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)...

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?