Refer to given Exercise about the trend in number of persons per household.
a. Using statistical software, determine the least squares line for these data. Use the equation of this line to estimate the number of persons per household in the year 2010 (Data source: perhouse dataset on the website for this book).
b. What is the slope of the line? Interpret the slope in the context of these variables.
c. Based on the regression line, what would be the predicted persons per household in the year 2200? Realistically, what is the lowest possible value of the persons per household number? How does the estimate for 2200 compare to this value?
d. Part (c) illustrates that the observed pattern can't possibly continue in the same manner forever. Sketch the pattern for the trend in persons per household that you think might occur between now and the year 2200.
Exercise
U.S. Census Bureau estimates of the average number of persons per household in the United States for census years between 1850 and 2000 are shown in the following table. (These data are in the file perhouse on the companion website.)
a. Draw a scatterplot for the relationship between persons per household and year. Is the relationship linear or curvilinear? Is the association between persons per household and year positive or negative?
b. On your scatterplot, add a line that you believe fits the data pattern. Extend this line to the year 2010. On the basis of this line, estimate the number of persons per household in the United States in the year 2010.