Question

A health insurance company recorded the annual mortality rate (deaths per 100,000) for residents in 20 towns in a certain region. They also collected data on the water hardness, measured by the calcium concentration (parts per million, ppm) in the drinking water. The following regression output was obtained:

Variable	Coefficient	Standard error
Intercept	1,722	640.387
Calcium (ppm)	-2.088	1.468

(a) Interpret the slope of the regression line.

For every 1 ppm increase in calcium concentration in drinking water, the mortality rate is expected to decrease by 2.088 deaths per 100,000 people, on average.For every one additional death per 100,000 people, calcium concentration in drinking water is expected to decreaseby 2.088 ppm, on average.     For every one additional death per 100,000 people, calcium concentration in drinking water is expected to increase by 2.088 ppm, on average.For every 1 ppm increase in calcium concentration in drinking water, the mortality rate is expected to increase by 2.088 deaths per 100,000 people, on average.

(b) If the calcium concentration is 42 ppm, how many deaths out of 100,000 are to be expected?  (round to the nearest integer)

Answer 1

a)

In general, the units for slope are the units of the Y variable per units of the X variable. It’s a ratio of change in Y per change in X.

The correct option is

For every 1 ppm increase in calcium concentration in drinking water, the mortality rate is expected to decrease by 2.088 deaths per 100,000 people, on average.

b)

Given

y-intercept = 1722

slope = -2.088

The equation of regression line is

where

y = estimated number of death

x = calcium concentration ( ppm)

Given

x = 42 ppm

So,

The expected number of death is 1634.