Question

(1 point) The table below shows (lifetime) peptic ulcer rates (per 100 population), UU, for various family incomes, xx, as reported by the 1989 National Health Interview Survey.

Income	4000	6000	8000	12000	16000	20000	30000	45000	60000
Ulcer rate	14.2	13.6	12.9	12.8	12.9	12.4	11.5	9.4	7.9

(a) Find the equation of the regression line.

Ulcer rate, U(x)=U(x)=  .

(b) Estimate the peptic ulcer rate for an income level of x0=x0= 28000 according to the linear model in part (a).

Ulcer rate, U(x0)=U(x0)=  .

Answer 1

Solution:

First of all, we have to find the regression model for the prediction of the dependent variable Ulcer rate based on the independent variable as family income. We have to use this regression model for answering question based on it. Required regression model by using excel is given as below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.988644584
R Square	0.977418113
Adjusted R Square	0.974192129
Standard Error	0.329339867
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	32.86296899	32.86297	302.9829	5.08093E-07
Residual	7	0.759253237	0.108465
Total	8	33.62222222
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	14.31195423	0.174293234	82.11423	1.05E-11	13.89981622	14.72409224
Income	-0.00010551	6.06158E-06	-17.4064	5.08E-07	-0.000119844	-9.1177E-05

Part a

Find the equation of the regression line.

From above output, equation of the regression line for the prediction of dependent variable Ulcer rate is given as below:

Ulcer rate = 14.311954 – 0.000106*Income

Y = 14.311954 – 0.000106*X

U(X) =14.311954 – 0.000106*X

Part b

Here, we have to estimate the peptic ulcer rate for an income level of X₀ = 28000

Ulcer rate = 14.311954 – 0.000106*Income

Ulcer rate = 14.311954 – 0.000106*28000

Ulcer rate = 14.311954 - 2.968

Ulcer rate =11.343954

U(X₀) = 11.343954