Question

Use the least squares regression line of this data set to predict a value.
Farid is a math teacher at a large school. He wonders if his test problems are too wordy. Farid is curious whether the wordiness is affecting student performance.
For the last several tests, Farid computes the average number of words in each question, x, as well as the average percentage scores on the tests, y.
Average question length Average student score
13.26 71.88
18.59 76.75
46.49 64.78
48.26 71.65
49.68 64.32
The least squares regression line of this data set is:
y=
–
0.216x+77.484
What average percentage score does this line predict for a test with an average question length of 14.95 words?
Round your answer to the nearest thousandth.
percentage

Answer 1

To predict the average percentage score \( y \) for a test with an average question length \( x = 14.95 \) words using the least squares regression line given by the equation:

\[ y = -0.216x + 77.484 \]

we can substitute \( x = 14.95 \) into the equation:

\[
y = -0.216(14.95) + 77.484
\]

Calculating \( -0.216 \times 14.95 \):

\[
-0.216 \times 14.95 = -3.2282
\]

Now, substitute this value back into the equation:

\[
y = -3.2282 + 77.484
\]

Calculating \( -3.2282 + 77.484 \):

\[
y = 74.2558
\]

Rounding this result to the nearest thousandth, we get:

\[
y \approx 74.256
\]

Therefore, the predicted average percentage score for a test with an average question length of 14.95 words is **74.256**.