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 ModifyingAbove y with caret equals negative 0.0592 x plus 2.9306y=−0.0592x+2.9306. (a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is 2.462.46. (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 decrease by . 0592.0592 points, on average. (c) If appropriate, interpret the y-intercept.

Step-by-step explanation:

given that 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.

x=number of hours of video game playing each week

y= grade-point average,

The regression line found out using least squares method is

a) The grade-point average of a student who plays video games 8 hours per week.

=

2.45844 is the answer.

Round off to 2.46

b) Slope = -0.0592 means For each additional hour that a student spends playing video games in a week, the grade-point average will decrease by . 0592. points, on average

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

c

step-by-step explanation: