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 correct least squares regression line for the data set is: y = - 0.334x + 90.793 use it to complete the following sentence: if the average question length increased by one word, the least squares regression line predicts that the average percentage score would decrease by

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the regression line \(y=-0.334x + 90.793\), the coefficient of \(x\) is the slope.

Step2: Interpret the slope

The slope \(m=-0.334\). In the context of the regression line, when \(x\) (average question length) changes by \(\Delta x = 1\), the change in \(y\) (average student score) is given by \(\Delta y=m\Delta x\). Substituting \(\Delta x = 1\) into the formula \(\Delta y=m\Delta x\), we get \(\Delta y=- 0.334\times1=-0.334\)

Answer:

\(0.334\)