Chapter 10.5, Problem 18BB

Sum of Squares Criterion In addition to the value of R², another measurement used to assess tile quality of a model is the sum of squares of the residuals. Recall from Section 10-2 that a residual is the difference between an observed y value and the value of y predicted from the model, which is denoted as ŷ. Better models have smaller sums of squares. Refer to the data in Table 10-7 on page 523.

a. Find Σ(y − ŷ)², the sum of squares of the residuals resulting from the linear model.

b. Find the sum of squares of residuals resulting from the quadratic model.

c. Verify that according to the sum of squares criterion, the quadratic model is better than the linear model.

Table 10-7 lists the population of the United States for different 20-year intervals. Find a mathematical model for the population size, then predict the size of the U.S. population in the year 2040.

TABLE 10-7 Population (in millions) of the United States