Question

4. The chart below records number of hours 12 students spent online during the weekend and the Math test scores they achieved the following Monday.

Hours on-line (x)	0	7	5	2	3	5	1	3	5	10	7	6
Test scores (y)	96	75	84	82	74	76	85	95	68	50	65	58

1. Draw the scatter plot
2. Is there a positive, negative or no relationship between the number of hours spent online and the exam grade?
3. Find the value of “r” , the linear regression constant, and discuss whether this value confirms your answer to part (b)?
4. Find the equation of the regression line.
5. Using the regression line, predict, if possible, the Math exam grade if a student was online for:

i)   4 hours                             ii) 5.5 hours                          iii) 15 hours.

Answer 1

a.

b. As we see the decreasing trend hence there is a negative relationship between the number of hours spent online and the exam grade.

c.

X Values
∑ = 54
Mean = 4.5
∑(X - M_x)² = SS_x = 89

Y Values
∑ = 908
Mean = 75.667
∑(Y - M_y)² = SS_y = 2130.667

X and Y Combined
N = 12
∑(X - M_x)(Y - M_y) = -362

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -362 / √((89)(2130.667)) = -0.8313
d.

Sum of X = 54
Sum of Y = 908
Mean X = 4.5
Mean Y = 75.6667
Sum of squares (SS_X) = 89
Sum of products (SP) = -362

Regression Equation = ŷ = bX + a

b = SP/SS_X = -362/89 = -4.0674

a = M_Y - bM_X = 75.67 - (-4.07*4.5) = 93.9700

ŷ = -4.0674X + 93.9700

e. i. for x=4, ŷ = (-4.0674*4)+ 93.9700=77.7004

ii. for x=5.5, ŷ = (-4.0674*5.5)+ 93.9700=71.5993

iii. for x=15, ŷ = (-4.0674*15)+ 93.9700=32.959