#23 A student at a junior college conducted a survey of 20 randomly selected ful

Question

#23

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 y = -0.0534X + 2.9318.

(a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is _. (round to the nearest hundredth as needed.)

(b) Interpret the slope.

For each additional hour that a student spends playing video games in a week, the grade-point average will 1) increase or decrease, by _ points, on average.

(c) If appropriate, interpret the y-intercept.

A) The average number of video games played in a week by students is 2.9318

B) The grade-point average of a student who does not play video games is 2.9318

C) It cannot be interpreted without more information.

(d) A student who plays video games 7 hours per week has a grade-point average of 2.67. Is the students grade-point average above or below average among all students who play video games 7 hours per week?

The students grade-point average is above or below average for those who play video games 7 hours per week.

Explanation / Answer

Ans: Perdicted y=-0.0534X+2.9318

a)When X=8

perdicted value of y=-0.0534*8+2.9318=2.5046

b)Cofficient of X gives the slope value,hence slope is -0.0534

For each additional hour that a student spends playing video games in a week, the grade-point average will decrease, by 0.0534 points, on average.

c)y-intercept

The intercept (often labeled the constant) is the expected mean value of Y when all X=0. Start with a regression equation with one predictor, X. If X sometimes = 0, the intercept is simply the expected mean value of Y at that value.

here,y indicates the grade point average and x is number of hours of video game playing each week

So,For zero number of hours video game playing each week,y intercept is expected or average grade point.

Hence,Option B is true.

d)perdicted value of y for x=7 hrs,

y=-0.0534*7+2.9318=2.558

Actual value=2.67

Actual value>perdicted value

Hence,the students grade-point average is above average for those who play video games 7 hours per week.

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