Part (a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).
we have the ordered pairs
(1999, 2,196) -------> (0,2,196)
(2019,7,186) -------> (20,7,196)
Find out the slope
where
t -----> is the number of years since 1999
P ----> the cost
m=(7,196-2,196)/(20-0)
m=5,000/20
m=250
Find the equation of the linear model in slope-intercept form
P=mt+b
we have
m=250
point (0,2,196)
substitute and solve for b
2,196=250(0)+b
b=2,196
therefore
P=250t+2,196
Part b
Using this linear model, predict the cost of insurance in 2030
For t=2030=2030-1999=31 years
substitute
P=250(31)+2,196
P=$9,946
Part c
According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute in the linear model
12,000=250t+2,196
250t=12,000-2,196
250t=9,804
t=39 years
therefore
1999+39=year 2038
Part d
Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of
P0 and d to the nearest dollar
using a regression calculator
the equation is
ŷ = 239.15065X + 2406.39827
y=239x+2,406
Part e
Using the regression model, predict the cost of insurance in 2030
For t=2030-1999=31 years
P=239(31)+2,406
P=$9,815
Part f
According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute
12,000=239x+2,406
239x=12,000-2,406
239x=9,594
t=40 years
year=1999+40=2039