Question

for each day, clarence notes the number of minutes playing video games, x. he also takes the number of pages shannon reads and divides it by the total number of pages assigned, y.

the correct least squares regression line for the data set is:

( y = - 1.795x + 250.212 )

use it to complete the following sentence:

if shannon spends an additional minute playing video games, the least squares regression line predicts her completion percentage drops by points.

Explanation:

Step1: Recall the slope - intercept form of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the regression line \(y=-1.795x + 250.212\), \(x\) represents the number of minutes playing video games and \(y\) represents the percentage of the reading assignment.

Step2: Interpret the slope

The slope \(m=-1.795\). The slope \(m=\frac{\Delta y}{\Delta x}\). When \(\Delta x = 1\) (an additional minute of playing video games), \(\Delta y=m\times\Delta x\). Substituting \(\Delta x = 1\) into the formula for the change in \(y\) (since \(m=\frac{y_2 - y_1}{x_2 - x_1}\) and \(x_2-x_1 = 1\)), we get \(\Delta y=- 1.795\times1\).

Answer:

\(1.795\)