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
3,194 232
3,728 136
8,464 283
15,690 302
18,644 421
The least squares regression line of this data set is:
y=0.013x+143.922
How many bugs does this line predict would be found in a project with 10,373 lines of code?
Round your answer to the nearest integer.
bugs
Answers
GPT-4o mini
To predict the number of bugs in a project with 10,373 lines of code using the least squares regression line \( y = 0.013x + 143.922 \), we can substitute \( x = 10,373 \) into the equation.
Here’s how you do it:
1. Substitute \( x \) with 10,373 in the regression equation:
\[
y = 0.013(10,373) + 143.922
\]
2. Calculate \( 0.013 \times 10,373 \):
\[
0.013 \times 10,373 = 137.849
\]
3. Now, add this value to 143.922:
\[
y = 137.849 + 143.922 = 281.771
\]
4. Round the result to the nearest integer:
\[
y \approx 282
\]
Thus, the predicted number of bugs for a project with 10,373 lines of code is **282** bugs.
Here’s how you do it:
1. Substitute \( x \) with 10,373 in the regression equation:
\[
y = 0.013(10,373) + 143.922
\]
2. Calculate \( 0.013 \times 10,373 \):
\[
0.013 \times 10,373 = 137.849
\]
3. Now, add this value to 143.922:
\[
y = 137.849 + 143.922 = 281.771
\]
4. Round the result to the nearest integer:
\[
y \approx 282
\]
Thus, the predicted number of bugs for a project with 10,373 lines of code is **282** bugs.