Question

Average Remaining Lifetimes for Men

Age	Years
0	75.8
15	61.5
35	41.7
65	16.0
75	10.6

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

R=

Speed (mph)	0.0	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0
Pulse (bpm)	61	66	69	75	76	81	85	91	94

-Find the least-squares regression for these data where speed is the independent variable, x, and pulse rate in beats per minute (bpm) is the dependent variable. (Enter a mathematical expression. Round your numerical answers to two decimal places.)

ŷ =

-Assuming the regression line is accurate for higher speeds, what is the expected pulse rate (in bpm) for someone traveling 5 mph? Round to the nearest whole number. (Enter a number.)

Answer 1

X Values
∑ = 190
Mean = 38
∑(X - Mx)2 = SSx = 4080

Y Values
∑ = 205.6
Mean = 41.12
∑(Y - My)2 = SSy = 3180.868

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = -3595.8

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

r = -3595.8 / √((4080)(3180.868)) = -0.9981

Sum of X = 18
Sum of Y = 698
Mean X = 2
Mean Y = 77.5556
Sum of squares (SSX) = 15
Sum of products (SP) = 122.5

Regression Equation = ŷ = bX + a

b = SP/SSX = 122.5/15 = 8.17

a = MY - bMX = 77.56 - (8.17*2) = 61.22

ŷ = 8.17X + 61.22

For x=5, ŷ = (8.17*5) + 61.22=102.07=102