Question

The total amount of consumer credit has been increasing steadily in recent years. The following table gives the total outstanding consumer credit. Answer part a. through e.

Year |2003 |2004 |2005 |2006 |2007

Consumer credit (in billions of dollars.) |2219.5 |2350.8 |2415.0 |2517.9 |2595.1

a. Find an equation for the least squares line, letting x equal the number of years since 2001.

b. Use part a to find, at approximately what rate is the consumer credit growing per year?

c. Use the result from part a to predict the amount of consumer credit in the year 2016.

d. If this trend continues linearly, in what year will the total debt first exceed $4000 billion?

e. Find and interpret the correlation coefficient.

Answer 1

from above:

a)

from above :Yhat=2052.34+91.83x

b)

rate with the consumer credit growing per year =91.83 billions of dollars /Year

c)

predicted value=2052.34+91.83*15=3429.79

d)

here 4000 =2052.34+91.83x

x=21.20

in year terms it is ~ 2001+21.2~ 2023.2 ~ 2024

hence in year 2024 the total debt first exceed $4000 billion

e)

correlation coefficient r=

Sxy/(√Sxx*Syy)               =

0.995

this tells us that there is a strong and posiitive correlation between increasing number of years from 2001 and Consumer credit