Question

kathleen is a math teacher at a large school. she wonders if her test problems are too wordy. kathleen is curious whether the wordiness is affecting student performance.
for the last several tests, kathleen computes the average number of words in each question, x, as well as the average percentage scores on the tests, y.
the least squares regression line of this data set is:
y = -0.488x + 88.253
what average percentage score does this line predict for a test with an average questic length of 45.55 words?

Explanation:

Step1: Substitute the value of \(x\) into the regression equation

Given the regression line \(y = - 0.488x+88.253\) and \(x = 45.55\).
Substitute \(x = 45.55\) into the equation: \(y=-0.488\times45.55 + 88.253\).

Step2: Calculate the product

First, calculate \(-0.488\times45.55\).
\(-0.488\times45.55=-0.488\times(45 + 0.55)=-0.488\times45-0.488\times0.55=-21.96-0.2684=-22.2284\).

Step3: Calculate the value of \(y\)

Then, calculate \(y=-22.2284 + 88.253\).
\(y = 66.0246\approx66.02\).

Answer:

\(66.02\)