Question

Age (years)	74	68	63	55	50	45	38	31	26	21	16
Time (hours)	0	2	4	6	8	10	12	14	16	18	20

1. Find the equation of a linear regression line for the data where age is the independent variable, x, and time is the dependent variable. (Enter a mathematical expression. Round your numerical answers to three decimal places.)

ŷ =

2. Using the equation from part (a), estimate the number of hours a person 30 years old spends on the internet. (Enter a number. Round your answer to the nearest hour.)

3. Find the linear correlation coefficient. (Enter a number. Round your answer to the nearest four decimal places.)

R=

Answer 1

1.

Sum of X = 487
Sum of Y = 110
Mean X = 44.2727
Mean Y = 10
Sum of squares (SSX) = 3836.1818
Sum of products (SP) = -1298

Regression Equation = ŷ = bX + a

b = SP/SSX = -1298/3836.18 = -0.338

a = MY - bMX = 10 - (-0.34*44.27) = 24.98

ŷ = -0.338X + 24.98

2. For x=30, ŷ = (-0.338*30)+ 24.98=14.84

3.

X Values
∑ = 487
Mean = 44.273
∑(X - Mx)2 = SSx = 3836.182

Y Values
∑ = 110
Mean = 10
∑(Y - My)2 = SSy = 440

X and Y Combined
N = 11
∑(X - Mx)(Y - My) = -1298

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -1298 / √((3836.182)(440)) = -0.9991