Question

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	13	13.6	13.3	13.2	12.2	12	10.6	9	8

(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= 23000 according to the linear model in part (a).

Ulcer rate, U(x0)=U(x0)=

Answer 1

Solution:

We can use the excel regression data analysis tool to find the answer to the given questions. The excel steps are:

Enter the data in excel.

Click on Data > Data analysis > Regression > Ok

Input Y range: Select all the data under Ulcer rate including label

Input X range: Select all the data under Income including label

Mark the labels

Choose the output range and the output is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9866
R Square	0.9734
Adjusted R Square	0.9696
Standard Error	0.3522
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	31.7541	31.7541	256.0377	0.0000
Residual	7	0.8681	0.1240
Total	8	32.6222
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	13.971857	0.1864	74.9670	0.0000	13.5312	14.4126
Income	-0.000104	0.0000	-16.0012	0.0000	-0.0001	-0.0001

(a) The equation of the regression line is:

(b) The peptic ulcer rate for an income level of x0=23000 is: