Question

read the following description of a data set. tucker is a math teacher at a large school. he wonders if his test problems are too wordy. tucker is curious whether the wordiness is affecting student performance. for the last several tests, tucker 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 = -0.565x + 78.184 what average percentage score does this line predict for a test with an average question length of 17.33 words? round your answer to the nearest thousandth.

Explanation:

Step1: Identify the regression - line equation

The regression line is $y=-0.565x + 78.184$.

Step2: Substitute the value of $x$

We are given $x = 17.33$. Substitute $x=17.33$ into the equation: $y=-0.565\times17.33 + 78.184$.

Step3: Calculate the value of $y$

First, calculate $-0.565\times17.33=-9.78145$. Then, $y=-9.78145 + 78.184$.
$y = 68.40255$.

Step4: Round the result

Rounding $68.40255$ to the nearest thousandth gives $y\approx68.403$.

Answer:

$68.403$