Question

Mr. Dotson is trying to convince his middle school typing students that it is better to slow down when they are learning to type. He argues that students who type too quickly make too many errors.
To prove his point, Mr. Dotson has students type a sample paragraph. He records their average typing speed (in words per minute), x, and the number of errors they made, y.
The least squares regression line of this data set is:
y=0.946x–8.864
How many errors does this line predict a student would make if they were to type the sample paragraph at 47.69 words per minute?
Round your answer to the nearest integer.
errors

Answer 1

To predict the number of errors for a typing speed of 47.69 words per minute using the given least squares regression line \( y = 0.946x - 8.864 \), we can substitute \( x = 47.69 \) into the equation.

1. Substitute \( x \) into the equation:

\[
y = 0.946(47.69) - 8.864
\]

2. Calculate \( 0.946 \times 47.69 \):

\[
0.946 \times 47.69 \approx 45.08034
\]

3. Now, substitute this back into the equation:

\[
y \approx 45.08034 - 8.864 \approx 36.21634
\]

4. Round 36.21634 to the nearest integer:

\[
\text{Predicted errors} \approx 36
\]

Thus, the predicted number of errors a student would make typing at 47.69 words per minute is **36**.