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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.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. YearPer House 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 2011. (b) What is the slope of the line? (c) Based on the regression line, what would be the predicted persons per household in the year 2300? (d) What is the lowest possible value of the persons per household number?
(a)The least squares regression line is
y = 44.392 – 0.0209x
where x is the year and the estimate for 2011 would be 2.36 persons.
(b)The slope is therefore -0.0209 persons per year.
That means the average occupancy is falling by about one person every 50 years.
(c)For x = 2300, y = -3.7, which is clearly nonsense.
(d)The minimum occupancy could be zero, if everyone was a vagrant and no one ever lived at an address; or 1.0 if everyone has to be listed as living somewhere !
The problem with this analysis arises from the assumption that the relationship is a straight line.Obviously it’s not.