Question

Use the least squares regression line of this data set to predict a value.
Mr. Tyler 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. Tyler 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.
Typing speed Errors
32 5
45 13
56 16
68 15
76 19
The least squares regression line of this data set is:
y=0.273x–1.502
How many errors does this line predict a student would make if they were to type the sample paragraph at 43 words per minute?
Round your answer to the nearest integer.
errors

Answer 1

To predict the number of errors \( y \) a student would make if they type at a speed of 43 words per minute using the least squares regression line \( y = 0.273x - 1.502 \), we substitute \( x = 43 \) into the equation:

\[
y = 0.273(43) - 1.502
\]

Calculating \( 0.273 \times 43 \):

\[
0.273 \times 43 = 11.709
\]

Now, substituting this value back into the equation:

\[
y = 11.709 - 1.502 = 10.207
\]

Rounding \( 10.207 \) to the nearest integer, we get:

\[
y \approx 10
\]

Thus, the predicted number of errors a student would make typing at 43 words per minute is **10 errors**.