Question

Hormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on

x = percent of women using HRT and

y = breast cancer incidence (cases per 100,000 women)

for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence.

HRT Use	Breast Cancer Incidence
46.30	103.30
40.60	105.00
39.50	100.00
36.60	93.80
30.00	83.50

(a)

What is the equation of the estimated regression line? (Round your answers to three decimal places.)

ŷ = __+(___x)

(b)

What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to three decimal places.)

cases per 100,000 women

(c)

What would you predict the breast cancer incidence (in cases per 100,000 women) to be in a year when HRT use was 34%? (Round your answer to three decimal places.)

cases per 100,000 women

(d)

Should you use this regression model to predict breast cancer incidence for a year when HRT use was 13%? Explain.

(e)

Calculate the value of

r².

(Round your answer to three decimal places.)Interpret the value of

r².

(f)

Calculate the value of

s_e.

(Round your answer to three decimal places.)Interpret the value of

Answer 1

a.

Sum of X = 193
Sum of Y = 485.6
Mean X = 38.6
Mean Y = 97.12
Sum of squares (SS_X) = 142.06
Sum of products (SP) = 189.71

Regression Equation = ŷ = bX + a

b = SP/SS_X = 189.71/142.06 = 1.335

a = M_Y - bM_X = 97.12 - (1.34*38.6) = 45.573

ŷ = 1.335X + 45.573

b. Here the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use is the slope and so answer here is 1.335

c. For x=34, ŷ = 1.335*34 + 45.573=90.963

d. For x=13, ŷ = 1.335*13 + 45.573=62.928

13 is the value which is not in the range of HRT use

e.

X Values
∑ = 193
Mean = 38.6
∑(X - M_x)² = SS_x = 142.06

Y Values
∑ = 485.6
Mean = 97.12
∑(Y - M_y)² = SS_y = 305.108

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 189.71

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

r = 189.71 / √((142.06)(305.108)) = 0.9112

Hence r^2=0.9112^2=0.8303

Hence 83.03% of variation in y is explained by x