A student at a junior college conducted a survey of 20 randomly selected full ti

Question

A student at a junior college conducted a survey of 20 randomly selected full time students to determine the return between the number of hours of video game playing each week x, and grade point average y she found that a linear relation exacts between the two variables. the least squares regression line the descries this relation is y = -0.0539 + 2.9388. The predicted grade point average is (b) Interpret the slope For each additional hour that a student spends playing video games in a week, the grade point average will by points on average. (C) If appropriate interpret the y-intercept

Explanation / Answer

y = - 0.0539x + 2.9065

(a) For x = 8:

y = - 0.0539 X 8 + 2.9065 = 2.4753

(b) slope = - 0.0539

Slope indicates the steepness of the line. The greater the magnitude of the slope, the steeper the line and the grater the rate of change. Since, here, slope is only - 0.0539, the line is not steep and the rate of change is also small.

The negative sign of slope indicates the inverse relation between x and y.

When x increases by 1, y decreases by 0.0539.

(c) y intercept = 2.9065

The intercet indicates the location where the line intersects y axis.

The value of the y intercept (2.9065) indicates the grade point average of a student who does not play video game at all.

So, correct option is:

B. The grade point average of a student who does not play video games is 2.9065.

(d) For x = 7:

y = - 0.0539 X 7 + 2.9065

   = 2.5292

Given, y = 2.44

So, the student's grade point is below the average among all students who play video games 7 hours per week.

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