Question

The amount of time a random person spends watching Netflix is being compared to the time that person spends exercising. Times are in hours per week.

Time on Netflix	Time Exercising
14	7
8	12
3	9
24	2
19	5
11	12

a) Determine the value of the correlation coefficient and interpret its meaning.

b) Suppose the time on Netflix is being used to predict the time spent exercising. What would be the equation of the regression line? Express the slope and intercept with three digits past the decimal point.

c) Estimate the number of hours per week someone would exercise if they watched 15 hours of Netflix. Round your answer to the nearest hour.

Answer 1

a.

X Values
∑ = 79
Mean = 13.167
∑(X - M_x)² = SS_x = 286.833

Y Values
∑ = 47
Mean = 7.833
∑(Y - M_y)² = SS_y = 78.833

X and Y Combined
N = 6
∑(X - M_x)(Y - M_y) = -122.833

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

r = -122.833 / √((286.833)(78.833)) = -0.8169
As r is negative and near to 1 so there is strong negative correlation

b.

Sum of X = 79
Sum of Y = 47
Mean X = 13.1667
Mean Y = 7.8333
Sum of squares (SS_X) = 286.8333
Sum of products (SP) = -122.8333

Regression Equation = ŷ = bX + a

b = SP/SS_X = -122.83/286.83 = -0.4282

a = M_Y - bM_X = 7.83 - (-0.43*13.17) = 13.4718

ŷ = -0.4282X + 13.4718

c. For x=15,

ŷ = (-0.4282*15) + 13.4718=7.0488