Chapter 9, Problem 33E

(a)

To determine

To make a scatterplot showing the trend in consumer prices and describe what you see.

Explanation of Solution

The consumer price index (CPI) tracks the prices of consumer goods in United States which is shown in the data given in the question. Thus, the scatterplot of the Consumer price index against years is as:

  

In this scatterplot, the consumer price index in on the vertical axis and the years is on the horizontal axis. The regression line is also given in the scatterplot along the points. By looking at the scatterplot we see that the scatterplot is clearly non-linear but however, the last years do appear to be linear also it explains $\text{78}\text{.02\%}$ variations in the variables of the data.

(b)

To determine

To justify decisions you made in creating your model.

Explanation of Solution

The consumer price index (CPI) tracks the prices of consumer goods in United States which is shown in the data given in the question. Now by scatterplot given in part (a), we have the regression line, that is,

  $\text{<mover accent="true"><mo>C</mo> <mo>^</mo></mover> PI}=-3661+1.899\text{years}$

Thus, if using the data from $1970\text{ to 2006}$ gives the $r=0.997$ and $\text{<mover accent="true"><mo>C</mo> <mo>^</mo></mover> PI}=-9052.42+4.61\text{years}$ . Thus, from this predicted CPI for year is $\text{2016}=241.34$ , which is an extrapolation of doubtful accuracy.