 488
The least squares regression line of this data set is:
y=0.012x+215.604
How many bugs does this line predict would be found in a project with 13,030 lines of code?
Round your answer to the nearest integer.
bugs
Answers
GPT-4o mini
To predict the number of bugs for a project with 13,030 lines of code using the least squares regression line equation \( y = 0.012x + 215.604 \), we substitute \( x \) with 13,030.
The calculation is as follows:
\[
y = 0.012(13030) + 215.604
\]
Calculating \( 0.012 \times 13030 \):
\[
0.012 \times 13030 = 156.36
\]
Now add this value to 215.604:
\[
y = 156.36 + 215.604 = 371.964
\]
Now, rounding to the nearest integer, we get:
\[
y \approx 372
\]
Therefore, the least squares regression line predicts that approximately **372 bugs** would be found in a project with 13,030 lines of code.
The calculation is as follows:
\[
y = 0.012(13030) + 215.604
\]
Calculating \( 0.012 \times 13030 \):
\[
0.012 \times 13030 = 156.36
\]
Now add this value to 215.604:
\[
y = 156.36 + 215.604 = 371.964
\]
Now, rounding to the nearest integer, we get:
\[
y \approx 372
\]
Therefore, the least squares regression line predicts that approximately **372 bugs** would be found in a project with 13,030 lines of code.