Chapter 1.2, Problem 23E

The table shows (lifetime) peptic ulcer rates (per 100 population) for various family incomes as reported by the National Health Interview Survey.

Income	Ulcer rate (per 100 population)
$4, 000 $6, 000 $8, 000 $12, 000 $16, 000 $20, 000 $30, 000 $45, 000 $60, 000	14.1 13.0 13.4 12.5 12.0 12.4 10.5 9.4 8.2

(a) Make a scatter plot of these data and decide whether a linear model is appropriate.

(b) Find and graph a linear model using the first and last data points.

(c) Find and graph the least squares regression line.

(d) Use the linear model in part (c) to estimate the ulcer rate for an income of $25, 000.

(e) According to the model, how likely is someone with an income of $80, 000 to suffer from peptic ulcers?

(f) Do you think it would be reasonable to apply the model to someone with an income of $200, 000?

Formula Formula Point-slope equation: The point-slope equation of a line passing through the point (x 1 , y 1 ) with slope m , is given by the following formula: y - y 1 = m x - x 1 Example: The point-slope equation of a line passing through (2, -6) with slope 5 is given by: y - (-6) = 5(x - 2) y + 6 = 5(x - 2)