The scatterplot that follows shows monthly values of consumer sentiment plotted versus inflation (see Exercise 31 for the definition of these variables). For this plot, we’ve shown the full history of the consumer survey back to January 1978. The subset of the points in black shows data since 2004.
(a) Describe the association between these two variables over the full time period. Is the association strong? Is the relationship linear?
(b) Does the addition of the older data change your impression of the association between these two variables? To see a scatterplot of only the data since 2004, see Exercise 31.
(c) Do you think that the addition of the data prior to 2004 increases or decreases the size of the correlation?
Exercise 31
The following timeplot shows the values of two indices of the economy in the United States: inflation (left axis, in red, measured as the year-over-year percentage change in the Consumer Price Index) and the Survey of Consumer Sentiment (right axis, in blue, from the University of Michigan). Both series are monthly and span January 2004 through April 2011.
(a) From the chart, do you think that the two sequences are associated?
(b) The scatterplot shown above displays the same time series, with consumer sentiment plotted versus inflation. Does this scatterplot change your impression of the association between the two?
(c) Visually estimate the correlation between these two series.
(d) For looking at the relationship between two time series, what are the advantages of these two plots? Each shows some things, but hides others. Which helps you visually estimate the correlation? Which tells you the timing of the extreme lows and highs of each series?
(e) Does either plot prove that inflation causes changes in consumer sentiment?