Question

for the last several tests, gabriel 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 = -0.334x + 90.793 what average percentage score does this line predict for a test with an average question length of 30.53 words? round your answer to the nearest thousandth.

Explanation:

Step1: Substitute \(x = 30.53\) into the regression equation

We have the regression equation \(y=-0.334x + 90.793\). Substitute \(x = 30.53\) into it:
\(y=-0.334\times30.53+90.793\)

Step2: Calculate the product

First, calculate \(-0.334\times30.53\).
\(-0.334\times30.53=-0.334\times(30 + 0.53)=-0.334\times30-0.334\times0.53=-10.02-0.17702=-10.19702\)

Step3: Calculate the value of \(y\)

Now, find \(y\) using \(y=-10.19702 + 90.793\)
\(y=90.793-10.19702 = 80.59598\)

Answer:

\(80.596\)