Chapter 1.3, Problem 10E

Business and Economics

Consumer Durable Goods The total value of consumer durable goods (goods purchased by households for their nonbusiness use with a life expectancy of at least three years) has grown at an approximately linear rate in recent years. The annual data for the years 2003 through 2012 can be summarized as follows, where x represents the years since 2000 and y the total value of consumer durable goods in trillions of dollars. Source: Bureau of Economic Analysis.

$\begin{array}{ccc}n=10& {\displaystyle \sum x=75}& {\displaystyle \sum x^2=645}\\ {\displaystyle \sum y=43.792}& {\displaystyle \sum y^2=193.0496}& {\displaystyle \sum xy=338.271}\end{array}$

(a) Find an equation for the least squares line.

(b) Use your result from part (a) to predict the total value of consumer durable goods in the year 2020.

(c) If this growth continues linearly, in what year will the total value of consumer durable goods first reach at least 6 trillion dollars?

(d) Find and interpret the correlation coefficient.