Question

a student at a junior college conducted a survey of 20 randomly selected full - time students to determine the relation between the number of hours of video game playing each week, x, and grade - point average, y. she found that a linear relation exists between the two variables. the least - squares regression line that describes this relation is \\( \hat { y } = - 0.0502 x + 2.9223 \\). assume that observations near \\( x = 0 \\) exist in the data.
(a) predict the grade - point average of a student who plays video games 8 hours per week.
the predicted grade - point average is \\( \square \\)
(round to the nearest hundredth as needed.)

Explanation:

Step1: Substitute \(x = 8\) into the regression equation

We have the regression equation \(\hat{y}=-0.0502x + 2.9223\). Substitute \(x = 8\) into it: \(\hat{y}=-0.0502\times8+2.9223\).

Step2: Calculate the value of \(\hat{y}\)

First, calculate \(-0.0502\times8=-0.4016\). Then, \(\hat{y}=- 0.4016+2.9223 = 2.5207\).

Answer:

\(2.52\)