The retail sales y (in billions of dollars) of stores selling auto parts, accessories

Chapter 8, Problem 28

(choose chapter or problem)

Modeling Data The retail sales y (in billions of dollars) of stores selling auto parts, accessories, and tires in the United States from 2009 through 2013 are given by the ordered pairs of the form (t, y(t)), where t = 9 represents 2009. (Source: U.S. Census Bureau)

(9, 74.1)        (10, 77.7)          (11, 82.7)

(12, 83.9)      (13, 82.8)

The coefficients of the least squares regression parabola \(y=a t^{2}+b t+c\) can be found by solving the system

\(\left\{\begin{aligned} 80,499 a+6985 b+615 c &=49,853.8 \\ 6985 a+615 b+55 c &=4436.8 \\ 615 a+55 b+5 c &=401.2 \end{aligned}\right.\)

(a) Use Cramer’s Rule to solve the system and write the least squares regression parabola for the data.

(b) Use a graphing utility to graph the parabola with the data. How well does the model fit the data?

(c) Is this a good model for predicting retail sales in future years? Explain.

Text Transcription:

y = at^2 + bt + c

{_615a + 55b + 5c = 401.2  ^6985a + 615b + 55c = 4436.8  ^^80,499a + 6985b + 615c = 49,853.8

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